WO2024090393A1 - Spherical display device, and manufacturing method and designing method for spherical display device - Google Patents

Spherical display device, and manufacturing method and designing method for spherical display device Download PDF

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Publication number
WO2024090393A1
WO2024090393A1 PCT/JP2023/038240 JP2023038240W WO2024090393A1 WO 2024090393 A1 WO2024090393 A1 WO 2024090393A1 JP 2023038240 W JP2023038240 W JP 2023038240W WO 2024090393 A1 WO2024090393 A1 WO 2024090393A1
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Prior art keywords
pixel
display device
spherical display
spherical
unit
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PCT/JP2023/038240
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French (fr)
Japanese (ja)
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明典 辻
一宏 中西
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国立大学法人徳島大学
中西産業株式会社
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Publication of WO2024090393A1 publication Critical patent/WO2024090393A1/en

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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09F—DISPLAYING; ADVERTISING; SIGNS; LABELS OR NAME-PLATES; SEALS
    • G09F9/00—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09F—DISPLAYING; ADVERTISING; SIGNS; LABELS OR NAME-PLATES; SEALS
    • G09F9/00—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements
    • G09F9/30—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements in which the desired character or characters are formed by combining individual elements
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09F—DISPLAYING; ADVERTISING; SIGNS; LABELS OR NAME-PLATES; SEALS
    • G09F9/00—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements
    • G09F9/30—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements in which the desired character or characters are formed by combining individual elements
    • G09F9/302—Indicating arrangements for variable information in which the information is built-up on a support by selection or combination of individual elements in which the desired character or characters are formed by combining individual elements characterised by the form or geometrical disposition of the individual elements
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L33/00—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof

Definitions

  • the present invention relates to a spherical display device, a manufacturing method for a spherical display device, and a design method.
  • Liquid crystal displays are used for display devices such as monitors. For large displays over 100 inches, LED displays using light emitting diodes (LEDs) are used. LED displays combine red, green, and blue LEDs for each pixel to achieve a full color display.
  • LEDs light emitting diodes
  • LED displays are constructed by arranging an LED for each pixel in a rectangular display area, generally the larger the screen size of the display, the more LEDs are used, and the power consumption increases accordingly.
  • One way to reduce the amount of LEDs used is to reduce the pixel density. The larger the gap (pitch) between pixels, the less LEDs are used, but conversely, the display resolution becomes lower.
  • LEDs are point light sources, they tend to travel in a straight line, and as the pitch increases the difference between the light-emitting and non-light-emitting areas becomes more pronounced, giving the impression of more dots and resulting in an uneven, rough screen.
  • Each pixel unit is composed of a reflective structure with a hexagonal columnar outer shape and a hollow interior with one open end, a light-transmitting diffusion sheet arranged to close the open end of the reflective structure, and a light-emitting diode capable of emitting red, green, and blue light arranged in the center of the other edge of the reflective structure.
  • a large display area is formed by stacking multiple pixel units with the hexagonal columnar side surfaces of each pixel unit and placing the pixel emission areas formed by the diffusion sheet on the top surface adjacent to each other.
  • Goldberg polyhedrons are commonly known as polygons that are constructed in a spherical shape.
  • Goldberg polyhedrons are a combination of hexagons and pentagons, and can be used to arrange a flat surface approximately into a sphere.
  • a gap GP would be created between adjacent pixel units in the depth direction of each pixel unit 100X, i.e., in the radial direction of the sphere.
  • the gap GP becomes wider as it moves outward in the depth direction. If there are gaps between pixel units, the pixel density will decrease, the resolution of the display unit will decrease, and the external appearance will also deteriorate.
  • the present invention has been made in light of this background.
  • One of the objects of the present invention is to provide a display device and pixel unit that makes it easy to construct a display device such as a spherical LED display.
  • a method for manufacturing a spherical display device in which a plurality of pixel units, a first pixel unit in the shape of a hexagonal prism and a second pixel unit in the shape of a pentagonal prism, are arranged adjacent to each other, the method comprising the steps of: setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit; determining unit equilateral triangles based on the diameter or radius of the display device for each equilateral triangular surface constituting a regular icosahedron inscribed in the spherical display device, based on the set number of first pixel units and second pixel units, so that the hexagonal and pentagonal surfaces constituting a Goldberg polyhedron approximating the
  • the method includes the steps of: designing a right-angled triangle block corresponding to a right-angled triangle divided into six equal parts by perpendicular lines drawn to the sides by combining a plurality of first pixel units and second pixel units having the set height and a hexagon and pentagon formed by combining the unit equilateral triangles as bases; designing an isosceles triangle block by combining an inverted right-angled triangle block obtained by inverting the right-angled triangle block with the right-angled triangle block; designing a pixel block corresponding to one of the equilateral triangular faces constituting the regular icosahedron by combining a first rotated isosceles triangle block obtained by rotating the isosceles triangle block by 120°, a second rotated isosceles triangle block obtained by further rotating the first rotated isosceles triangle block by 120°, and the isosceles triangle block; and creating 20 pixel blocks based on the design of the pixel block and combining the 20 pixel blocks to form a sp
  • the size of the first pixel unit is not constant.
  • the unit equilateral triangle is a triangle divided based on either class I or class II of the Goldberg polyhedron.
  • the step of setting the parameters includes setting the GP(m,n) of the Goldberg polyhedron.
  • the step of setting the parameters includes a step of calculating the length of one side of a triangle in an isometric view from the length L of one side of the unit equilateral triangle using equation 1. [Equation 1]
  • the step of setting the parameters includes setting at least one of the side L of the unit equilateral triangle, the side a of the equilateral triangle in the isometric view, and the height h of the equilateral triangle in the isometric view.
  • the step of setting the parameters includes at least one of calculating one side L of the unit equilateral triangle based on a radius ru of the spherical display device, calculating one side a of the equilateral triangle in the isometric view based on Equation 2, and calculating the height h of the equilateral triangle in the isometric view based on Equation 4.
  • the process of creating 20 pixel blocks is performed by deposition printing using a 3D printer.
  • the step of creating 20 pixel blocks based on the design of the pixel block and combining the 20 pixel blocks to form the spherical display section of the spherical display device includes the step of dividing the pixel block into a plurality of divided blocks and joining the plurality of divided blocks to form each pixel block. This allows the division at the time of design to match the division at the time of modeling, and provides the advantage that data at the time of design can be converted into data at the time of modeling.
  • the divided blocks are divided into isosceles triangles with each side of the triangle of the pixel block as the base.
  • the bottom surface of the divided block or a part thereof that is stack-printed by the 3D printer has a shape that is close to a flat surface.
  • the step of creating 20 pixel blocks based on the design of the pixel blocks and combining the 20 pixel blocks to form the spherical display section of the spherical display device includes the step of arranging light-emitting elements on the bottom plate of each of the first pixel unit and the second pixel unit that form the pixel block.
  • any of the above methods further includes a step of constructing a spherical frame, in which 20 pixel blocks are created based on the design of the pixel blocks, and the step of combining the 20 pixel blocks to construct the spherical display section of the spherical display device includes a step of fixing each pixel block to the surface of the spherical frame and electrically wiring the light-emitting elements of each pixel block.
  • the spherical display portion is formed in a hemispherical shape, a 1/3 sphere, or a 2/3 sphere.
  • a method for designing a spherical display device having a plurality of pixel units, a first pixel unit in the shape of a hexagonal prism and a second pixel unit in the shape of a pentagonal prism, arranged adjacent to each other includes a step of setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit, and a step of setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit, based on the diameter or radius of the display device, so that for each equilateral triangular face constituting a regular ico
  • the spherical display device is a spherical display device in which a plurality of pixel units are arranged adjacent to each other, the spherical display unit being composed of a plurality of first pixel units, each of which is hexagonal prism-shaped and has a first light-emitting element arranged on a first bottom plate closing an end face of each hexagonal prism, and a plurality of second pixel units, each of which is pentagonal prism-shaped and has a second light-emitting element arranged on a second bottom plate closing an end face of each pentagonal prism, a lighting drive circuit that drives and lights the first light-emitting elements and the second light-emitting elements, and a spherical frame that supports the spherical display unit, and the side surfaces of each first pixel unit that constitute the hexagonal prism are inclined so as to expand toward the outer edge of the sphere, and the side surfaces of each second
  • the spherical frame comprises an annular latitude line section and a plurality of annular meridian sections that intersect with the latitude line section on the latitude line section, are spaced apart from each other on the equator, and have their tops and bottoms fixed at the respective poles.
  • the first light-emitting element and the second light-emitting element have variable light emission colors.
  • the spherical display portion is formed in a hemispherical shape, a 1/3 sphere, or a 2/3 sphere.
  • a program for designing a spherical display device having a plurality of pixels arranged adjacent to one another having a function for setting parameters including at least one of the number of pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the pixel unit, and a function for determining unit equilateral triangles constituting the hexagonal and pentagonal faces constituting a Goldberg polyhedron, which is a polygonal approximation of a spherical surface, based on the setting of at least one of the number of pixel units, the diameter or radius of the display device, and the height of the pixel unit.
  • the computer is made to realize a function of designing a right-angled triangular block by combining a plurality of pixel units having the specified height and a hexagon formed by combining the unit equilateral triangles as a base, a function of designing an inverted right-angled triangular block by inverting the right-angled triangular block and an isosceles triangular block by combining the right-angled triangular blocks, and a function of designing a pixel block by combining a first rotated isosceles triangular block by rotating the isosceles triangle by 120°, a second rotated isosceles triangular block by further rotating the first rotated isosceles triangular block by 120°, and the isosceles triangular block.
  • the above configuration makes it possible to easily design a spherical display device.
  • the computer-readable recording medium or storage device stores the design program for the spherical display device.
  • FIG. 1 is a schematic diagram showing a spherical display device according to an embodiment of the present invention
  • 2 is a perspective view showing a base portion for fixing the spherical display portion of FIG. 1.
  • FIG. 13A and 13B are diagrams illustrating a fixing structure of a spherical display unit according to a modified example.
  • 3 is a front view showing a spherical frame supporting the spherical display unit of FIG. 2.
  • FIG. 5 is a plan view of the spherical frame of FIG. 4 .
  • 6 is a cross-sectional view of the spherical frame taken along line VI-VI of FIG. 5.
  • 7 is a cross-sectional view of the spherical frame taken along line VII-VII of FIG. 6.
  • FIG. 10 is an enlarged perspective view showing the support bracket of FIG. 9 .
  • FIG. 11 is an exploded perspective view of the support bracket of FIG. 10 .
  • FIG. 10 is a perspective view showing a state in which a meridian plate is fixed to the support bracket of FIG. 9 .
  • FIG. 13 is a perspective view showing a state in which a boat-shaped plate is fixed to the meridian plate of FIG. 12 .
  • 1 is a perspective view showing the state in which the template is placed on the surface of the hull template.
  • FIG. FIG. 11 is a schematic vertical cross-sectional view showing a state in which the pixel unit is fixed to a boat-shaped plate.
  • FIG. 2 is a schematic vertical sectional view of a pixel unit.
  • FIG. 13 is a schematic cross-sectional view showing an example of expressing a spherical surface by combining prisms.
  • 18 is a schematic cross-sectional view showing an example in which the shape of the prism in FIG. 17 is modified to express a spherical surface.
  • FIG. 2 is a block diagram showing a drive circuit that controls lighting for each pixel unit of the spherical display device of FIG. 1.
  • FIG. 13 is a block diagram showing a drive circuit that controls lighting for each pixel unit of a spherical display device according to a modified example.
  • 1 is a flowchart showing a design procedure for a honeycomb sphere.
  • FIG. 1 is a perspective view of a honeycomb sphere.
  • 23A is a perspective view showing a geodesic polyhedron of class I
  • FIG. 23B is a perspective view showing a geodesic polyhedron of class II
  • FIG. 23C is a perspective view showing a geodesic polyhedron of class III.
  • FIG. 24A is a perspective view showing the class definitions of Class I
  • FIG. 24B is a perspective view showing the class definitions of Class II
  • FIG. 24C is a perspective view showing the class definitions of Class III geodesic polyhedra.
  • 25A is a regular icosahedron
  • FIG. 25B is an equilateral triangle constituting one face of FIG. 25A
  • 25C is a perspective view showing how the regular icosahedron of FIG. 25A is converted into a geodesic polyhedron using the equilateral triangle of FIG. 25A.
  • 26A and 26B are schematic diagrams showing an example of division of an equilateral triangle of class I
  • FIGS. 26C to 26H are schematic diagrams showing an example of division of class II
  • FIGS. 26I to 26J are schematic diagrams showing an example of division of class III.
  • FIG. 27A is a schematic diagram showing a Goldberg polyhedron of class I
  • FIG. 27B is a schematic diagram showing a Goldberg polyhedron of class II
  • FIG. 27C is a schematic diagram showing a Goldberg polyhedron of class III.
  • FIG. 28A is a perspective view of a regular icosahedron
  • FIG. 28B is a geodesic polyhedron
  • FIG. 28C is a perspective view showing how FIG. 28B is converted into a Goldberg polyhedron
  • FIG. 29A is a perspective view showing a geodesic polyhedron of class II, G(3,3)
  • FIG. 29B is a perspective view showing a Goldberg polyhedron of class I, GP(3,0) converted from FIG. 29A.
  • 3 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the first embodiment
  • FIG. FIG. 11 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the second embodiment.
  • FIG. 11 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the third embodiment.
  • 1 is a flowchart showing a design procedure for a geodesic polyhedron G(m, n).
  • FIG. 1 is a plan view showing an isometric view.
  • FIG. 1 is a plan view showing how to create the equilateral triangles that make up the isometric view.
  • FIG. 36 is a plan view showing how the equilateral triangle in FIG. 35 is copied in the horizontal direction.
  • FIG. 37 is a plan view showing how the equilateral triangle in FIG. 36 is copied obliquely.
  • FIG. 38 is a plan view showing how the equilateral triangle in FIG. 37 is copied in the horizontal direction.
  • FIG. 39 is a plan view showing how the equilateral triangle in FIG. 38 is copied in row order.
  • FIG. 40 is a plan view showing how to create an isometric view from FIG. 39.
  • FIG. 41 is a plan view showing how lines of vectors m and n are drawn on the isometric view of FIG.
  • FIG. 41 is a plan view showing how to draw an equilateral triangle.
  • FIG. 43 is a plan view showing how discrete points are arranged on right-angled triangles obtained by dividing the equilateral triangle in FIG. 42 into six equal parts.
  • FIG. 44 is a perspective view showing how to draw perpendicular lines of radius (ru) to the discrete points in FIG. 43 .
  • FIG. 46 is a perspective view showing how dotted lines are drawn from each discrete point in FIG. 45 to the center (O).
  • FIG. 49 is a perspective view showing line segments of radius (ru) passing through each discrete point from the center (O) of FIG. 48.
  • FIG. 50 is a perspective view showing a state in which line segments of radius (ru) passing through each discrete point on the equilateral triangle in FIG. 49 are mapped onto a sphere.
  • FIG. 51 is an enlarged perspective view of FIG. 50.
  • FIG. 52 is a perspective view showing how a minute equilateral triangle is created by connecting the tips of line segments that pass through each of the discrete points in FIG. 51 with lines.
  • FIG. 53 is a perspective view showing how to create a small equilateral triangular surface in the state shown in FIG. 52. This is a perspective view showing the state in which the side surface is filled in from the state shown in Figure 53. This is an oblique view showing the entire right-angled pyramid obtained in Figure 54.
  • FIG. 52 is a perspective view showing how a minute equilateral triangle is created by connecting the tips of line segments that pass through each of the discrete points in FIG. 51 with lines.
  • FIG. 53 is a perspective view showing how to create a small equilateral
  • FIG. 56 is a perspective view of the right-angled pyramid of FIG. 55 from a different angle. This is a perspective view showing how to obtain an isosceles pyramid from the right-angled pyramid of Figure 56.
  • 58 is a perspective view showing how to obtain a regular pyramid from the isosceles pyramid of FIG. 57. This is a perspective view showing the entire regular triangular pyramid obtained in Figure 58.
  • FIG. 60 is a perspective view showing how the internal boundary surfaces of the regular triangular pyramid in FIG. 59 are hidden.
  • 61 is a perspective view showing the state in which all regular pyramids in FIG. 60 have been selected. This is an oblique view showing the entire regular triangular pyramid obtained in Figure 61.
  • 63 is a perspective view showing how the regular triangular pyramid in FIG.
  • FIG. 64 is a perspective view showing how the regular triangular pyramid is further rotated and copied from the state shown in FIG. 63 to create three faces of the regular triangular pyramid.
  • 65 is a perspective view showing how the regular triangular pyramid in the state shown in FIG. 64 is further rotated and copied to create four faces of the regular triangular pyramid.
  • This is a perspective view showing how to create half of a sphere from the state shown in Figure 65.
  • FIG. 13 is a perspective view showing how to create the entire surface of the sphere from the state shown in Figure 66.
  • FIG. 13 is a perspective view showing how a geodesic polyhedron is obtained from the state shown in FIG. X.
  • FIG. 69 is an enlarged perspective view of the geodesic polyhedron of FIG. 70 is a perspective view showing how a small equilateral triangle is converted into a hexagon and a pentagon in the state shown in FIG. 69.
  • This is a perspective view showing how to create hexagonal and pentagonal faces from the state shown in Figure 70.
  • FIG. 72 is a perspective view showing how a pixel block, which is one face of a Goldberg polyhedron, is obtained via FIG. 71 .
  • FIG. 1 is a perspective view of a honeycomb sphere.
  • FIG. 74 is an exploded view of one section constituting the honeycomb sphere of FIG. 73.
  • FIG. 1 is a perspective view showing a regular icosahedron.
  • FIG. 2 is a schematic development of a regular icosahedron.
  • FIG. 77 is a schematic diagram showing one section that constitutes the regular icosahedron of FIG. 76.
  • FIG. 78 is an exploded schematic diagram of one section shown in FIG. 77.
  • FIG. 76 is a development of the regular icosahedron of FIG.
  • FIG. 2 is a diagram showing a pixel block formed by combining pixel units.
  • FIG. 2 is a diagram showing a first pixel block.
  • FIG. 11 is a diagram showing a second pixel block.
  • FIG. 81 is a diagram showing 22 types of pixel units that constitute the pixel block of FIG. 80.
  • FIG. 11 is a plan view showing how an equilateral triangle is divided into two isosceles triangles.
  • FIG. 85 is a diagram showing 22 types of pixel units among the pixel units in FIG. 83, which correspond to the isosceles triangle in the lower part of FIG. 84.
  • FIG. 84 is a diagram showing a pixel unit corresponding to a first pixel block among the pixel units in FIG. 83.
  • FIG. 84 is a diagram showing a pixel unit corresponding to a second pixel block among the pixel units in FIG. 83.
  • 1 is a flowchart showing a procedure for creating a Goldberg polyhedron from a geodesic polyhedron. A perspective view of a 12v geodesic polyhedron.
  • FIG. 90 is a perspective view showing the triangles on one face of the geodesic polyhedron of FIG. 89.
  • FIG. 90 is a perspective view showing the triangles on one face of the geodesic polyhedron of FIG. 89.
  • FIG. 91 is a plan view showing the state in which the triangles in FIG. 90 are replaced with faces that constitute a Goldberg polyhedron.
  • FIG. 2 is a perspective view showing a right-angled triangular block.
  • FIG. 1 is a perspective view showing stitching of faces of a Goldberg polyhedron.
  • FIG. 94 is a perspective view showing the application of loft to the center of the ball in comparison with FIG. 93.
  • FIG. 95 is a perspective view showing the state of selecting a loft for FIG. 94. This is an image showing the GUI for selecting Solid ⁇ Loft (NEW Body).
  • FIG. 13 is a plan view showing how to draw a curved line on the outside.
  • FIG. 98 is an enlarged perspective view showing the pattern obtained in FIG. 97.
  • FIG. 98 is an enlarged perspective view showing the pattern obtained in FIG. 97.
  • FIG. 98 is a plan view showing how a sketch is created for FIG. 97.
  • FIG. 1 is a cross-sectional view showing a Goldberg polyhedron and a circumscribing circle.
  • FIG. 99 is a perspective view showing the removal of the inner surface from FIG.
  • FIG. 102 is a perspective view showing how to set the thickness of the reflector in FIG. 101 .
  • FIG. 103 is a perspective view showing the state of selecting an inner layer line from FIG. 102 .
  • FIG. 104 is a perspective view showing the pattern obtained by FIG. 103.
  • FIG. 105 is a perspective view showing how a face is selected from the back side in FIG. 104 . This is a perspective view showing the selection of the inside and outside of two hemispheres from Figure 105.
  • FIG. 107 is a perspective view showing the state in which unnecessary hemispheres are hidden from view in FIG. 106 .
  • FIG. 108 is a perspective view showing the result of executing non-display in FIG. 107.
  • This is a perspective view of Figure 108 seen from the front side.
  • FIG. 13 is a plan view showing how the orientation becomes unrecognizable when the image is turned upside down.
  • FIG. 93 is a perspective view of the right-angled triangular block of FIG. 92 as seen from the rear side.
  • FIG. 93 is a perspective view showing how the right-angled triangular block in FIG. 92 is inverted and copied to obtain an equivalent isosceles triangle.
  • 10 is a flowchart showing a procedure for producing a reflector.
  • FIG. 2 is a perspective view showing a reflective structure from which a reflector is to be made;
  • FIG. 115 is a perspective view showing the opening of the reflecting structure of FIG. 114 surrounded by a line.
  • FIG. 116 is a perspective view showing the state in which the outline is selected from FIG. 115 and projected onto the xy plane.
  • 117 is a perspective view showing how to select an opening area from FIG. 116 and create a surface.
  • FIG. 118 is a perspective view showing how a thickness equivalent to that of the reflector plate in FIG. 117 is created by extrusion.
  • 119 is a perspective view showing how an inclined surface from FIG. 118 is arranged on a plane. This is a perspective view showing how FIG.
  • FIG. 119 is placed on the xy plane and lines are drawn on the back side.
  • This is a perspective view showing how the pink dots in Figure 120 are connected with lines.
  • 122 is a perspective view showing the state of being moved from FIG. 121 to the origin position.
  • FIG. This is a plan view showing how a constraint is applied vertically from FIG. 122 to align a line with the x-axis.
  • FIG. 124 is a perspective view showing how the reflector in FIG. 123 is saved as a D ⁇ F file.
  • 125 is a plan view showing how to check the D ⁇ F file saved in FIG. 124.
  • 1 is a flowchart showing a procedure for assembling a honeycomb sphere.
  • FIG. 13 is an exploded view showing an example of dividing a pixel block into three.
  • FIG. 13 is an image diagram showing how to design pixel division blocks 1 to 3 divided into three.
  • 1 is a photograph showing an example of a first pixel block.
  • FIG. 2 is a schematic diagram showing how to divide an equilateral triangular face of a geodesic polyhedron G(8,0) of class I.
  • FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a class II G(5,2) geodesic polyhedron.
  • FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a class III G(4,3) geodesic polyhedron.
  • FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a G(5,2) geodesic polyhedron of class III.
  • FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a G(6,2) geodesic polyhedron of class III.
  • the spherical display device 1000 shown in this figure includes a spherical display unit 1, a controller 70, and a power supply unit 2.
  • the spherical display unit 1 is formed on a spherical surface having a certain thickness.
  • the spherical display unit 1 is composed of a plurality of pixel units 100. Specifically, it is composed of a first pixel unit 100A having a hexagonal prism shape and a second pixel unit 100B having a pentagonal prism shape. Each of these pixel units 100 has a light-emitting element 50 arranged on a bottom plate 25 that closes the end faces of the prism shape.
  • the first pixel unit 100A has a first light-emitting element 50A arranged on a first bottom plate 25a that closes the end faces of each hexagonal prism.
  • the second pixel unit 100B has a second light-emitting element 50B arranged on a second bottom plate 25b that closes the end faces of each pentagonal prism. Note that closing the end faces with a bottom plate means that a bottom plate is provided at the opening end, and does not mean that an opening is prohibited from being provided in the bottom plate.
  • the first light-emitting element 50A and the second light-emitting element 50B are controlled by the controller 70.
  • the first light-emitting element 50A and the second light-emitting element 50B may have a variable light-emitting color.
  • the first light-emitting element 50A and the second light-emitting element 50B may be the same, preferably a semiconductor light-emitting element such as a light-emitting diode.
  • the light-emitting color may also be controlled by the controller 70.
  • the power supply device 2 is a circuit for supplying driving power to the controller 70 and the light-emitting element 50, and is composed of, for example, a converter that converts a commercial power source into a DC voltage and a power supply stabilization circuit.
  • a secondary battery or the like may be used, or it may be connected to a generator such as a solar panel. In this case, the spherical display device can be used even in places where there is no commercial power source.
  • the spherical shape of the spherical display device or spherical display unit does not mean a perfect sphere, but may be a partially distorted sphere.
  • the spherical shape does not need to constitute the entire surface of a sphere, and may be partially missing.
  • some pixel units may be partially missing.
  • It may also be a hemisphere, or a part of the sphere, such as 1/4, 1/3, or 2/3.
  • a hemispherical display may be constructed. (Base portion 4)
  • the spherical display unit 1 is formed as a honeycomb sphere formed in a spherical shape. As shown in FIG. 2, the spherical display unit 1 is placed on a base 4 and fixed on a floor surface.
  • the base 4 is formed in a cylindrical shape with an outer diameter shorter than the diameter of the cylindrical spherical display unit 1.
  • the base 4 is made of a metal tube having strength.
  • the base 4 is designed to have a short height in the example of FIG. 2, but may be made taller, for example, like a pole or tower. When made taller, it is preferable that the base be made in a shape that flares out toward the base.
  • the fixing structure for fixing the spherical display unit is not limited to this configuration, and may be configured to hang the spherical display unit 1B from the ceiling with a hanging body 4B such as a wire, chain, or pipe, as shown in FIG. 3, for example.
  • a hanging body 4B such as a wire, chain, or pipe, as shown in FIG. 3, for example.
  • the spherical display unit 1 is supported by a spherical frame 30.
  • a spherical frame 30 supporting the spherical display unit 1 fixed to the base 4 in FIG. 2 is shown in FIGS. 4 to 7.
  • These figures show the internal spherical frame 30, omitting the surface parts such as the pixel unit 100 and the ship-shaped plate 36 of the spherical display unit 1.
  • the spherical frame 30 shown in these figures is composed of a ring-shaped latitude line portion 31 and a plurality of ring-shaped meridian lines 32 that intersect with the latitude line portion 31. In the example shown in FIGS.
  • the latitude line portion 31 is composed of three parts: a first latitude line portion 31a that runs along the equator, and a second latitude line portion 31b and a third latitude line portion 31c that are spaced apart above and below the first latitude line portion 31a.
  • the meridian line portion 32 is formed in a ring shape that passes through poles 33 located at the north pole and south pole of the honeycomb sphere, as shown in FIG. 5.
  • 18 shape line portions are provided spaced apart from each other at 10° intervals.
  • These latitude and longitude sections 31 and 32 are made of strong metallic pipes, such as steel pipes.
  • a reinforcing tube 34 is provided in the middle of the honeycomb sphere, and a plurality of reinforcing shafts 35 are provided at intervals of 60° from the reinforcing tube 34 to the first latitude line portion 31a.
  • the reinforcing tube 34 is preferably configured by extending the base portion 4 as shown in Fig. 4. This allows the spherical display portion 1 to be supported more stably. (Ship form plate 36)
  • a spherical frame 30 can directly support the spherical display unit 1, it is preferable that the spherical display unit 1 is indirectly supported.
  • a plurality of ship-shaped plates 36 as shown in Fig. 8 are prepared, these ship-shaped plates 36 are fixed to the surface of the spherical frame 30, and the spherical display unit 1 is fixed to the surface of the ship-shaped plates 36.
  • each ship-shaped plate 36 is configured so that both sides are supported by the latitude line parts 31. In the example of Fig. 4 etc., 18 latitude line parts 31 are provided, so nine ship-shaped plates 36 are fixed to the surface of the spherical frame 30.
  • the ship-shaped plates 36 are made of metal plates such as steel or aluminum. (Support bracket 40)
  • support brackets 40 are protruded from the latitude section 31 that constitutes the spherical frame 30, and the hull plate 36 is fixed with the support brackets 40.
  • the support brackets 40 have two curved plates 41 that clamp the pipe of the meridian section 32 from the front and back. Also, a pair of shafts 42 extend through both sides of the curved plates 41, and horizontal plates 43 are fixed to the tips of the shafts 42.
  • the ship-shaped plate 36 may be fixed directly to the side plates 43. For fixing, screws or adhesives may be used. Alternatively, as shown in FIG. 12, a meridian plate 44 may be fixed to each side plate 43, and the ship-shaped plate 36 may be fixed to the surface of the meridian plate 44 as shown in FIG. 13.
  • the spherical display unit 1 is fixed to the surface of the spherical frame 30 to which the boat-shaped plate 36 is attached, thus obtained.
  • the pixel units 100 constituting the spherical display unit 1 are fixed to the boat-shaped plate 36.
  • the pixel units 100 may be fixed to the entire spherical surface, or may be fixed by dividing the spherical surface into the northern and southern hemispheres, or may be fixed to each portion, such as 1/3 or 1/4 of the spherical surface.
  • a template 26 may be placed on the surface of the boat-shaped plate 36 for each pixel unit 100, as shown in FIG. 14.
  • the template 26 is temporarily placed to position the pixel units 100, and is removed after the placement position of each pixel unit 100 is determined.
  • Cardboard or a plastic plate can be used for such a template 26.
  • an opening corresponding to the window 37 can be provided in the template 26, and the opening position of the window 37 can be specified in addition to the positioning of the pixel units.
  • each pixel unit 100 is fixed in a predetermined position.
  • Each pixel unit 100 can be fixed by screwing or adhesive.
  • the light-emitting element 50 provided on the bottom surface of each pixel unit 100 is wired inside the spherical display unit 1 through the window 37. (Pixel unit 100)
  • the pixel unit 100 is a polygonal prism having a predetermined height, such as a hexagonal prism or a pentagonal prism.
  • a schematic cross-sectional view of each pixel unit 100 is shown in FIG. 16.
  • the pixel unit 100 includes a reflective structure 10, a diffusion sheet 20, and a light-emitting element 50.
  • a first pixel unit 100A having a hexagonal prism shape with a hexagonal bottom surface is shown.
  • the second pixel unit 100B having a pentagonal prism shape with a pentagonal bottom surface has the same structure as the first pixel unit 100A, except for the shape. Therefore, the first pixel unit 100A will be described below as a representative example of the pixel unit 100.
  • the reflective structure 10 has a hexagonal or pentagonal prism shape, is hollow inside, and has an open end on one side.
  • the diffusion sheet 20 is a light-transmitting member arranged to close the open end of the reflective structure 10. This diffusion sheet 20 constitutes the pixel light-emitting area. This diffusion sheet 20 is composed of a reflector 22.
  • Acrylic plate, polycarbonate, polypropylene, polyvinyl chloride resin, PET resin, etc. can be suitably used for the reflector 22.
  • the thickness of the reflector 22 is preferably 1 mm to 5 mm.
  • the color of the reflector 22 is preferably milky white and semi-transparent.
  • the diffusion sheet 20 may also be constructed by combining a reflector 22 with a diffusion film 24.
  • the diffusion film 24 is a resin film sheet coated with a diffusing material, and is laminated onto the surface of the reflector 22 when used.
  • a polyester film is suitable for use as this type of diffusion film 24.
  • the thickness of the diffusion film 24 is set according to the thickness of the LED light source and the acrylic plate, and is preferably 38 ⁇ m to 125 ⁇ m. Here, a 38 ⁇ m-thick polyester film manufactured by Tochiman technical paper co. ltd is used.
  • the diffusion film 24 may be made of paper instead of resin.
  • the reflector and diffusion film may also be constructed from a single sheet, or may be made even thinner.
  • the light-emitting element 50 is an optical element located in the center of the other edge of the reflective structure 10.
  • the light-emitting element 50 can be one that is capable of emitting different colors such as red, green, and blue.
  • a light-emitting element 50 a light-emitting diode, a semiconductor laser, or a semiconductor light-emitting element such as an organic electroluminescence (EL) can be suitably used.
  • EL organic electroluminescence
  • a light-emitting diode (LED) that is capable of emitting red, green, and blue colors is used as the light-emitting element 50.
  • a large display area is formed by stacking a plurality of pixel units 100 with their prismatic side surfaces facing each other, and placing the pixel light-emitting areas formed by the diffusion sheet 20 on the top surface next to each other.
  • the light from the point light source of the light-emitting element 50 is spread in a planar manner by the diffusion sheet 20, and the planar light-emitting areas formed by the diffusion sheet 20 are placed next to each other, thereby solving the problem of the display surface being uneven in the conventional LED display because the areas between the LEDs are not emitting light.
  • the pixels are made planar light sources and are placed close to each other, reducing the non-light-emitting areas between the pixels as in the conventional display area, and uniform light emission is obtained throughout the display area.
  • the pixel unit 100 is made prismatic, which provides sufficient strength and has the advantage of not losing its shape even when a large number of pixel units 100 are stacked. (Reflective structure 10)
  • the reflective structure 10 has a hexagonal or pentagonal prism shape, with a diffusion sheet 20 disposed on the front side.
  • the other edge, i.e., the bottom, of the reflective structure 10 is closed with a bottom plate 25.
  • An opening OP is formed in the center of the bottom plate 25, and the light-emitting element 50 is inserted into the reflective structure 10 through this opening OP.
  • the inside of the reflective structure 10 is made of a color and material with excellent reflectivity. For example, by making the inner surface white, the reflectivity of the inside of the reflective structure 10 can be easily increased.
  • it is desirable that the side surface of the reflective structure 10 does not transmit light from the light-emitting element.
  • the reflective structure of the pixel unit 100 in a prismatic shape in this way, the reduction in the amount of light around the periphery of the hexagonal or pentagonal pixel display region, particularly at the vertices, is reduced, and color unevenness is suppressed.
  • the hexagonal or pentagonal shape makes it possible to irradiate the corners uniformly.
  • the reflective structure of the pixel unit 100 in a prismatic shape, as shown in the vertical cross-sectional view of Figure 16, more light is reflected from the side surfaces inside the pixel unit 100 than in a structure such as a cube, and the upper layer of the pixel, i.e., the pixel display region, can be filled with light. (Sloping side)
  • the reflective structure is not a prism with parallel sides as shown in FIG. 17, but has inclined side surfaces that are inclined so as to expand toward the outer edge of the honeycomb sphere as shown in FIG. 18.
  • the side surfaces of each first pixel unit 100A that configure the hexagonal prism are not parallel, but are inclined so as to expand toward the outer edge of the sphere.
  • the side surfaces of each second pixel unit 100B that configure the pentagonal prism are not parallel, but are inclined so as to expand toward the outer edge of the sphere. If the side surfaces are parallel prisms, the design is simple, but as shown in FIG. 17, a gap GP is formed between the pixel units 100X, which reduces the display quality of the display. Therefore, by using a hexagonal prism pixel unit 100 with inclined side surfaces as shown in FIG. 18, the gap can be eliminated.
  • a hexagonal prism-shaped pixel unit 100 with such inclined side surfaces is not easy.
  • Simply approximating a spherical surface with a hexagon or pentagon is already known.
  • a Goldberg polyhedron is a combination of hexagons and pentagons, and allows the plane to be arranged approximately in a spherical shape.
  • simply attaching light-emitting elements 50 such as LEDs to the surfaces of the hexagons and pentagons results in a strong dot-like appearance of the light-emitting elements 50, making it impossible to achieve uniform surface emission.
  • multiple pixel units are prepared in which the light-emitting element 50 is arranged on the bottom surface of the above-mentioned deep hexagonal prism, and then these are combined with pentagonal prism-shaped pixel units and arranged in a spherical shape, resulting in uniform surface emission with reduced dotted appearance.
  • deep hexagonal or pentagonal prism-shaped pixel units as they are on a spherical surface, as shown in FIG. 17, gaps GP will be generated between adjacent pixel units 100X in the depth direction of each pixel unit 100X, i.e., in the radial direction of the sphere.
  • the gaps GP become wider as they move outward in the depth direction. If there are gaps between pixel units 100X, the pixel density will decrease, the resolution of the display will decrease, and the external appearance will also deteriorate.
  • an LED display can be constructed using honeycomb spheres in which pixel units 100 are arranged in a honeycomb shape, and uniform surface emission can be obtained for each pixel. It is also possible to reduce the design labor required for such honeycomb spheres, and to optimize the combination of pixel units 100 required for manufacturing. As a result, it is possible to provide an optimal design and manufacturing method for honeycomb spheres. In addition, by making the honeycomb LED display into a sphere, it is possible to obtain the advantage of being able to construct a display with a unique design that can be seen from all directions.
  • the diameter of the circumscribing circle of the hexagon at the base of the hexagonal prism is preferably 8 cm or more and 16 cm or less.
  • the length of one side of the hexagon is preferably 4 cm to 8 cm.
  • the height of the hexagonal prism is preferably greater than the length of one side of the hexagon. This allows for uniform surface emission. (Drive circuit)
  • FIG. 19 shows a block diagram of a drive circuit that drives each pixel unit 100 to light.
  • the light-emitting element 50 of each light-emitting unit is connected to a controller 70.
  • the controller 70 receives information on the content to be displayed in the display area, such as still images, moving images, text, etc., input from an external image source or set in advance, and determines the position of the pixels to be lit and the color of light to be emitted accordingly, and controls the necessary pixels. For example, it adjusts the amount of drive current and the lighting timing of the red LED, green LED, and blue LED so that they emit light with the desired brightness and chromaticity.
  • the controller 70 also receives power from an external power source and supplies the necessary drive power to the light-emitting element 50 of each pixel unit 100.
  • the driving circuit for driving the light-emitting elements 100 is configured and controlled by a common controller 70, but a driving circuit may be provided for each pixel unit.
  • a communication circuit 72 for wireless communication with an external device may be added to the controller 70.
  • the communication circuit 72 is a member for enabling the external device to control the lighting of the light-emitting elements by wireless operation.
  • the wireless connection method for the communication circuit 72 to receive wireless operation from the external device can be radio waves, microwaves, optical communication, etc. In the case of radio waves, short-distance wireless, wireless PAN, wireless LAN, etc. can be used.
  • standardized wireless communication such as WiFi, Bluetooth, ZigBee, 6LoWPAN, Sub-1GHz (all product names) can be used to implement and introduce the system at low cost.
  • a communication method that supports low power consumption such as Bluetooth Low Energy (BLE).
  • BLE Bluetooth Low Energy
  • a device with an app installed on a smartphone it is possible to easily control the lighting of the LED wirelessly from outside.
  • standardized methods such as the general DMx as a control signal for LED lighting, it is also possible to use a dedicated control signal.
  • communication with an external device can be configured to control the lighting of the light-emitting elements, as well as to allow the external device to receive information distributed from the display device.
  • the display device can be used as a monitor for a gaming device, and the external device can be operated as a controller.
  • the external device can be used for games such as Othello (registered trademark) and Minesweeper (registered trademark).
  • the display device can be used for POP advertising.
  • beacon technology such as iBeacon (registered trademark) for iOS or Eddystone (registered trademark) for Android OS.
  • the display perform a display operation such as showing a special bonus video to a user who has used a coupon.
  • connection between each pixel unit 100 and the controller 70 can be a parallel connection as shown in Fig. 19, or a daisy chain system as shown in Fig. 20.
  • the daisy chain system is particularly preferable because it connects a large number of pixel units in series, making it easy to change the number of connections without being subject to restrictions on the number of units that can be connected. (Method of manufacturing a spherical display device)
  • step S2101 one face (equilateral triangle) of a regular icosahedron is divided into equal parts.
  • the equilateral triangular surfaces ETS (FIG. 25B) constituting each face are divided into unit equilateral triangles UT.
  • step S2102 the divided equilateral triangles are mapped onto the sphere.
  • the size of the mapped unit equilateral triangle mapped onto the sphere from the unit equilateral triangle UT varies depending on the position on the sphere.
  • step S2103 the obtained units of the mapped equilateral triangular surfaces are rotated and copied to form a geodesic polyhedron.
  • step S2104 hexagonal and pentagonal faces (vertices of a regular icosahedron) are created based on the faces of the equilateral triangles that are mapping units of the geodesic polyhedron.
  • step S2105 the obtained unit of the mapped equilateral triangular surface is rotated and copied to create a honeycomb sphere.
  • step S2106 a honeycomb structure is created so that the light-emitting element and reflector 22 can be attached to the obtained unit.
  • step S2107 the honeycomb structure that was created is rotated and copied to create a honeycomb sphere display. In this way, a honeycomb sphere can be obtained.
  • the honeycomb structure unit created can be decomposed into three parts. That is, an isosceles triangle can be decomposed into three isosceles triangles, which are rotated 120 degrees at the center of the triangle. Furthermore, each isosceles triangle can be divided into right-angled triangles by a perpendicular line drawn from the vertex to the base. Therefore, if a pixel unit corresponding to a right-angled triangle is designed, the rest can be obtained by copying. In this way, in classes I and II of geodesic polyhedrons, the design of 1/6 of an equilateral triangle is sufficient due to the symmetry of each part, and the design of the honeycomb sphere can be simplified.
  • the spherical display section 1 of the spherical display device 1000 is configured by combining a plurality of honeycomb-shaped pixel units 100 as shown in Fig. 22.
  • a honeycomb sphere is called a honeycomb sphere.
  • Known examples of such approximations of a sphere include the geodesic polyhedron and the Goldberg polyhedron. (geodesic polyhedron)
  • Geodesic polyhedrons are polyhedrons that are close to spheres and are made up of triangles, and three types are known: Class I shown in Fig. 23A, Class II shown in Fig. 23B, and Class III shown in Fig. 23C.
  • the geodesic polyhedron of Class I shown in Fig. 23A is G(6,0), that of Class II shown in Fig. 23B is G(3,3), and that of Class III shown in Fig. 23C is G(5,2). (Class definition of a geodesic polyhedron)
  • a pentagonal part formed by five tiny triangles is called vertex AX.
  • Each geodesic polyhedron is expressed by G(m,n).
  • (m,n) is the number of divisions of the line segment from vertex AX to vertex AX.
  • the frequency is the total number of line segments from vertex to vertex of a triangle. The frequency indicates the compactness of the geodesic polyhedron, and the higher the frequency, the greater the number of faces.
  • Fig. 24A shows a geodesic polyhedron of class I, G(6,0).
  • Fig. 24B shows a geodesic polyhedron of class II, G(3,3), and
  • Fig. 24C shows a geodesic polyhedron of class III, G(5,2).
  • each face of the regular icosahedron RI is an equilateral triangle.
  • the characteristics of this regular icosahedron RI are that the number of equilateral triangular faces is 20, the number of ridges RL is 30, the number of vertices AX is 12, the number of vertices of each face is 3, and the number of faces that meet at the vertices AX is 5.
  • the equilateral triangular faces ETS constituting one face of the regular icosahedron RI are shown in FIG. 25B.
  • the equilateral triangular faces ETS in FIG. 25B are used to convert to a geodesic polyhedron shown in FIG. 25C.
  • the equilateral triangular faces ETS constituting each face of the regular icosahedron RI are divided into 36 equal parts into minute equilateral triangles. These minute equilateral triangles are called unit equilateral triangles UT.
  • the division method for regularly dividing the equilateral triangular surface ETS into unit equilateral triangles UT differs depending on the class of the geodesic polyhedron.
  • the arrangement of the geodesic polyhedron and, in turn, the honeycomb spheres also changes.
  • division examples of class I are shown in Figures 26A and 26B
  • division examples of class II are shown in Figures 26C to 26H
  • division examples of class III are shown in Figures 26I to 26J.
  • each side of the equilateral triangular surface ETS coincides with one side of the divided unit equilateral triangle UT.
  • each side of the equilateral triangular surface ETS does not coincide with one side of the divided unit equilateral triangle UT, but coincides with one side (base) of the right triangle obtained by bisecting the unit equilateral triangle UT. Therefore, in these classes I and II, it is not necessary to individually design all the unit equilateral triangles UT constituting the equilateral triangular surface ETS. If 1/6 of the equilateral triangular surface ETS is designed by utilizing the symmetry of the geometric figure, the other parts can be filled in by inverted or rotated copies, and the design of the honeycomb sphere as a whole can be simplified.
  • each side of the equilateral triangular surface ETS does not coincide with the side of the unit equilateral triangle UT, and it is not line-symmetrical, so it is necessary to design 1/3 of the equilateral triangular surface ETS. Therefore, in the following, we will mainly consider classes I and II of geodesic polyhedrons, which are easy to design. (Goldberg polyhedron)
  • Goldberg polyhedrons are polyhedrons that are close to a sphere and are composed of hexagons and pentagons, and three types are known: Class I, Class II, and Class III, as shown in Figures 27A to 27C.
  • Class I, as shown in Figure 27A, is GP(4,0)
  • Class II, as shown in Figure 27B, is GP(3,3)
  • Class III, as shown in Figure 27C is GP(4,1).
  • the symmetry of a regular icosahedron is utilized.
  • the regular icosahedron shown in FIG. 28A is converted into a geodesic polyhedron shown in FIG. 28B.
  • a hexagon consisting of six unit regular triangles UT and a pentagon consisting of five unit regular triangles UT are used to obtain a Goldberg polyhedron shown in FIG. 28C.
  • the unit regular triangles UT constituting the geodesic polyhedron are reconstructed to obtain hexagonal and pentagonal faces.
  • 29A corresponds to the Goldberg polyhedron of class I, GP(3,0) shown in FIG. 29B.
  • a honeycomb sphere by combining pixel units 100 in the form of a hexagonal prism or pentagonal prism with depth from hexagonal or pentagonal faces using Goldberg polyhedrons will be described. Note that the side faces of the hexagonal prism or pentagonal prism are not parallel to each other, but are inclined so as to be slightly flared toward the outer periphery. (Pixel block)
  • the Goldberg polyhedron is based on a regular icosahedron, and one surface corresponding to each face of the regular icosahedron is shown in Figure 30.
  • a Goldberg polyhedron GP(4,4) is obtained from a geodesic polyhedron G(12,0).
  • a surface that constitutes such a Goldberg polyhedron is called a pixel block IB.
  • the symmetry of the regular icosahedron is used to design only one pixel block IB as shown in Figure 30, rather than designing the entire sphere, i.e., pixel blocks IB for 20 faces, and the other 19 faces can be accommodated by duplicating them. Note that when combining pixel blocks IB, some overlapping pixel units may be deleted as appropriate.
  • the pixel block IB in FIG. 30 is composed of 31 pixel units 100.
  • the shape of these 31 pixel units 100 is rotationally symmetrical with the pixel block IB being roughly equilateral triangular, and overlaps when rotated 120° around the center of gravity. Therefore, it can be decomposed into three isosceles triangular blocks ITB, each divided by a line segment connecting the center of the pixel block IB to each vertex. Furthermore, each isosceles triangular block ITB is bilaterally symmetric.
  • the isosceles triangular block ITB can be decomposed into right-angled triangular blocks RTB, which are bisected by a perpendicular line extending from the vertex to the middle of the base. If the pixel unit 100 is designed for the right-angled triangular block RTB obtained in this way, the rest can be handled by modifying the data of this right-angled triangular block RTB. That is, the isosceles triangular block ITB is obtained by joining the opposite sides corresponding to the height of the right-angled triangular block RTB and the inverted right-angled triangular block RTB. The pixel block IB is obtained by joining three isosceles triangular blocks ITB, each rotated 120° around the apex.
  • the spherical display unit 1 can be constructed by creating 20 faces of the obtained pixel blocks IB.
  • a spherical surface can be constructed by designing pixel units 100 only for an area of 1/6 of 1/20 of the entire spherical surface, i.e., 1/120, and this makes it possible to significantly reduce the labor required for designing a spherical display device 1000 that combines hexagonal prism-shaped and pentagonal prism-shaped pixel units 100, which was previously troublesome.
  • a manufacturing method for the spherical display device 1000 will be described in detail below. (Number of pixel units required for a honeycomb sphere) [Embodiment 1]
  • the number of pixel units required to form a honeycomb sphere will be explained.
  • the number of pixel units required will be explained when a Goldberg polyhedron GP(4,4) is obtained from a geodesic polyhedron G(12,0) as a spherical display device according to embodiment 1.
  • the pixel block IB in this case will be as shown in FIG. 30 above. In other words, it is sufficient to design only one surface of the Goldberg polyhedron, rather than the entire sphere. In this figure, a unique shape is extracted by utilizing the symmetry of the pixel block IB.
  • the pixel block IB in FIG. 30 is 12v, and is composed of 31 pixel units. In this case, 10 types of pixel units are used, as shown by IU1 to IU10 in FIG. 30.
  • the pentagonal pixel unit of IU1 (second pixel unit 100B) is placed at each vertex AX of the Goldberg polyhedron, so the number of pentagonal pixel units required is the number of vertices AX, i.e. 12.
  • the pixel unit of IU5 is located at the center of the pixel block IB, there is one for each pixel block IB, so 20 units are required for 20 faces.
  • the pixel unit of IU9 is located in the center of edge line RL, so 30 units are required, for 30 edges.
  • IU2, IU3, IU4, IU7, IU8, and IU10 can be created collectively.
  • the number of pixel units required when a Goldberg polyhedron of GP(4,4) is obtained from a geodesic polyhedron of G(12,0) has been described.
  • the number of pixel units varies depending on the size of the triangles constituting the geodesic polyhedron, i.e., the size of the hexagons and pentagons of the Goldberg polyhedron.
  • a spherical display device according to embodiment 2 a case where a Goldberg polyhedron of GP(6,6) is obtained from a geodesic polyhedron of G(18,0) is considered.
  • This pixel block IB is as shown in FIG. 31, and the number of pixel units required is different from that in FIG. 30.
  • the characteristics of the regular icosahedron are the same as those in FIG. 30, with 20 faces, 12 vertices AX, 30 edges RL, 3 vertices on each face, and 5 faces gathering at the vertices AX.
  • the number of pixel units required for the geodesic polyhedron G(10,10) to the Goldberg polyhedron GP(10,0) will be considered.
  • step S3301 a Goldberg polyhedron GP(m,n) to be designed is determined.
  • step S3302 a geodesic polyhedron G(m,n) to be designed is determined based on the Goldberg polyhedron. Here, it is confirmed whether G(m,n) can be constructed from GP(m,n). (Isometric design)
  • step S3303 one side of the triangle in the isometric view is found from the length L of one side of the unit equilateral triangle UT that constitutes the geodesic polyhedron.
  • the following formula is used.
  • the isometric view allows the design of all classes as shown in Fig. 34.
  • An isometric drawing is then created. For example, as shown in Figure 35, an equilateral triangle is drawn with its apex coinciding with the origin O. This equilateral triangle is then repeated horizontally. For example, as shown in Figure 36, it is copied successively to the right. Furthermore, as shown in Figure 37, the apexes are stacked on top of each other so that the hypotenuse forms a straight line. Similarly, this equilateral triangle is then repeated horizontally. For example, as shown in Figure 38, it is copied successively to the right. Furthermore, the set of triangles obtained is copied row by row. For example, as shown in Figure 39, two rows of triangles are copied and stacked so that the hypotenuse forms a straight line. In this way, an isometric drawing such as that shown in Figure 40 is created.
  • a template or format that has been prepared in advance may be used.
  • the isometric drawing data that has already been created may be used after modification, such as changing the size of the equilateral triangle. (Drawing the unit equilateral triangle UT)
  • step S3305 the unit equilateral triangle UT that constitutes the regular icosahedron is drawn.
  • vectors m and n are drawn on the XY plane of the created isometric drawing data using the sketch creation function of the 3D design CAD, as shown in Figure 41.
  • an equilateral triangle is drawn with lines, as shown in Figure 42.
  • the equilateral triangle is positioned so that one side coincides with the vertical axis (X-axis).
  • step S3306 discrete points DP are placed within the equilateral triangle.
  • line segments are drawn connecting each vertex and the center point to create an isosceles triangle, and the isosceles triangle is then bisected by a perpendicular line drawn from the vertex to the base to obtain a right-angled triangle.
  • discrete points DP are placed on this right-angled triangle.
  • Each discrete point DP is placed at each vertex of the isometric drawing.
  • a perpendicular line is drawn to the discrete point DP.
  • a YZ plane is displayed as shown in FIG. 44 in comparison with the XY plane on which the triangle with the discrete points DP shown in FIG. 43 is drawn.
  • a perpendicular line is then drawn from the center of the equilateral triangle.
  • the length of the perpendicular line is the radius of the sphere (ru), but it is not limited to this and can be any suitable length.
  • a line of radius (ru) is drawn from the vertices of the equilateral triangle.
  • a perpendicular line is drawn from one of the vertices of the equilateral triangle (the right side in the figure), and the length of this line segment is set to the radius (ru).
  • the intersection point of the perpendicular line and the line segment of the radius (ru) is set to the center (O) of the sphere.
  • line segments of radius (ru) are drawn from each of the remaining two vertices of the triangle to their respective intersection points.
  • auxiliary lines are drawn from the discrete points DP within the equilateral triangle to the center (O).
  • auxiliary lines are drawn from each discrete point DP to the center (O).
  • Fusion360 product name
  • a solid line is drawn from the center (O) onto each dotted line.
  • a solid line is drawn from the center (O) onto all auxiliary lines.
  • the center (O) and the dots are not connected, but the solid line goes partway through.
  • the length can be arbitrary.
  • Fusion360 product name
  • the line is drawn with the cursor becoming a mouth at the center (O) and an x on the line.
  • Perpendicular lines are also selected and set as "auxiliary lines" before the line is drawn. Note that where the lines overlap, the direction is changed by rotating the coordinate system display as appropriate before performing the work.
  • step S3311 all solid lines are set to a radius (ru).
  • all solid lines drawn from the center (O) are set to a radius (ru).
  • Fusion360 product name
  • each discrete point DP within the triangle becomes a radius (ru) from the center (O).
  • a state is obtained in which each discrete point DP on an equilateral triangle is mapped onto a sphere of radius (ru), as shown in FIG. 50.
  • a minute equilateral triangle is created on the sphere.
  • the tips of the lines are connected with a line to create a triangle on the sphere.
  • the size of the minute triangle becomes smaller from the center of the equilateral triangle to the apex.
  • the direction of the display angle of the coordinate system and the like are appropriately adjusted.
  • Fusion360 product name
  • the line is drawn while checking that the cursor becomes a mouth at the tip of the line. If the triangle is connected correctly, it turns to "light blue".
  • sketch1 (coordinate) may be set to hidden. In this way, a minute equilateral triangle is obtained at a position extended from a discrete point DP in a right-angled triangle as shown in FIG. 52. (Creating a right-angled pyramid)
  • step S3313 the surface of a tiny equilateral triangle is created.
  • a surface that fills the tiny equilateral triangle is created by patching.
  • Fusion360 product name
  • Change to Surface mode and select Create ⁇ Patch Then patch all the triangles on the surface.
  • ProfileNN is displayed and turns ochre. All the side areas are also selected and surfaces are created by patching.
  • the shape shown in Figure 54 is obtained.
  • a triangular pyramid block with a right-angled triangular base formed by bisecting an isosceles triangle, that is, a right-angled triangular pyramid RTP is obtained, as shown in Figures 55 and 56. Thereafter, this right-angled triangular pyramid RTP is copied to construct a spherical surface.
  • an isosceles triangular pyramid ITP is obtained from a right-angled triangular pyramid RTP.
  • the right-angled triangular pyramid RTP is inverted and copied and joined.
  • Fusion360 product name
  • drag the right-angled triangular pyramid RTP to select all of them display the MirrorPlane by Surface mode ⁇ Create ⁇ Mirror, select the side, and click OK.
  • FIG. 57 a block with an isosceles triangular base, that is, an isosceles triangular pyramid ITP, is obtained.
  • a regular triangular pyramid ETP is obtained from the isosceles triangular pyramid ITP. Specifically, the isosceles triangular pyramid ITP is rotated and copied by 120° each time, and three isosceles triangular pyramid ITPs are joined. For example, in Fusion360 (product name), drag to select all the isosceles triangular pyramid ITPs, select Surface mode ⁇ Create ⁇ Pattern ⁇ Circular Pattern, click the center line (perpendicular line) with A ⁇ is, and set Quantity to 3. In this way, as shown in Figure 58, a block with an equilateral triangular base, that is, a regular triangular pyramid ETP, is obtained. The regular triangular pyramid ETP obtained in this way is shown in Figure 59. It is one of the 20 faces that make up the geodesic polyhedron. In this state, the face is created with a patch, and the inside is hollow.
  • step S3316 the boundary surfaces are hidden.
  • Fusion360 product name
  • all of the boundary surfaces inside the regular triangular pyramid ETP are selected and hidden. Specifically, go to Browser -> Bodies -> select the body of the boundary surface and hide it. In this way, the regular triangular pyramid ETP in Figure 60 is obtained.
  • a body is created by stitching. For example, in Fusion360 (product name), select all faces by going to Surface mode -> Modify -> Stitch. Selection is done by dragging, and when selected it turns blue. If there are any unselected faces, select them from Browser -> Bodies. In this way, a regular triangular pyramid ETP is selected as shown in Figure 61. At this point, one Body (solid) has been created by stitching, as shown in Figure 62.
  • step S3318 a rotational copy is performed.
  • Fusion360 product name
  • an axis is selected with A ⁇ is by selecting Create ⁇ pattern ⁇ Circular pattern, and one body is then selected.
  • Quantity: 2 a rotational copy is performed as shown in Figure 63, creating two faces of the regular triangular pyramid ETP in Figure 59.
  • step S3319 the rotation copy is continued.
  • Fusion360 product name
  • Create ⁇ pattern ⁇ Circular pattern is selected, an axis is selected with A ⁇ is, one body is further selected, Angle: 72, Quantity: 2 are set, and the rotation copy is executed as shown in FIG. 64, and the three faces of the regular triangular pyramid ETP in FIG. 62 are created.
  • step S3320 the rotation copy is continued.
  • Fusion360 product name
  • select Create ⁇ pattern ⁇ Circular pattern select the axis with A ⁇ is, further select one body, set Angle: 72, Quantity: 2, and execute the rotation copy as shown in Figure 65 to create the four faces of the regular triangular pyramid ETP in Figure 62.
  • step S3321 the same rotational copy is repeated.
  • Axis axis is selected in Create->pattern->Circular pattern, four bodies are selected, AngularSpacing: Full, Quantity: 5 are set, and the block shown in FIG. (geodesic polyhedron)
  • step S3322 the bodies are combined.
  • Fusion360 product name
  • all the bodies (20 bodies) are selected and combined in Solid mode by Modify ⁇ Combine to obtain the block shown in Figure X.
  • the geodesic polyhedron shown in Figure 68 is obtained. Note that at this stage, the height of the pixel unit has not yet been designed. (Sketching pentagons and hexagons)
  • a honeycomb sphere is designed based on the obtained Goldberg polyhedron.
  • a honeycomb sphere composed of hexagonal and pentagonal pixel units as shown in FIG. 73 is designed.
  • a development of one section SC constituting this honeycomb sphere is shown in FIG. 74.
  • a regular icosahedron is considered, in which the surfaces of the sphere are composed of multiple equilateral triangles, as shown in FIG. 75.
  • the characteristics of a regular icosahedron are that it has 20 equilateral triangular faces, 30 edge lines RL, 12 vertices AX, 3 vertices AX on each face, and 5 faces that meet at the vertices AX.
  • each surface of such a honeycomb sphere With a 3D printer.
  • the 20 equilateral triangles can be developed as shown in FIG. 76. In this figure, it can be considered as a set of five sets of four equilateral triangles as shown in FIG. 77.
  • a set of four equilateral triangles is called one section SC.
  • the development of the honeycomb sphere constituting one section SC corresponds to FIG. 74 mentioned above.
  • one section SC shown in FIG. 77 can be decomposed into an equilateral triangle, an edge line RL, and a vertex AX, as shown in FIG. 78.
  • the equilateral triangle is classified into three first pixel blocks IB1 and one second pixel block IB2. Note that to avoid overlapping vertices AX when joining edge lines RL or equilateral triangles, vertices AX are added or omitted as necessary.
  • the edge line RL in FIG. 77 corresponds to the edge line RL of the honeycomb sphere shown in FIG. 74.
  • a honeycomb sphere with a regular icosahedron can be used to represent images to be displayed on a display unit of a display device when the display unit of a display device is constructed using the honeycomb sphere obtained.
  • Fig. 79 shows a development of a honeycomb sphere approximating the honeycomb sphere with the regular icosahedron of Fig. 75. By displaying an image on this development, an image to be displayed on the entire surface of the honeycomb sphere can be approximately represented on one screen. (Pixel units required to create a honeycomb sphere)
  • the surface data required for manufacturing a honeycomb sphere will be described.
  • the surface data which is data for designing a triangular pixel block IB required for creating a Goldberg polyhedron GP(10,0) with a radius of 125 cm.
  • the total number of pixel units in this honeycomb sphere is 1002, of which 12 vertices AX and 36 pixel units constituting one surface, totaling 720 for 20 surfaces.
  • Each edge line RL has 9 pixel units, and there are 30 edges, totaling 270.
  • the pixel block IB which is a combination of pixel units, is as shown in FIG. 80.
  • the pixel block IB shown in this figure shows a state including an equilateral triangle, an edge line RL, and an apex AX.
  • Two types of pixel blocks IB are prepared by combining these equilateral triangles, edge lines RL, and apexes AX: a first pixel block IB1 shown in FIG. 81, which includes two edge lines RL corresponding to the hypotenuse of the triangle, and a second pixel block IB2 shown in FIG. 82, which does not include an edge line RL.
  • the pixel block IB shown in FIG. 80 has a side of 1314 mm, a circumscribing circle of 18 cm to 10 cm, and a depth (height) of 10 cm. (Pixel block IB)
  • the number of pixel units in the honeycomb shape is 1002.
  • a total of 22 types of pixel units are required, including 21 types of hexagonal pixel units and one type of pentagonal pixel unit.
  • the vertices AX have 12 pentagonal pixel units
  • the faces have 720 (including pixel units 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (12 units) x 3 x 20 faces)
  • the ridges RL have 270 (including pixel units 13, 14, 15, 16, 17, 18, 19, 20, 21 (9 units) x 30 lines).
  • These 22 types of pixel units constitute the pixel block IB that forms one surface of the honeycomb sphere in FIG. 83.
  • equilateral triangle is regarded as an equilateral triangle, this equilateral triangle can be divided into three isosceles triangles by line segments connecting the center of the equilateral triangle to each vertex AX, as shown in FIG. 84.
  • pixel units in Fig. 83 pixel units corresponding to this isosceles triangle are shown in Fig. 85.
  • the isosceles triangular area shown in Fig. 85 also includes pixel units that correspond to the edge line RL. Specifically, nine types of pixel units 13, 14, 15, 16, 17, 18, 19, 20, and 21 correspond to the edge line RL. (First pixel block IB1)
  • the first pixel block IB1 uses 36 pixel units of 12 types, IU1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, which correspond to an equilateral triangle, as shown in FIG. 86.
  • 2 pixel units of 9 types, IU13, 14, 15, 16, 17, 18, 19, 20, and 21, which correspond to two edge lines RL (the left and right oblique sides in FIG. 86) are used, for a total of 18 pixel units. That is, the first pixel block IB1 uses 36 pixel units + 18 pixel units, for a total of 54 pixel units.
  • the second pixel block IB2 is shown in Figure 87.
  • the second pixel block IB2 uses 3 of each of the 12 types of pixel units IU1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, which correspond to equilateral triangles, for a total of 36.
  • the second pixel block IB2 does not include meridians. Therefore, the number of pixel units per second pixel block IB2 is 36.
  • a regular icosahedron requires 12 vertices AX.
  • the vertices AX are the pentagonal second pixel units 100B.
  • the pentagonal pixel units may be included in the honeycomb pixel units.
  • the Goldberg polyhedron of the honeycomb sphere is approximated by the regular icosahedron of FIG. 75 and FIG.
  • the number of equilateral triangular faces is 20, so that there are 3 pixel units of 12 types per face, i.e., 36 pixel units per pixel block IB, for a total of 720 pixel units for the 20 faces.
  • step S8801 the surfaces are reconstructed.
  • triangles, pentagons, and hexagons are created from the triangular faces that make up the geodesic polyhedron shown in Figure 89.
  • Figure 89 shows a geodesic polyhedron, and for one face of this geodesic polyhedron, the edges of the triangle are enclosed as shown in Figure 90, and pentagonal and hexagonal patches are created for each of the 30 faces that make up the Goldberg polyhedron as shown in Figure 91.
  • a right-angled triangular block RTB is designed as shown in Figure 92.
  • Solid ⁇ Loft Stitch is performed on all surfaces to the center of the sphere. All 30 faces of the Goldberg polyhedron are selected and stitched as shown in Figure 93.
  • loft is applied to all faces to the center of the sphere as shown in Figure 94.
  • Solid ⁇ Loft (NEW Body) is selected as shown in Figures 95 and 96.
  • the outer line is first drawn with an ARC curve.
  • the radius (ru) is set to 10 mm.
  • the shape shown in Figure 98 is obtained.
  • the thickness of the pixel unit for example the thickness of the FRP resin part
  • Figure 99 creates a sketch as shown in Figure 99.
  • the design is based on the circle circumscribing the Goldberg polyhedron in cross section, so the height of the faces that make up the Goldberg polyhedron is up to 10 mm thinner than the arc.
  • each layer is displayed with isolate.
  • isolate is performed from the first layer in the browser. Specifically, all the surfaces viewed from above are selected and isolated, and each layer is processed one by one, and hidden after completion. Also, select Shell ⁇ all the surfaces ⁇ all the back surfaces ⁇ 2 mm, and display the thickness of the reflector 22, the area where the reflector 22 is placed, and the main body. In this state, if it is turned upside down as shown in Figure 110, the orientation cannot be determined, so it is preferable to add some kind of indicator, such as a mark to distinguish between upside and down.
  • an isosceles triangular block ITB is designed from the right-angled triangular block RTB.
  • the right-angled triangular block RTB in Fig. 92 is inverted and copied to obtain an isosceles triangle equivalent to that shown in Fig. 112. (Method of manufacturing the reflector 22)
  • the procedure for creating the reflector 22 will be described based on the flowchart in Figure 113.
  • the reflector 22 to be placed in the opening of the reflecting structure 10 is approximately created.
  • An acrylic plate is used as the material for this reflector 22.
  • step S11301 the reflective structure 10 is displayed.
  • the target reflective structure 10 is displayed. For example, it is displayed from the browser ⁇ body list.
  • step S11302 an outline drawing of the reflector 22 is created. That is, a sketch is created of the opening of the pixel unit where the reflector 22 is to be attached, and the outline drawing is drawn. For example, a sketch is created on the x-y plane. Then, as shown in FIG. 115, the opening of the reflecting structure 10 is surrounded by a line.
  • a surface is created based on the outline drawing.
  • a surface is created from the outline drawing to create the reflector 22. If the surface is nearly flat, first project it onto the x-Y plane using Project. For example, as shown in FIG. 116, select the outline lines (six lines) using Create ⁇ Project/Include ⁇ Project and project them onto the x-Y plane. Then create a plane with no thickness using Patch. For example, in Surface mode, select the opening area and create a Surface (surface) using Create ⁇ Patch as shown in FIG. 117. Then create the thickness of the surface using Extrude. For example, as shown in FIG. 118, in Solid mode, create a surface by extrusion with Create ⁇ Extrude to create a surface with a thickness equivalent to the reflector 22 (for example, 2 mm).
  • step S11304 the surface is moved onto a plane by alignment, and positioned horizontally.
  • execute Modify ⁇ Align In From:, select the back side of the surface, and in To:, select the Origin: x-Y plane, and click "OK.” This positions the tilted surface on a plane, as shown in Figure 119.
  • step S11305 the outline is created.
  • the surface is projected onto the x-Y plane to create an approximate outline drawing.
  • a sketch is created on the x-Y plane, and a line is drawn on the back side of the surface that was placed on the plane by alignment.
  • the outline is projected. If the surface is not completely on the x-Y plane, it is approximated by projecting onto the x-Y plane. For example, by clicking the vertices of the outline using Create ⁇ Sketch or Create ⁇ Project/Include ⁇ Project, they become pink points. Then, as shown in Figure 121, each pink point is connected with a line. The surface is then moved. Here, the origin is moved to the x-Y plane.
  • Modify ⁇ Move/Copy it is moved to the origin position as shown in Figure 122 (click Create Copy). Then, a vertical constraint is applied.
  • a vertical constraint is applied to align the line with the x-axis. For example, move it so that it does not touch the x-axis or y-axis, and delete the original outline drawing. Also, add an identification name to the sketch (for example, s1 to s14 laser).
  • step S11306 save it as a DxF file. For example, as shown in Figure 124, right-click on Sketch in the browser and select Save as DxF. At this point, make sure that nothing other than the target outline drawing is displayed. Then start Eagle, create a project, create a board (brd), and select File ⁇ Import ⁇ dxf.
  • step S11307 processing is performed by a laser processing machine.
  • the creation data is input to the laser processing machine, and the acrylic plate is cut along the outline of the DxF file.
  • write out the DxF file For example, go to File ⁇ Export ⁇ DxF, turn off the check box, and click OK.
  • have the laser processing machine read the DxF file.
  • start the laser processing program Read the DxF file and select the equipment to be used (for example, acrylic plate 2 mm). Also, specify the processing origin.
  • the reflector 22 is created. (Manufacturing method of honeycomb ball)
  • step S12601 pixel division blocks ISB1 to ISB3 divided into three parts are designed in advance as shown in FIG. 128. The detailed procedure is as described above.
  • step S12602 each pixel division block is created based on the design. For example, a 3D printer can be suitably used for creation.
  • ABS, ASA, PLA, PC, PP, PETG, TPU plastics biodegradable plastics derived from living organisms such as plants and wood, reinforced plastics containing glass fibers and carbon fibers, etc.
  • three isosceles triangular blocks ITB are created by joining pixel units IU1 to IU12 as shown in FIG. 85, and these are joined to create an equilateral triangular block ETB, which are then connected as shown in FIG. 127 to create five second pixel blocks IB2 as shown in FIG. 87.
  • the connections can be made using screws or plastic adhesive. When using screws, the advantage is that the gaps between the pixel units can be fine-tuned later when connecting the pixel units together.
  • first pixel blocks IB1 as shown in Figure 86 are created by adding edge blocks to which pixel units IU13 to IU21 are joined to the equilateral triangular block ETB. Again, three isosceles triangular blocks ITB are created and joined to obtain the first pixel block IB1 as shown in Figure 129.
  • step S12603 a light-emitting element 50 is added to the bottom surface of each pixel unit that makes up the honeycomb sphere, and wiring is performed.
  • step S12604 the first pixel block IB1 and the second pixel block IB2 are bonded together.
  • the second pixel unit 100B is added as the vertex AX.
  • the vertex AX may be formed as a separate member and bonded to the first pixel block IB1 and the second pixel block IB2, or may be added when the first pixel block IB1 and the second pixel block IB2 are formed using a 3D printer or the like. In this way, a honeycomb sphere, i.e., a spherical display unit 1 formed in a spherical shape, can be obtained.
  • the pixel block IB When designing the pixel block IB, it is preferable to design it so that the bottom surface is as close to flat as possible. This reduces the amount of support material used when modeling with a 3D printer, and also reduces the number of layers by making the model shorter, making it possible to reduce modeling costs and speed up modeling.
  • the pixel block IB itself does not need to be modeled with a 3D printer; for example, the pixel block may be divided into multiple divided blocks. This makes it easier to approximate the shape of the bottom surface of the modeling object to a flat surface.
  • 20 pixel blocks are created, and these 20 pixel blocks are combined to form the spherical display unit.
  • the pixel block may be divided into multiple parts, which may be created individually and then combined.
  • an equilateral triangular pixel block may be divided into three isosceles triangular blocks, and each of the isosceles triangular blocks may be rotated 120° and combined to form a pixel block.
  • it may be divided into six right-angled triangular blocks, and these may be combined to form an equilateral triangular pixel block.
  • These 20 pixel blocks are then combined to form the spherical display unit in a manner similar to constructing a regular icosahedron.
  • This process does not necessarily require the spherical display unit to be formed in pixel block units, and it goes without saying that it can be similarly divided into any unit or size, and the divided parts can be assembled to form the spherical display unit.
  • creating and combining 20 pixel blocks merely indicates the total amount of parts required to construct the spherical display unit 1, and does not require creation or assembly in pixel block units.
  • the unit for designing a honeycomb sphere from a geodesic polyhedron or a Goldberg polyhedron is a pixel block equivalent to one face of the regular icosahedron RI shown in FIG. 25A, i.e., the equilateral triangular surface ETS in FIG. 25B, which is the basis, and the entire honeycomb sphere is designed by copying the equilateral triangular surface ETS.
  • the equilateral triangular surface ETS equivalent to the equilateral triangular surface ETS as a unit.
  • the honeycomb sphere or the equilateral triangular surface ETS by dividing it into a size and shape suitable for the selected manufacturing method. In this way, in this embodiment, it is not necessary to match the unit for dividing the honeycomb sphere when designing it with the unit for dividing it when manufacturing it, and it is possible to select the unit for dividing that is suitable for design and manufacturing, respectively.
  • the constituent units of the pixel block at the time of design may be made to match the units at the time of modeling.
  • the pixel block may be divided into a plurality of divided blocks and modeled, and each pixel block may be configured by joining the plurality of modeled divided blocks.
  • the division at the time of design and the division at the time of modeling can be made to match, and there is an advantage that the data at the time of design can be converted into data at the time of modeling.
  • a honeycomb sphere can also be designed based on class III of a geodesic polyhedron. For example, consider designing a pixel block corresponding to one face of a regular icosahedron RI shown in FIG. 25A based on class I of a geodesic polyhedron. In this case, each side of the equilateral triangular surface ETS matches one side of the divided unit equilateral triangle UT. Therefore, if the equilateral triangular surface ETS in FIG.
  • each right-angled triangular area RTA is divided into six equal right-angled triangular areas RTA with perpendicular lines drawn from each vertex to the opposing base as division lines DL as shown in FIG. 130, the pattern of the unit equilateral triangle UT included in each right-angled triangular area RTA will be the same or a mirror image. Therefore, if a pixel block of a portion corresponding to one right-angled triangular area RTA is designed, the other portions can be filled by copying due to symmetry.
  • each side of the equilateral triangular surface ETS does not coincide with one side of the divided unit equilateral triangle UT, it does coincide with one side (base) of the right-angled triangular area RTA obtained by bisecting the unit equilateral triangle UT.
  • the division line DL that divides the equilateral triangular surface ETS into six parts coincides with a side of the unit equilateral triangle UT.
  • Figs. 132, 133, and 134 examples of dividing the equilateral triangular surface ETS of a regular icosahedron RI based on the class III of geodesic polyhedrons are shown in Figs. 132, 133, and 134.
  • Fig. 132 shows a class III geodesic polyhedron of G(4,3)
  • Fig. 133 shows G(5,2)
  • Fig. 134 shows G(6,2).
  • the spherical display device, manufacturing method and design method of the spherical display device of the present invention can be suitably used as a large-screen display for displaying characters and images, intelligent lighting, etc.

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Abstract

The present invention makes it possible to easily construct a spherical display device such as an LED display. This spherical display device, in which a plurality of pixels are arranged at fixed intervals, comprises: a spherical display unit 1 composed of a plurality of first pixel units, each of which is a hexagonal prism shape and in which a first light emitting element 50A is disposed on a first bottom surface plate 25a that closes off an end face of the hexagonal prism shape, and a plurality of second pixel units, each of which is a pentagonal prism shape and in which a second light emitting element 50B is disposed on a second bottom surface plate 25b that closes off an end face of the pentagonal prism shape; a lighting drive circuit that drives the lighting of the first light emitting elements 50A and the second light emitting elements 50B; and a spherical frame 30 that supports the spherical display unit 1. The side surfaces constituting the hexagonal prism shape of each first pixel unit are inclined so as to spread toward the outer edges of the sphere shape, and the side surfaces constituting the pentagonal prism shape of each second pixel unit are inclined so as to spread toward the outer edges of the sphere shape.

Description

球状表示装置、球状表示装置の製造方法及び設計方法Spherical display device, manufacturing method and design method for spherical display device
　本発明は、球状表示装置、球状表示装置の製造方法及び設計方法に関する。 The present invention relates to a spherical display device, a manufacturing method for a spherical display device, and a design method.
　ディスプレイ等の表示装置には液晶ディスプレイが用いられている。１００インチ以上といった大型のディスプレイにおいては、発光ダイオード（Light Emitting Diode：ＬＥＤ）を用いたＬＥＤディスプレイが利用されている。ＬＥＤディスプレイは、画素毎に赤色ＬＥＤ、緑色ＬＥＤ、青色ＬＥＤを組み合わせて、フルカラー表示を実現している。 Liquid crystal displays are used for display devices such as monitors. For large displays over 100 inches, LED displays using light emitting diodes (LEDs) are used. LED displays combine red, green, and blue LEDs for each pixel to achieve a full color display.
　このようなＬＥＤディスプレイは、矩形状の表示領域に、画素毎にＬＥＤを配置して構成しているため、一般にディスプレイの画面サイズが大きくなるほど、ＬＥＤの使用量が増え、これに応じて消費電力も増大していく。ＬＥＤの使用量を減らすには、画素の密度を小さくすることが考えられる。画素同士の間の隙間（ピッチ）を大きくするほど、ＬＥＤの使用量は減るが、逆に表示可能な解像度は低くなる。特にＬＥＤは点光源であるため、直進性が強く、ピッチが大きくなると発光部分と発光しない領域との差が顕著となってドット感が強く感じられるようになり、不均一な粗い画面となる。 Since such LED displays are constructed by arranging an LED for each pixel in a rectangular display area, generally the larger the screen size of the display, the more LEDs are used, and the power consumption increases accordingly. One way to reduce the amount of LEDs used is to reduce the pixel density. The larger the gap (pitch) between pixels, the less LEDs are used, but conversely, the display resolution becomes lower. In particular, since LEDs are point light sources, they tend to travel in a straight line, and as the pitch increases the difference between the light-emitting and non-light-emitting areas becomes more pronounced, giving the impression of more dots and resulting in an uneven, rough screen.
　このように、ＬＥＤの使用量の低減すなわち消費電力の低減と、表示品質とはトレードオフの関係にあり、特に大画面になるほどこの問題が顕著となり、低消費電力の大型ディスプレイを構築することは困難とされていた。また大型ディスプレイに限らず、近年は東日本大震災に伴う電力供給不足、原発の稼働停止や石油等天然資源の枯渇、ＣＯ2の削減といった地球環境への配慮が強く求められており、消費電力の削減は緊急の課題である。 Thus, there is a trade-off between reducing the amount of LED used, i.e. reducing power consumption, and display quality, and this problem becomes more pronounced as the screen size increases, making it difficult to build large displays with low power consumption. In addition, not only for large displays, but in recent years, there has been a strong demand for consideration of the global environment, such as the power supply shortage following the Great East Japan Earthquake, the suspension of nuclear power plant operations, the depletion of natural resources such as oil, and the reduction of CO2 emissions, making the reduction of power consumption an urgent issue.
　このような背景に鑑み、本願出願人は、六角柱状の画素ユニットで構築した表示装置を開発した（特許文献１）。各画素ユニットは、外形を六角柱状とし、内部を空洞として一方を開口端とした反射構造体と、反射構造体の開口端を閉塞するように配置された、透光性を有する拡散シートと、反射構造体の他方の端縁において、この端縁の中央部分に配置された、赤色、緑色、青色に発光可能な発光ダイオードとで構成している。この画素ユニットを、複数、各画素ユニットの六角柱状の側面同士を積層して、天面の拡散シートで構成される画素発光領域同士を隣接させて、大きな表示領域を構成する。 In light of this background, the applicant of the present application has developed a display device constructed from hexagonal columnar pixel units (Patent Document 1). Each pixel unit is composed of a reflective structure with a hexagonal columnar outer shape and a hollow interior with one open end, a light-transmitting diffusion sheet arranged to close the open end of the reflective structure, and a light-emitting diode capable of emitting red, green, and blue light arranged in the center of the other edge of the reflective structure. A large display area is formed by stacking multiple pixel units with the hexagonal columnar side surfaces of each pixel unit and placing the pixel emission areas formed by the diffusion sheet on the top surface adjacent to each other.
特許第６９２０７５０号公報書Patent Publication No. 6920750
　このような六角柱状の画素ユニットを用いて、平面状でなく球状の表示装置を構成することを考える。まず、球状の表示装置とするためには、表示画面を球状に構成する必要がある。一般に、多角形で球状に構成するものとして、ゴールドバーク多面体が知られている。ゴールドバーク多面体は、六角形と五角形の組み合わせで、近似的に平面を球状に配置することができる。 We are considering using such hexagonal columnar pixel units to construct a spherical display device rather than a flat one. First, in order to create a spherical display device, the display screen needs to be constructed in a spherical shape. Goldberg polyhedrons are commonly known as polygons that are constructed in a spherical shape. Goldberg polyhedrons are a combination of hexagons and pentagons, and can be used to arrange a flat surface approximately into a sphere.
　ただ、球状の表示装置を構成するために、球状の表面にＬＥＤ等の発光素子を貼り付けると、発光素子のドット感が強く表れてしまい、均一な面発光を実現できない。これを回避するために、上述した奥行きのある六角柱状の底面に発光素子を配置した画素ユニットを複数用意して、これに五角柱状の画素ユニットを組み合わせて、球状に配置することが考えられる。 However, if light-emitting elements such as LEDs are attached to the spherical surface to create a spherical display device, the dot-like appearance of the light-emitting elements becomes very apparent, making it impossible to achieve uniform surface emission. To avoid this, it is possible to prepare multiple pixel units in which light-emitting elements are arranged on the bottom surface of the deep hexagonal prism described above, combine these with pentagonal prism-shaped pixel units, and arrange them in a spherical shape.
　このような奥行きのある六角柱状や五角柱状の画素ユニットを、そのまま球状をなす表面に配置しようとすると、図１７の模式断面図に示すように、各画素ユニット１００Ｘの奥行き方向、すなわち球の半径方向において、隣接する画素ユニット間で隙間ＧＰが生じてしまう。隙間ＧＰは、奥行き方向の外側に向かうに従って広くなる。画素ユニット間の隙間があると、画素密度が低下して表示部の解像度が低下し、また外観上の見栄えも悪くなる。 If one were to place such deep hexagonal or pentagonal prism-shaped pixel units directly on the surface of a sphere, as shown in the schematic cross-sectional view of Figure 17, a gap GP would be created between adjacent pixel units in the depth direction of each pixel unit 100X, i.e., in the radial direction of the sphere. The gap GP becomes wider as it moves outward in the depth direction. If there are gaps between pixel units, the pixel density will decrease, the resolution of the display unit will decrease, and the external appearance will also deteriorate.
　このような隙間の発生を回避するためには、六角柱状や五角柱状の各画素ユニットを共通の形状とせず、図１８に示すように、球面の位置毎に、予め隣接する画素ユニット間の隙間を埋めるように個別に設計した画素ユニット１００を準備することが考えられる。 In order to avoid the occurrence of such gaps, it is conceivable to prepare pixel units 100 that are individually designed in advance to fill the gaps between adjacent pixel units for each position on the sphere, rather than making each hexagonal or pentagonal prism-shaped pixel unit have a common shape, as shown in Figure 18.
　しかしながら、球が大きくなるほど、あるいは画素ユニットの数を増やすほど、その設計は困難となる。例えば１０ｃｍ角の画素ユニットで直径２．５ｍの球状の表示装置を構成しようとすれば、約三千個の画素ユニットが必要となり、それぞれの画素ユニットを配置し、かつ、予め設計した位置に固定しなければならず、極めて煩雑な作業となってしまう。 However, the larger the sphere or the more pixel units there are, the more difficult the design becomes. For example, to create a spherical display device with a diameter of 2.5 m using pixel units that are 10 cm square, approximately 3,000 pixel units would be required, and each pixel unit would need to be arranged and fixed in a pre-designed position, making for an extremely cumbersome task.
　本発明は、このような背景に鑑みてなされたものであり。本発明の目的の一は、球状のＬＥＤディスプレイ等の表示装置を容易に構築できるようにした表示装置及び画素ユニットを提供することにある。 The present invention has been made in light of this background. One of the objects of the present invention is to provide a display device and pixel unit that makes it easy to construct a display device such as a spherical LED display.
課題を解決するための手段及び発明の効果Means for solving the problem and effects of the invention
　上記目的を達成するため、本発明の第１の形態に係る球状表示装置の製造方法によれば、複数の画素ユニットである六角柱状の第一画素ユニットと、五角柱状の第二画素ユニットを隣接して配置した球状の表示装置の製造方法であって、前記球状の表示装置を構成する前記第一画素ユニット及び第二画素ユニットの数と、前記球状の表示装置の直径又は半径と、前記第一画素ユニット及び第二画素ユニットの高さの少なくともいずれかを含むパラメータを設定する工程と、前記表示装置の直径又は半径に基づき、前記球状の表示装置に内接する正二十面体を構成する各正三角形面に対し、前記設定された第一画素ユニット及び第二画素ユニットの数に基づいて、前記球状の表面を多角形で近似したゴールドバーク多面体を構成する六角形の面と五角形の面を、それぞれ単位正三角形の組み合わせで構成するよう、単位正三角形を確定する工程と、前記正三角形面を、各頂点から対向する辺に下ろした垂線で六等分した直角三角形と対応する直角三角形ブロックを、前記単位正三角形を組み合わせた六角形と五角形を底面とし、前記設定された高さを有する第一画素ユニット及び第二画素ユニットを複数組み合わせて設計する工程と、前記直角三角ブロックを反転させた反転直角三角形ブロックと、前記直角三角形ブロックとを組み合わせた二等辺三角形ブロックを設計する工程と、前記二等辺三角形ブロックを１２０°回転させた第一回転二等辺三角形ブロックと、前記第一回転二等辺三角形ブロックをさらに１２０°回転させた第二回転二等辺三角形ブロックと、前記二等辺三角形ブロックとを組み合わせた、前記正二十面体を構成する各正三角形面の一面に相当する画素ブロックを設計する工程と、前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程とを含む。これにより、球状の表示装置の設計を容易に行うことが可能となる。特に球面の全てを設計するのでなく、ゴールドバーグ多面体の一面のみを設計し、他の面は複製することで対応でき、設計の作業量を約１／１２０に大幅に削減できる。 In order to achieve the above object, according to a first embodiment of the present invention, there is provided a method for manufacturing a spherical display device in which a plurality of pixel units, a first pixel unit in the shape of a hexagonal prism and a second pixel unit in the shape of a pentagonal prism, are arranged adjacent to each other, the method comprising the steps of: setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit; determining unit equilateral triangles based on the diameter or radius of the display device for each equilateral triangular surface constituting a regular icosahedron inscribed in the spherical display device, based on the set number of first pixel units and second pixel units, so that the hexagonal and pentagonal surfaces constituting a Goldberg polyhedron approximating the spherical surface with a polygon are each composed of a combination of unit equilateral triangles; and determining the equilateral triangular surfaces from each vertex of the equilateral triangular surface, based on the set number of first pixel units and second pixel units, so that the hexagonal and pentagonal surfaces constituting a Goldberg polyhedron approximating the spherical surface are each composed of a combination of unit equilateral triangles. The method includes the steps of: designing a right-angled triangle block corresponding to a right-angled triangle divided into six equal parts by perpendicular lines drawn to the sides by combining a plurality of first pixel units and second pixel units having the set height and a hexagon and pentagon formed by combining the unit equilateral triangles as bases; designing an isosceles triangle block by combining an inverted right-angled triangle block obtained by inverting the right-angled triangle block with the right-angled triangle block; designing a pixel block corresponding to one of the equilateral triangular faces constituting the regular icosahedron by combining a first rotated isosceles triangle block obtained by rotating the isosceles triangle block by 120°, a second rotated isosceles triangle block obtained by further rotating the first rotated isosceles triangle block by 120°, and the isosceles triangle block; and creating 20 pixel blocks based on the design of the pixel block and combining the 20 pixel blocks to form a spherical display unit of a spherical display device. This makes it possible to easily design a spherical display device. In particular, instead of designing the entire surface of a sphere, it is possible to design only one face of a Goldberg polyhedron and duplicate the other faces, significantly reducing the amount of design work by approximately 1/120.
　また、第２の形態に係る球状表示装置の製造方法によれば、上記方法において、前記第一画素ユニットの大きさが一定でない。 Furthermore, according to the second embodiment of the method for manufacturing a spherical display device, the size of the first pixel unit is not constant.
　さらに、第３の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記単位正三角形が、ゴールドバーク多面体のクラスＩ又はクラスＩＩのいずれかに基づいて分割された三角形である。 Furthermore, according to the third embodiment of the method for manufacturing a spherical display device, in any of the above methods, the unit equilateral triangle is a triangle divided based on either class I or class II of the Goldberg polyhedron.
　さらにまた、第４の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記パラメータを設定する工程が、前記ゴールドバーク多面体のＧＰ（ｍ，ｎ）の設定を含む。 Furthermore, according to a fourth embodiment of the method for manufacturing a spherical display device, in any of the above methods, the step of setting the parameters includes setting the GP(m,n) of the Goldberg polyhedron.
　さらにまた、第５の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記パラメータを設定する工程が、前記単位正三角形の一辺の長さＬから、等角図の三角形の一辺の長さを、数１から求める工程を含む球状表示装置の製造方法。
［数１］ Furthermore, according to a fifth aspect of the manufacturing method for a spherical display device, in any of the above methods, the step of setting the parameters includes a step of calculating the length of one side of a triangle in an isometric view from the length L of one side of the unit equilateral triangle using equation 1.
[Equation 1]
　Ｌ＝ｓｑｒｔ（ｍ＊ｍ＋ｎ＊ｎ＋ｍ＊ｎ）×ａ 　L＝sqrt(m*m+n*n+m*n)×a
　さらにまた、第６の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記パラメータを設定する工程が、前記単位正三角形の一辺Ｌと、等角図の正三角形の一辺ａと、等角図の正三角形の高さｈの設定の少なくとも何れかを含む。 Furthermore, according to the sixth embodiment of the method for manufacturing a spherical display device, in any of the above methods, the step of setting the parameters includes setting at least one of the side L of the unit equilateral triangle, the side a of the equilateral triangle in the isometric view, and the height h of the equilateral triangle in the isometric view.
　さらにまた、第７の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記パラメータを設定する工程が、前記球状の表示装置の半径ｒｕに基づき、前記単位正三角形の一辺Ｌを、数２に基づき演算し、等角図の正三角形の一辺ａを、数３に基づき演算し、等角図の正三角形の高さｈを、数４に基づき演算することの少なくとも何れかを含む。
［数２］ Furthermore, according to a seventh embodiment of the manufacturing method for a spherical display device, in any of the above methods, the step of setting the parameters includes at least one of calculating one side L of the unit equilateral triangle based on a radius ru of the spherical display device, calculating one side a of the equilateral triangle in the isometric view based on Equation 2, and calculating the height h of the equilateral triangle in the isometric view based on Equation 4.
[Equation 2]
　Ｌ＝ｒｕ／０．９５１０５６５１６３
［数３］ L = ru / 0.9510565163
[Equation 3]
　ａ＝Ｌ／ｓｑｒｔ（ｍ＊ｍ＋ｎ＊ｎ＋ｍｎ）
［数４］ a = L / sqrt (m * m + n * n + mn)
[Equation 4]
　ｈ＝ａ＊ｓｑｒｔ（３）／２ h = a * sqrt(3) / 2
　さらにまた、第８の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程において、前記画素ブロックを作成する工程が、３Ｄプリンタを用いた堆積印刷にて行われる。 Furthermore, according to the eighth embodiment of the method for manufacturing a spherical display device, in any of the above methods, in the process of creating 20 pixel blocks based on the design of the pixel blocks and combining the 20 pixel blocks to form the spherical display section of the spherical display device, the process of creating the pixel blocks is performed by deposition printing using a 3D printer.
　さらにまた、第９の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、前記画素ブロックを、複数の分割ブロックに分割し、前記複数の分割ブロックを接合して各画素ブロックを構成する工程を含む。これにより、設計時の分割と造形時の分割を一致させることができ、設計時のデータを造形時のデータに転用できる利点が得られる。 Furthermore, according to the ninth embodiment of the method for manufacturing a spherical display device, in any of the above methods, the step of creating 20 pixel blocks based on the design of the pixel block and combining the 20 pixel blocks to form the spherical display section of the spherical display device includes the step of dividing the pixel block into a plurality of divided blocks and joining the plurality of divided blocks to form each pixel block. This allows the division at the time of design to match the division at the time of modeling, and provides the advantage that data at the time of design can be converted into data at the time of modeling.
　さらにまた、第１０の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記分割ブロックが、前記画素ブロックの三角形状の各辺を底辺とする二等辺三角形状に分割されている。 Furthermore, according to a tenth embodiment of the method for manufacturing a spherical display device, in any of the above methods, the divided blocks are divided into isosceles triangles with each side of the triangle of the pixel block as the base.
　さらにまた、第１１の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記３Ｄプリンタで堆積印刷される前記分割ブロック又はその一部の底面が、平面に近い形状である。上記構成により、３Ｄプリンタによる積層印刷時にサポート材の使用量を低減して効率良く造形できる。 Furthermore, according to the eleventh embodiment of the method for manufacturing a spherical display device, in any of the above methods, the bottom surface of the divided block or a part thereof that is stack-printed by the 3D printer has a shape that is close to a flat surface. With the above configuration, the amount of support material used during stack printing by the 3D printer can be reduced, allowing efficient modeling.
　さらにまた、第１２の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、当該画素ブロックを構成する前記第一画素ユニット及び第二画素ユニットにそれぞれ、底面板に発光素子を配置する工程を含む。 Furthermore, according to the twelfth embodiment of the method for manufacturing a spherical display device, in any of the above methods, the step of creating 20 pixel blocks based on the design of the pixel blocks and combining the 20 pixel blocks to form the spherical display section of the spherical display device includes the step of arranging light-emitting elements on the bottom plate of each of the first pixel unit and the second pixel unit that form the pixel block.
　さらにまた、第１３の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、さらに、球状フレームを構成する工程を含み、前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、前記球状フレームの表面に、各画素ブロックを固定し、各画素ブロックの発光素子を電気的に配線する工程を含む。 Furthermore, according to a thirteenth embodiment of the method for manufacturing a spherical display device, any of the above methods further includes a step of constructing a spherical frame, in which 20 pixel blocks are created based on the design of the pixel blocks, and the step of combining the 20 pixel blocks to construct the spherical display section of the spherical display device includes a step of fixing each pixel block to the surface of the spherical frame and electrically wiring the light-emitting elements of each pixel block.
　さらにまた、第１４の形態に係る球状表示装置の製造方法によれば、上記何れかの方法において、前記球状表示部が、半球状又は１／３球、２／３球のいずれかに形成されている。 Furthermore, according to the 14th embodiment of the method for manufacturing a spherical display device, in any of the above methods, the spherical display portion is formed in a hemispherical shape, a 1/3 sphere, or a 2/3 sphere.
　さらにまた、第１５の形態に係る球状表示装置の設計方法によれば、複数の画素ユニットである六角柱状の第一画素ユニットと、五角柱状の第二画素ユニットを隣接して配置した球状の表示装置の設計方法であって、前記球状の表示装置を構成する前記第一画素ユニット及び第二画素ユニットの数と、前記球状の表示装置の直径又は半径と、前記第一画素ユニット及び第二画素ユニットの高さの少なくともいずれかを含むパラメータを設定する工程と、前記表示装置の直径又は半径に基づき、前記球状の表示装置に内接する正二十面体を構成する各正三角形面に対し、前記設定された第一画素ユニット及び第二画素ユニットの数に基づいて、前記球状の表面を多角形で近似したゴールドバーク多面体を構成する六角形の面と五角形の面を、それぞれ単位正三角形の組み合わせで構成するよう、単位正三角形を確定する工程と、前記正三角形面を、各頂点から対向する辺に下ろした垂線で六等分した直角三角形と対応する直角三角形ブロックを、前記単位正三角形を組み合わせた六角形と五角形を底面とし、前記設定された高さを有する第一画素ユニット及び第二画素ユニットを複数組み合わせて設計する工程と、前記直角三角ブロックを反転させた反転直角三角形ブロックと、前記直角三角形ブロックとを組み合わせた二等辺三角形ブロックを設計する工程と、前記二等辺三角形ブロックを１２０°回転させた第一回転二等辺三角形ブロックと、前記第一回転二等辺三角形ブロックをさらに１２０°回転させた第二回転二等辺三角形ブロックと、前記二等辺三角形ブロックとを組み合わせた、前記正二十面体を構成する各正三角形面の一面に相当する画素ブロックを設計する工程とを含む。これにより、球状の表示装置の設計を容易に行うことが可能となる。特に球面の全てを設計するのでなく、ゴールドバーグ多面体の一面のみを設計し、他の面は複製することで対応でき、設計の作業量を約１／１２０に大幅に削減できる。 Furthermore, according to a fifteenth embodiment of the design method for a spherical display device, a method for designing a spherical display device having a plurality of pixel units, a first pixel unit in the shape of a hexagonal prism and a second pixel unit in the shape of a pentagonal prism, arranged adjacent to each other, includes a step of setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit, and a step of setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit, based on the diameter or radius of the display device, so that for each equilateral triangular face constituting a regular icosahedron inscribed in the spherical display device, the hexagonal faces and the pentagonal faces constituting a Goldberg polyhedron approximating the spherical surface with a polygon are each constituted by a combination of unit equilateral triangles based on the number of the first pixel units and the second pixel units set, The method includes a step of determining a unit equilateral triangle, a step of designing a right-angled triangle block corresponding to a right-angled triangle obtained by dividing the equilateral triangular surface into six equal parts by perpendicular lines drawn from each vertex to the opposing side, by combining a plurality of first pixel units and second pixel units having the set height and a hexagon and pentagon formed by combining the unit equilateral triangles as bases, a step of designing an isosceles triangular block by combining an inverted right-angled triangular block obtained by inverting the right-angled triangular block with the right-angled triangular block, and a step of designing a pixel block corresponding to one side of each equilateral triangular surface constituting the regular icosahedron by combining a first rotated isosceles triangular block obtained by rotating the isosceles triangular block by 120°, a second rotated isosceles triangular block obtained by further rotating the first rotated isosceles triangular block by 120°, and the isosceles triangular block. This makes it possible to easily design a spherical display device. In particular, instead of designing the entire spherical surface, only one side of the Goldberg polyhedron is designed and the other sides are duplicated, which significantly reduces the amount of design work to about 1/120.
　さらにまた、第１６の形態に係る球状表示装置によれば、複数の画素ユニットを隣接して配置した球状の表示装置であって、それぞれが六角柱状で、各六角柱状の端面を閉塞する第一底面板に第一発光素子を配置した、複数の第一画素ユニットと、それぞれが五角柱状で、各五角柱状の端面を閉塞する第二底面板に第二発光素子を配置した、複数の第二画素ユニットと、で構成された、球状表示部と、前記第一発光素子及び第二発光素子を点灯駆動させる点灯駆動回路と、前記球状表示部を支持する球状フレームと、を備え、各第一画素ユニットの、前記六角柱状を構成する側面は、前記球状の外縁に向かって拡がるよう傾斜されており、各第二画素ユニットの、前記五角柱状を構成する側面は、前記球状の外縁に向かって拡がるよう傾斜されている。 Furthermore, according to a spherical display device of the 16th embodiment, the spherical display device is a spherical display device in which a plurality of pixel units are arranged adjacent to each other, the spherical display unit being composed of a plurality of first pixel units, each of which is hexagonal prism-shaped and has a first light-emitting element arranged on a first bottom plate closing an end face of each hexagonal prism, and a plurality of second pixel units, each of which is pentagonal prism-shaped and has a second light-emitting element arranged on a second bottom plate closing an end face of each pentagonal prism, a lighting drive circuit that drives and lights the first light-emitting elements and the second light-emitting elements, and a spherical frame that supports the spherical display unit, and the side surfaces of each first pixel unit that constitute the hexagonal prism are inclined so as to expand toward the outer edge of the sphere, and the side surfaces of each second pixel unit that constitute the pentagonal prism are inclined so as to expand toward the outer edge of the sphere.
　さらにまた、第１７の形態に係る球状表示装置によれば、上記何れかの構成において、前記球状フレームが、環状の緯線部と、前記緯線部上において、該緯線部と交差すると共に、赤道上で互いに離間され、上下を各極点で固定した、環状の複数の経線部とを備える。 Furthermore, according to a seventeenth embodiment of the spherical display device, in any of the above configurations, the spherical frame comprises an annular latitude line section and a plurality of annular meridian sections that intersect with the latitude line section on the latitude line section, are spaced apart from each other on the equator, and have their tops and bottoms fixed at the respective poles.
　さらにまた、第１８の形態に係る球状表示装置によれば、上記何れかの構成において、前記第一発光素子及び第二発光素子が、その発光色を可変としている。 Furthermore, according to the spherical display device of the eighteenth embodiment, in any of the above configurations, the first light-emitting element and the second light-emitting element have variable light emission colors.
　さらにまた、第１９の形態に係る球状表示装置によれば、上記何れかの構成において、前記球状表示部が、半球状又は１／３球、２／３球のいずれかに形成されている。 Furthermore, according to the spherical display device of the 19th embodiment, in any of the above configurations, the spherical display portion is formed in a hemispherical shape, a 1/3 sphere, or a 2/3 sphere.
　さらにまた、第２０の形態に係る球状表示装置の設計プログラムによれば、複数の画素を隣接して配置した球状の表示装置を設計するためのプログラムであって、前記球状の表示装置を構成する画素ユニットの数と、前記球状の表示装置の直径又は半径と、画素ユニットの高さの少なくともいずれかを含むパラメータを設定する機能と、前記設定された画素ユニットの数と、表示装置の直径又は半径と、画素ユニットの高さの少なくとも何れかの設定に基づいて、球状の表面を多角形で近似したゴールドバーク多面体を構成する六角形の面と五角形の面を、構成する単位正三角形を確定する機能と、前記単位正三角形を組み合わせた六角形を底面とし、前記指定された高さを有する画素ユニットを複数組み合わせた直角三角ブロックを設計する機能と、前記直角三角ブロックを反転させた反転直角三角形ブロックと、前記直角三角形ブロックを組み合わせた二等辺三角形ブロックを設計する機能と、前記二等辺三角形を１２０°回転させた第一回転二等辺三角形ブロックと、前記第一回転二等辺三角形ブロックをさらに１２０°回転させた第二回転二等辺三角形ブロックと、前記二等辺三角形ブロックを組み合わせた、画素ブロックを設計する機能とをコンピュータに実現させる。上記構成により球状の表示装置の設計を容易に行うことが可能となる。 Furthermore, according to the design program for a spherical display device of the 20th embodiment, there is provided a program for designing a spherical display device having a plurality of pixels arranged adjacent to one another, the program having a function for setting parameters including at least one of the number of pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the pixel unit, and a function for determining unit equilateral triangles constituting the hexagonal and pentagonal faces constituting a Goldberg polyhedron, which is a polygonal approximation of a spherical surface, based on the setting of at least one of the number of pixel units, the diameter or radius of the display device, and the height of the pixel unit. The computer is made to realize a function of designing a right-angled triangular block by combining a plurality of pixel units having the specified height and a hexagon formed by combining the unit equilateral triangles as a base, a function of designing an inverted right-angled triangular block by inverting the right-angled triangular block and an isosceles triangular block by combining the right-angled triangular blocks, and a function of designing a pixel block by combining a first rotated isosceles triangular block by rotating the isosceles triangle by 120°, a second rotated isosceles triangular block by further rotating the first rotated isosceles triangular block by 120°, and the isosceles triangular block. The above configuration makes it possible to easily design a spherical display device.
　さらにまた、第２１の形態に係るコンピュータで読み取り可能な記録媒体または記憶した機器は、上記球状表示装置の設計プログラムを記録したものである。 Furthermore, the computer-readable recording medium or storage device according to the twenty-first embodiment stores the design program for the spherical display device.
本発明の一実施形態に係る球状表示装置を示す模式図である。1 is a schematic diagram showing a spherical display device according to an embodiment of the present invention; 図１の球状表示部を固定する台座部を示す斜視図である。2 is a perspective view showing a base portion for fixing the spherical display portion of FIG. 1. FIG. 変形例に係る球状表示部の固定構造を示す図である。13A and 13B are diagrams illustrating a fixing structure of a spherical display unit according to a modified example. 図２の球状表示部を支持する球状フレームを示す正面図である。3 is a front view showing a spherical frame supporting the spherical display unit of FIG. 2. 図４の球状フレームの平面図である。FIG. 5 is a plan view of the spherical frame of FIG. 4 . 図５の球状フレームのＶＩ－ＶＩ線における断面図である。6 is a cross-sectional view of the spherical frame taken along line VI-VI of FIG. 5. 図６の球状フレームのＶＩＩ－ＶＩＩ線における断面図である。7 is a cross-sectional view of the spherical frame taken along line VII-VII of FIG. 6. 船型板を示す平面図である。FIG. 船型フレームに支持金具を設けた状態を示す斜視図である。This is an oblique view showing the state in which support brackets are attached to the boat-shaped frame. 図９の支持金具を示す拡大斜視図である。FIG. 10 is an enlarged perspective view showing the support bracket of FIG. 9 . 図１０の支持金具の分解斜視図である。FIG. 11 is an exploded perspective view of the support bracket of FIG. 10 . 図９の支持金具に経線板を固定した状態を示す斜視図である。FIG. 10 is a perspective view showing a state in which a meridian plate is fixed to the support bracket of FIG. 9 . 図１２の経線板に船型板を固定した状態を示す斜視図である。FIG. 13 is a perspective view showing a state in which a boat-shaped plate is fixed to the meridian plate of FIG. 12 . 型板を船型板の表面に配置した状態を示す斜視図である。1 is a perspective view showing the state in which the template is placed on the surface of the hull template. FIG. 画素ユニットを船型板に固定した状態を示す模式垂直断面図である。FIG. 11 is a schematic vertical cross-sectional view showing a state in which the pixel unit is fixed to a boat-shaped plate. 画素ユニットの模式垂直断面図である。FIG. 2 is a schematic vertical sectional view of a pixel unit. 角柱を組み合わせて球面を表現する例を示す模式断面図である。FIG. 13 is a schematic cross-sectional view showing an example of expressing a spherical surface by combining prisms. 図１７の角柱の形状を変形して、球面を表現する例を示す模式断面図である。18 is a schematic cross-sectional view showing an example in which the shape of the prism in FIG. 17 is modified to express a spherical surface. FIG. 図１の球状表示装置の画素ユニット毎の点灯制御を行う駆動回路を示すブロック図である。2 is a block diagram showing a drive circuit that controls lighting for each pixel unit of the spherical display device of FIG. 1. 変形例に係る球状表示装置の画素ユニット毎の点灯制御を行う駆動回路を示すブロック図である。FIG. 13 is a block diagram showing a drive circuit that controls lighting for each pixel unit of a spherical display device according to a modified example. ハニカム球の設計手順を示すフローチャートである。1 is a flowchart showing a design procedure for a honeycomb sphere. ハニカム球の斜視図である。FIG. 1 is a perspective view of a honeycomb sphere. 図２３ＡはクラスＩ、図２３ＢはクラスＩＩ、図２３ＣはクラスＩＩＩのジオデシック多面体を示す斜視図である。23A is a perspective view showing a geodesic polyhedron of class I, FIG. 23B is a perspective view showing a geodesic polyhedron of class II, and FIG. 23C is a perspective view showing a geodesic polyhedron of class III. 図２４ＡはクラスＩ、図２４ＢはクラスＩＩ、図２４ＣはクラスＩＩＩのジオデシック多面体のクラス定義を示す斜視図である。FIG. 24A is a perspective view showing the class definitions of Class I, FIG. 24B is a perspective view showing the class definitions of Class II, and FIG. 24C is a perspective view showing the class definitions of Class III geodesic polyhedra. 図２５Ａは正二十面体、図２５Ｂは図２５Ａの一面を構成する正三角形、図２５Ｃは図２５Ａの正二十面体から図２５Ａの正三角形を用いてジオデシック多面体に変換する様子を示す斜視図である。25A is a regular icosahedron, FIG. 25B is an equilateral triangle constituting one face of FIG. 25A, and FIG. 25C is a perspective view showing how the regular icosahedron of FIG. 25A is converted into a geodesic polyhedron using the equilateral triangle of FIG. 25A. 図２６Ａ、図２６ＢはクラスＩの正三角形の分割例、図２６Ｃ～図２６ＨはクラスＩＩの分割例、図２６Ｉ～図２６ＪはクラスＩＩＩの分割例を、それぞれ示す模式図である。26A and 26B are schematic diagrams showing an example of division of an equilateral triangle of class I, FIGS. 26C to 26H are schematic diagrams showing an example of division of class II, and FIGS. 26I to 26J are schematic diagrams showing an example of division of class III. 図２７ＡはクラスＩ、図２７ＢはクラスＩＩ、図２７ＣはクラスＩＩＩのゴールドバーグ多面体を示す模式図である。FIG. 27A is a schematic diagram showing a Goldberg polyhedron of class I, FIG. 27B is a schematic diagram showing a Goldberg polyhedron of class II, and FIG. 27C is a schematic diagram showing a Goldberg polyhedron of class III. 図２８Ａは正二十面体、図２８Ｂはジオデシック多面体、図２８Ｃは図２８Ｂをゴールドバーク多面体に変換する様子を示す斜視図である。28A is a perspective view of a regular icosahedron, FIG. 28B is a geodesic polyhedron, and FIG. 28C is a perspective view showing how FIG. 28B is converted into a Goldberg polyhedron. 図２９ＡはクラスＩＩ、Ｇ（３，３）のジオデシック多面体、図２９Ｂは図２９Ａを変換したクラスＩ、ＧＰ（３，０）のゴールドバーク多面体を示す斜視図である。FIG. 29A is a perspective view showing a geodesic polyhedron of class II, G(3,3), and FIG. 29B is a perspective view showing a Goldberg polyhedron of class I, GP(3,0) converted from FIG. 29A. 実施形態１に係るゴールドバーグ多面体を構成する画素ブロックを示す図である。3 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the first embodiment; FIG. 実施形態２に係るゴールドバーグ多面体を構成する画素ブロックを示す図である。FIG. 11 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the second embodiment. 実施形態３に係るゴールドバーグ多面体を構成する画素ブロックを示す図である。FIG. 11 is a diagram showing pixel blocks that form a Goldberg polyhedron according to the third embodiment. ジオデシック多面体Ｇ（ｍ，ｎ）の設計手順を示すフローチャートである。1 is a flowchart showing a design procedure for a geodesic polyhedron G(m, n). 等角図を示す平面図である。FIG. 1 is a plan view showing an isometric view. 等角図を構成する正三角形を作成する様子を示す平面図である。FIG. 1 is a plan view showing how to create the equilateral triangles that make up the isometric view. 図３５の正三角形を水平方向にコピーする様子を示す平面図である。FIG. 36 is a plan view showing how the equilateral triangle in FIG. 35 is copied in the horizontal direction. 図３６の正三角形を斜め方向にコピーする様子を示す平面図である。FIG. 37 is a plan view showing how the equilateral triangle in FIG. 36 is copied obliquely. 図３７の正三角形を水平方向にコピーする様子を示す平面図である。FIG. 38 is a plan view showing how the equilateral triangle in FIG. 37 is copied in the horizontal direction. 図３８の正三角形を行段位でコピーする様子を示す平面図である。FIG. 39 is a plan view showing how the equilateral triangle in FIG. 38 is copied in row order. 図３９から等角図を作成する様子を示す平面図である。FIG. 40 is a plan view showing how to create an isometric view from FIG. 39. 図４０の等角図にベクトルｍ、ｎの線を引く様子を示す平面図である。FIG. 41 is a plan view showing how lines of vectors m and n are drawn on the isometric view of FIG. 図４１に正三角形を描く様子を示す平面図である。FIG. 41 is a plan view showing how to draw an equilateral triangle. 図４２の正三角形を６等分した直角三角形に離散点を配置する様子を示す平面図である。FIG. 43 is a plan view showing how discrete points are arranged on right-angled triangles obtained by dividing the equilateral triangle in FIG. 42 into six equal parts. 図４３の離散点に半径（ｒｕ）の垂線を引く様子を示す斜視図である。FIG. 44 is a perspective view showing how to draw perpendicular lines of radius (ru) to the discrete points in FIG. 43 . 図４４の正三角形の各頂点から中心（Ｏ）に半径（ｒｕ）の線分を引く様子を示す斜視図である。This is a perspective view showing how to draw line segments of radius (ru) from each vertex of the equilateral triangle in Figure 44 to the center (O). 図４５の各離散点から中心（Ｏ）に点線を引く様子を示す斜視図である。FIG. 46 is a perspective view showing how dotted lines are drawn from each discrete point in FIG. 45 to the center (O). 図４６の中心（Ｏ）から各点線上に青線を引く様子を示す斜視図である。This is a perspective view showing how blue lines are drawn on each dotted line from the center (O) of Figure 46. 図４７において中心（Ｏ）からの青線を半径（ｒｕ）とする様子を示す斜視図である。This is a perspective view showing how the blue line from the center (O) in Figure 47 is taken as the radius (ru). 図４８の中心（Ｏ）から各離散点を通る半径（ｒｕ）の線分を示す斜視図である。FIG. 49 is a perspective view showing line segments of radius (ru) passing through each discrete point from the center (O) of FIG. 48. 図４９の正三角形上の各離散点を貫く半径（ｒｕ）の線分が球面上にマッピングされた状態を示す斜視図である。FIG. 50 is a perspective view showing a state in which line segments of radius (ru) passing through each discrete point on the equilateral triangle in FIG. 49 are mapped onto a sphere. 図５０の拡大斜視図である。FIG. 51 is an enlarged perspective view of FIG. 50. 図５１の各離散点を貫通する線分の先端同士を線で結び微小正三角形を作成する様子を示す斜視図である。FIG. 52 is a perspective view showing how a minute equilateral triangle is created by connecting the tips of line segments that pass through each of the discrete points in FIG. 51 with lines. 図５２の状態で微小正三角形の面を作成する様子を示す斜視図である。FIG. 53 is a perspective view showing how to create a small equilateral triangular surface in the state shown in FIG. 52. 図５３の状態で側面を埋めた様子を示す斜視図である。This is a perspective view showing the state in which the side surface is filled in from the state shown in Figure 53. 図５４で得られた直角三角錐の全体を示す斜視図である。This is an oblique view showing the entire right-angled pyramid obtained in Figure 54. 図５５の直角三角錐を異なる角度から見た斜視図である。FIG. 56 is a perspective view of the right-angled pyramid of FIG. 55 from a different angle. 図５６の直角三角錐から二等辺三角錐を得る様子を示す斜視図である。This is a perspective view showing how to obtain an isosceles pyramid from the right-angled pyramid of Figure 56. 図５７の二等辺三角錐から正三角錐を得る様子を示す斜視図である。58 is a perspective view showing how to obtain a regular pyramid from the isosceles pyramid of FIG. 57. 図５８で得られた正三角錐の全体を示す斜視図である。This is a perspective view showing the entire regular triangular pyramid obtained in Figure 58. 図５９の正三角錐の内部の境界面を非表示にする様子を示す斜視図である。FIG. 60 is a perspective view showing how the internal boundary surfaces of the regular triangular pyramid in FIG. 59 are hidden. 図６０ですべての正三角錐が選択された状態を示す斜視図である。61 is a perspective view showing the state in which all regular pyramids in FIG. 60 have been selected. 図６１で得られた正三角錐の全体を示す斜視図である。This is an oblique view showing the entire regular triangular pyramid obtained in Figure 61. 図６２の正三角錐を回転コピーして正三角錐の２面分を作成する様子を示す斜視図である。63 is a perspective view showing how the regular triangular pyramid in FIG. 62 is rotated and copied to create two regular triangular pyramids. 図６３の状態から正三角錐をさらに回転コピーして正三角錐の３面分を作成する様子を示す斜視図である。FIG. 64 is a perspective view showing how the regular triangular pyramid is further rotated and copied from the state shown in FIG. 63 to create three faces of the regular triangular pyramid. 図６４の状態から正三角錐をさらに回転コピーして正三角錐の４面分を作成する様子を示す斜視図である。65 is a perspective view showing how the regular triangular pyramid in the state shown in FIG. 64 is further rotated and copied to create four faces of the regular triangular pyramid. 図６５の状態から球の半面分を作成する様子を示す斜視図である。This is a perspective view showing how to create half of a sphere from the state shown in Figure 65. 図６６の状態から球の全面分を作成する様子を示す斜視図である。This is a perspective view showing how to create the entire surface of the sphere from the state shown in Figure 66. 図Ｘの状態からジオデシック多面体を得る様子を示す斜視図である。FIG. 13 is a perspective view showing how a geodesic polyhedron is obtained from the state shown in FIG. X. 図６８のジオデシック多面体の拡大斜視図である。FIG. 69 is an enlarged perspective view of the geodesic polyhedron of FIG. 図６９の状態で、微小正三角形から六角形、五角形に変換する様子を示す斜視図である。70 is a perspective view showing how a small equilateral triangle is converted into a hexagon and a pentagon in the state shown in FIG. 69. 図７０の状態から、六角形、五角形の面を作成する様子を示す斜視図である。This is a perspective view showing how to create hexagonal and pentagonal faces from the state shown in Figure 70. 図７１を経てゴールドバーク多面体の一面分である画素ブロックを得る様子を示す斜視図である。FIG. 72 is a perspective view showing how a pixel block, which is one face of a Goldberg polyhedron, is obtained via FIG. 71 . ハニカム球の斜視図である。FIG. 1 is a perspective view of a honeycomb sphere. 図７３のハニカム球を構成する一セクションの展開図である。FIG. 74 is an exploded view of one section constituting the honeycomb sphere of FIG. 73. 正二十面体を示す斜視図である。FIG. 1 is a perspective view showing a regular icosahedron. 正二十面体の模式展開図である。FIG. 2 is a schematic development of a regular icosahedron. 図７６の正二十面体を構成する一セクションを示す模式図である。FIG. 77 is a schematic diagram showing one section that constitutes the regular icosahedron of FIG. 76. 図７７に示す一セクションを分解した模式図である。FIG. 78 is an exploded schematic diagram of one section shown in FIG. 77. 図７５の正二十面体の展開図である。FIG. 76 is a development of the regular icosahedron of FIG. 画素ユニットを組み合わせた画素ブロックを示す図である。FIG. 2 is a diagram showing a pixel block formed by combining pixel units. 第一画素ブロックを示す図である。FIG. 2 is a diagram showing a first pixel block. 第二画素ブロックを示す図である。FIG. 11 is a diagram showing a second pixel block. 図８０の画素ブロックを構成する２２種類の画素ユニットを示す図である。FIG. 81 is a diagram showing 22 types of pixel units that constitute the pixel block of FIG. 80. 正三角形を二等辺三角形二分割する様子を示す平面図である。FIG. 11 is a plan view showing how an equilateral triangle is divided into two isosceles triangles. 図８３の画素ユニットの内、図８４の下部の二等辺三角形に相当する２２種類の画素ユニットを示す図である。FIG. 85 is a diagram showing 22 types of pixel units among the pixel units in FIG. 83, which correspond to the isosceles triangle in the lower part of FIG. 84. 図８３の画素ユニットの内、第一画素ブロックに相当する画素ユニットを示す図である。FIG. 84 is a diagram showing a pixel unit corresponding to a first pixel block among the pixel units in FIG. 83. 図８３の画素ユニットの内、第二画素ブロックに相当する画素ユニットを示す図である。FIG. 84 is a diagram showing a pixel unit corresponding to a second pixel block among the pixel units in FIG. 83. ジオデシック多面体からゴールドバーク多面体を作成する手順を示すフローチャートである。1 is a flowchart showing a procedure for creating a Goldberg polyhedron from a geodesic polyhedron. １２ｖのジオデシック多面体を示す斜視図である。A perspective view of a 12v geodesic polyhedron. 図８９のジオデシック多面体の一面分の三角形を示す斜視図である。FIG. 90 is a perspective view showing the triangles on one face of the geodesic polyhedron of FIG. 89. 図９０の三角形をゴールドバーク多面体を構成する面に置き換えた状態を示す平面図である。FIG. 91 is a plan view showing the state in which the triangles in FIG. 90 are replaced with faces that constitute a Goldberg polyhedron. 直角三角形ブロックを示す斜視図である。FIG. 2 is a perspective view showing a right-angled triangular block. ゴールドバーグ多面体の面にスティッチを行う様子を示す斜視図である。FIG. 1 is a perspective view showing stitching of faces of a Goldberg polyhedron. 図９３に対し球の中心にロフトを適用する様子を示す斜視図である。FIG. 94 is a perspective view showing the application of loft to the center of the ball in comparison with FIG. 93. 図９４に対しロフトを選択する様子を示す斜視図である。FIG. 95 is a perspective view showing the state of selecting a loft for FIG. 94. Ｓｏｌｉｄ→ロフト（ＮＥＷ　Ｂｏｄｙ）を選択するＧＵＩを示すイメージ図である。This is an image showing the GUI for selecting Solid → Loft (NEW Body). 外側に曲線を引く様子を示す平面図である。FIG. 13 is a plan view showing how to draw a curved line on the outside. 図９７で得られた図形を示す拡大斜視図である。FIG. 98 is an enlarged perspective view showing the pattern obtained in FIG. 97. 図９７に対しスケッチ作成を行う様子を示す平面図である。FIG. 98 is a plan view showing how a sketch is created for FIG. 97. ゴールドバーク多面体と外接円を示す断面図である。FIG. 1 is a cross-sectional view showing a Goldberg polyhedron and a circumscribing circle. 図９９から内面を削除する様子を示す斜視図である。FIG. 99 is a perspective view showing the removal of the inner surface from FIG. 図１０１に対し反射板を置く厚さを設定する様子を示す斜視図である。FIG. 102 is a perspective view showing how to set the thickness of the reflector in FIG. 101 . 図１０２から内層の線を選択する状態を示す斜視図である。FIG. 103 is a perspective view showing the state of selecting an inner layer line from FIG. 102 . 図１０３により得られた図形を示す斜視図である。FIG. 104 is a perspective view showing the pattern obtained by FIG. 103. 図１０４で裏側から面を選択する様子を示す斜視図である。FIG. 105 is a perspective view showing how a face is selected from the back side in FIG. 104 . 図１０５から半球２個の内側・外側を選択する様子を示す斜視図である。This is a perspective view showing the selection of the inside and outside of two hemispheres from Figure 105. 図１０６から不要な半球を非表示とする状態を示す斜視図である。FIG. 107 is a perspective view showing the state in which unnecessary hemispheres are hidden from view in FIG. 106 . 図１０７で非表示を実行した結果を示す斜視図である。FIG. 108 is a perspective view showing the result of executing non-display in FIG. 107. 図１０８を表面側から見た斜視図である。This is a perspective view of Figure 108 seen from the front side. 上下反転させると向きが判別できなくなる様子を示す平面図である。FIG. 13 is a plan view showing how the orientation becomes unrecognizable when the image is turned upside down. 図９２の直角三角形ブロックを背面側から見た斜視図であるFIG. 93 is a perspective view of the right-angled triangular block of FIG. 92 as seen from the rear side. 図９２の直角三角形ブロックを反転コピーして二等辺三角形相当を得る様子を示す斜視図である。FIG. 93 is a perspective view showing how the right-angled triangular block in FIG. 92 is inverted and copied to obtain an equivalent isosceles triangle. 反射板を作成する手順を示すフローチャートである。10 is a flowchart showing a procedure for producing a reflector. 反射板の作成対象となる反射構造体を表示させた斜視図である。FIG. 2 is a perspective view showing a reflective structure from which a reflector is to be made; 図１１４の反射構造体の開口部分を線で囲む様子を示す斜視図である。FIG. 115 is a perspective view showing the opening of the reflecting structure of FIG. 114 surrounded by a line. 図１１５から外形線を選択し、×－Ｙ平面上に投影させた状態を示す斜視図である。FIG. 116 is a perspective view showing the state in which the outline is selected from FIG. 115 and projected onto the xy plane. 図１１６から開口部の領域を選択して面を作成する様子を示す斜視図である。117 is a perspective view showing how to select an opening area from FIG. 116 and create a surface. 図１１７から反射板に相当する厚みを押し出しにより作成する様子を示す斜視図である。FIG. 118 is a perspective view showing how a thickness equivalent to that of the reflector plate in FIG. 117 is created by extrusion. 図１１８から傾いた面を平面に配置する様子を示す斜視図である。119 is a perspective view showing how an inclined surface from FIG. 118 is arranged on a plane. 図１１９を×－Ｙ平面に置き、裏面に線を引く様子を示す斜視図である。This is a perspective view showing how FIG. 119 is placed on the xy plane and lines are drawn on the back side. 図１２０からピンク色の各点を線で結ぶ様子を示す斜視図である。This is a perspective view showing how the pink dots in Figure 120 are connected with lines. 図１２１から原点位置に移動させる様子を示す斜視図である。122 is a perspective view showing the state of being moved from FIG. 121 to the origin position. FIG. 図１２２から垂直方向に拘束をかけて、線を×軸に合わせる様子を示す平面図である。This is a plan view showing how a constraint is applied vertically from FIG. 122 to align a line with the x-axis. 図１２３の反射板をＤ×Ｆファイルとして保存する様子を示す斜視図である。FIG. 124 is a perspective view showing how the reflector in FIG. 123 is saved as a D×F file. 図１２４で保存されたＤ×Ｆファイルを確認する様子を示す平面図である。125 is a plan view showing how to check the D×F file saved in FIG. 124. ハニカム球を組み立てる手順を示すフローチャートである。1 is a flowchart showing a procedure for assembling a honeycomb sphere. 画素ブロックを三分割する例を示す分解図である。FIG. 13 is an exploded view showing an example of dividing a pixel block into three. 三分割された画素分割ブロック１～３を設計する様子を示すイメージ図である。FIG. 13 is an image diagram showing how to design pixel division blocks 1 to 3 divided into three. 第一画素ブロックの一例を示す写真である。1 is a photograph showing an example of a first pixel block. クラスＩのＧ（８，０）のジオデシック多面体の正三角形面を分割する様子を示す模式図である。FIG. 2 is a schematic diagram showing how to divide an equilateral triangular face of a geodesic polyhedron G(8,0) of class I. クラスＩＩのＧ（５，２）のジオデシック多面体の正三角形面を分割する様子を示す模式図である。FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a class II G(5,2) geodesic polyhedron. クラスＩＩＩのＧ（４，３）のジオデシック多面体の正三角形面を分割する様子を示す模式図である。FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a class III G(4,3) geodesic polyhedron. クラスＩＩＩのＧ（５，２）のジオデシック多面体の正三角形面を分割する様子を示す模式図である。FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a G(5,2) geodesic polyhedron of class III. クラスＩＩＩのＧ（６，２）のジオデシック多面体の正三角形面を分割する様子を示す模式図である。FIG. 1 is a schematic diagram showing how to divide an equilateral triangular face of a G(6,2) geodesic polyhedron of class III.
　以下、本発明の実施の形態を図面に基づいて説明する。ただし、以下に示す実施の形態は、本発明の技術思想を具体化するための表示装置を例示するものであって、本発明は表示装置を以下のものに特定しない。また、本明細書は請求の範囲に示される部材を、実施の形態の部材に特定するものでは決してない。特に実施の形態に記載されている構成部品の寸法、材質、形状、その相対的配置等は特定的な記載がない限りは、本発明の範囲をそれのみに限定する趣旨ではなく、単なる説明例にすぎない。なお、各図面が示す部材の大きさや位置関係等は、説明を明確にするため誇張していることがある。さらに以下の説明において、同一の名称、符号については同一もしくは同質の部材を示しており、詳細説明を適宜省略する。さらに、本発明を構成する各要素は、複数の要素を同一の部材で構成して一の部材で複数の要素を兼用する態様としてもよいし、逆に一の部材の機能を複数の部材で分担して実現することもできる。
（球状表示装置１０００） Hereinafter, an embodiment of the present invention will be described with reference to the drawings. However, the embodiment shown below is an example of a display device for embodying the technical idea of the present invention, and the present invention does not specify the display device as follows. In addition, this specification never specifies the members shown in the claims to the members of the embodiment. In particular, the dimensions, materials, shapes, and relative positions of the components described in the embodiment are not intended to limit the scope of the present invention, and are merely explanatory examples, unless otherwise specified. Note that the size and positional relationship of the members shown in each drawing may be exaggerated to clarify the explanation. Furthermore, in the following explanation, the same name and symbol indicate the same or similar members, and detailed explanation will be omitted as appropriate. Furthermore, each element constituting the present invention may be configured as a form in which multiple elements are composed of the same member and one member serves multiple elements, or conversely, the function of one member can be shared by multiple members.
(Spherical display device 1000)
　本発明の実施形態１に係る球状表示装置１０００を、図１に示す。この図に示す球状表示装置１０００は、球状表示部１と、コントローラ７０と、電源装置２を備えている。球状表示部１は、一定の厚さを有する球面に形成されている。また球状表示部１は、複数の画素ユニット１００で構成される。具体的には、六角柱状の第一画素ユニット１００Ａと、五角柱状の第二画素ユニット１００Ｂで構成される。これら画素ユニット１００は、それぞれ、角柱状の端面を閉塞する底面板２５に発光素子５０を配置している。具体的に、第一画素ユニット１００Ａは、各六角柱状の端面を閉塞する第一底面板２５ａに第一発光素子５０Ａを配置している。また第二画素ユニット１００Ｂは、各五角柱状の端面を閉塞する第二底面板２５ｂに第二発光素子５０Ｂを配置している。なお、底面板で端面を閉塞するとは、開口端に底面板を設けるという意味であって、底面板に開口を設けることを禁止する意味でない。これら第一発光素子５０Ａ、第二発光素子５０Ｂは、コントローラ７０で点灯制御される。なお第一発光素子５０Ａや第二発光素子５０Ｂは、その発光色を可変としてもよい。これら第一発光素子５０Ａ、第二発光素子５０Ｂは、同じもの、好適には発光ダイオード等の半導体発光素子を利用できる。発光色の制御も、コントローラ７０で行うことができる。電源装置２は、コントローラ７０や発光素子５０の駆動電力を供給するための回路であり、例えば商用電源を直流電圧に変換するコンバータや電源安定化回路で構成される。あるいは、二次電池等を用いてもよいし、ソーラーパネルなどの発電機と接続してもよい。この場合は商用電源がない場所でも球状表示装置を使用可能とできる。 1 shows a spherical display device 1000 according to a first embodiment of the present invention. The spherical display device 1000 shown in this figure includes a spherical display unit 1, a controller 70, and a power supply unit 2. The spherical display unit 1 is formed on a spherical surface having a certain thickness. The spherical display unit 1 is composed of a plurality of pixel units 100. Specifically, it is composed of a first pixel unit 100A having a hexagonal prism shape and a second pixel unit 100B having a pentagonal prism shape. Each of these pixel units 100 has a light-emitting element 50 arranged on a bottom plate 25 that closes the end faces of the prism shape. Specifically, the first pixel unit 100A has a first light-emitting element 50A arranged on a first bottom plate 25a that closes the end faces of each hexagonal prism. The second pixel unit 100B has a second light-emitting element 50B arranged on a second bottom plate 25b that closes the end faces of each pentagonal prism. Note that closing the end faces with a bottom plate means that a bottom plate is provided at the opening end, and does not mean that an opening is prohibited from being provided in the bottom plate. The first light-emitting element 50A and the second light-emitting element 50B are controlled by the controller 70. The first light-emitting element 50A and the second light-emitting element 50B may have a variable light-emitting color. The first light-emitting element 50A and the second light-emitting element 50B may be the same, preferably a semiconductor light-emitting element such as a light-emitting diode. The light-emitting color may also be controlled by the controller 70. The power supply device 2 is a circuit for supplying driving power to the controller 70 and the light-emitting element 50, and is composed of, for example, a converter that converts a commercial power source into a DC voltage and a power supply stabilization circuit. Alternatively, a secondary battery or the like may be used, or it may be connected to a generator such as a solar panel. In this case, the spherical display device can be used even in places where there is no commercial power source.
　なお本明細書において球状表示装置や球状表示部における球状とは、完全な球体を意味するものでなく、部分的に歪んだ球状であってもよい。また本明細書において球状とは、球の全面を構成している必要はなく、部分的に欠けていてもよい。例えば、一部の画素ユニットが部分的に欠落していてもよい。また半球状でもよいし、あるいは１／４や１／３、２／３など、球面の一部分でもよい。例えば半球状のディスプレイを構築することもできる。
（台座部４） In this specification, the spherical shape of the spherical display device or spherical display unit does not mean a perfect sphere, but may be a partially distorted sphere. In this specification, the spherical shape does not need to constitute the entire surface of a sphere, and may be partially missing. For example, some pixel units may be partially missing. It may also be a hemisphere, or a part of the sphere, such as 1/4, 1/3, or 2/3. For example, a hemispherical display may be constructed.
(Base portion 4)
　球状表示部１は、球状に形成されたハニカム球に形成されている。この球状表示部１は、図２に示すように、台座部４に載置されて、床面上に固定されている。台座部４は、円筒状球状表示部１の直径よりも短い外径の円柱状に形成されている。この台座部４は、強度を有する金属筒などで構成される。台座部４は、図２の例では短い高さに設計されているが、例えばポールやタワーのように高くしてもよい。高くする場合は、台座部を土台方向に向かって末広がりの形状とすることが好ましい。なお球状表示部を固定する固定構造は、このような構成に限られず、例えば図３に示すよう、球状表示部１Ｂを天井からワイヤーやチェーン、パイプ等の吊下体４Ｂで吊り下げるように構成してもよい。
（球状フレーム３０） The spherical display unit 1 is formed as a honeycomb sphere formed in a spherical shape. As shown in FIG. 2, the spherical display unit 1 is placed on a base 4 and fixed on a floor surface. The base 4 is formed in a cylindrical shape with an outer diameter shorter than the diameter of the cylindrical spherical display unit 1. The base 4 is made of a metal tube having strength. The base 4 is designed to have a short height in the example of FIG. 2, but may be made taller, for example, like a pole or tower. When made taller, it is preferable that the base be made in a shape that flares out toward the base. Note that the fixing structure for fixing the spherical display unit is not limited to this configuration, and may be configured to hang the spherical display unit 1B from the ceiling with a hanging body 4B such as a wire, chain, or pipe, as shown in FIG. 3, for example.
(Spherical Frame 30)
　球状表示部１は、球状フレーム３０で支持される。このような球状フレーム３０の一例として、図２の台座部４に固定された球状表示部１を支持する球状フレーム３０を図４～図７に示す。これらの図は、球状表示部１の画素ユニット１００や船型板３６などの表層部分を省いた、内部の球状フレーム３０を示している。これらの図に示す球状フレーム３０は、環状の緯線部３１と、この緯線部３１と交差する複数の環状の経線部３２で構成される。図４、図７に示す例では、緯線部３１は、赤道部分を走る第一緯線部３１ａと、その上下に離間してそれぞれ配置された第二緯線部３１ｂ、第三緯線部３１ｃの３つで構成される。また経線部３２は、図５に示すように、ハニカム球の上下の北極点、南極点に位置する極点３３を通る環状に形成されている。図５の例では１８本の形線部が１０°間隔で互いに離間して設けられている。これら緯線部３１や経線部３２は、強度を有する金属性のパイプ、例えば鋼管などで構成される。 The spherical display unit 1 is supported by a spherical frame 30. As an example of such a spherical frame 30, a spherical frame 30 supporting the spherical display unit 1 fixed to the base 4 in FIG. 2 is shown in FIGS. 4 to 7. These figures show the internal spherical frame 30, omitting the surface parts such as the pixel unit 100 and the ship-shaped plate 36 of the spherical display unit 1. The spherical frame 30 shown in these figures is composed of a ring-shaped latitude line portion 31 and a plurality of ring-shaped meridian lines 32 that intersect with the latitude line portion 31. In the example shown in FIGS. 4 and 7, the latitude line portion 31 is composed of three parts: a first latitude line portion 31a that runs along the equator, and a second latitude line portion 31b and a third latitude line portion 31c that are spaced apart above and below the first latitude line portion 31a. In addition, the meridian line portion 32 is formed in a ring shape that passes through poles 33 located at the north pole and south pole of the honeycomb sphere, as shown in FIG. 5. In the example of FIG. 5, 18 shape line portions are provided spaced apart from each other at 10° intervals. These latitude and longitude sections 31 and 32 are made of strong metallic pipes, such as steel pipes.
　さらに図６に示すように、ハニカム球の中間には補強管３４が設けられており、補強管３４から第一緯線部３１ａに複数の補強軸３５が、それぞれ６０°間隔で離間して設けられている。補強管３４は、好ましくは図４に示すように台座部４を延長して構成される。これによって、より安定的に球状表示部１を支持できる。
（船型板３６） Furthermore, as shown in Fig. 6, a reinforcing tube 34 is provided in the middle of the honeycomb sphere, and a plurality of reinforcing shafts 35 are provided at intervals of 60° from the reinforcing tube 34 to the first latitude line portion 31a. The reinforcing tube 34 is preferably configured by extending the base portion 4 as shown in Fig. 4. This allows the spherical display portion 1 to be supported more stably.
(Ship form plate 36)
　このような球状フレーム３０で、球状表示部１を直接支持することもできるが、好ましくは、間接的に球状表示部１を支持する。例えば図８に示すような複数枚の船型板３６を準備して、これら船型板３６を球状フレーム３０の表面に固定し、この船型板３６の表面に、球状表示部１を固定する。各船型板３６は、その両側を緯線部３１でそれぞれ支持するように構成することが好ましい。図４等の例では、１８本の緯線部３１を設けているため、９枚の船型板３６を球状球状フレーム３０の表面に固定する。船型板３６は、スチールやアルミニウム等の金属板で構成される。
（支持金具４０） Although such a spherical frame 30 can directly support the spherical display unit 1, it is preferable that the spherical display unit 1 is indirectly supported. For example, a plurality of ship-shaped plates 36 as shown in Fig. 8 are prepared, these ship-shaped plates 36 are fixed to the surface of the spherical frame 30, and the spherical display unit 1 is fixed to the surface of the ship-shaped plates 36. It is preferable that each ship-shaped plate 36 is configured so that both sides are supported by the latitude line parts 31. In the example of Fig. 4 etc., 18 latitude line parts 31 are provided, so nine ship-shaped plates 36 are fixed to the surface of the spherical frame 30. The ship-shaped plates 36 are made of metal plates such as steel or aluminum.
(Support bracket 40)
　また船型板３６を球状フレーム３０の表面に直接固定する他、好ましくは図９の斜視図に示すように、球状フレーム３０を構成する緯線部３１から、支持金具４０を突出させて、支持金具４０でもって船型板３６を固定する。支持金具４０は、図１０、図１１の拡大斜視図に示すように、経線部３２のパイプを前後からクランプする２枚の曲面板４１を有する。また曲面板４１の両側でそれぞれ貫通して、延長された一対のシャフト４２と、このシャフト４２の先端に固定された横板４３を備える。 In addition to directly fixing the hull plate 36 to the surface of the spherical frame 30, preferably, as shown in the perspective view of Figure 9, support brackets 40 are protruded from the latitude section 31 that constitutes the spherical frame 30, and the hull plate 36 is fixed with the support brackets 40. As shown in the enlarged perspective views of Figures 10 and 11, the support brackets 40 have two curved plates 41 that clamp the pipe of the meridian section 32 from the front and back. Also, a pair of shafts 42 extend through both sides of the curved plates 41, and horizontal plates 43 are fixed to the tips of the shafts 42.
　この横板４３に、船型板３６を直接固定してもいい。固定には、螺合や接着剤が利用できる。あるいは図１２に示すように、各横板４３に経線板４４を固定し、この経線板４４の表面に、図１３に示すように船型板３６を固定するようにしてもよい。 The ship-shaped plate 36 may be fixed directly to the side plates 43. For fixing, screws or adhesives may be used. Alternatively, as shown in FIG. 12, a meridian plate 44 may be fixed to each side plate 43, and the ship-shaped plate 36 may be fixed to the surface of the meridian plate 44 as shown in FIG. 13.
　このようにして得られた、船型板３６を貼った球状フレーム３０の表面に、球状表示部１を固定していく。具体的には球状表示部１を構成する画素ユニット１００を、船型板３６に固定する。なお、画素ユニット１００の固定作業は球面全体で行う他、例えば球面を北半球と南半球に分割して行ってもよいし、球面の１／３や１／４といった部分毎に行ってもよい。また画素ユニット１００を船型板３６に固定する際は、画素ユニット１００毎に、図１４に示すように型板２６を予め船型板３６の表面に配置することもできる。型板２６は画素ユニット１００の位置決めのために一時的に配置するものであり、各画素ユニット１００の配置位置を決めた後は取り外す。このような型板２６には、厚紙やプラスチック板が利用できる。また画素ユニット１００を固定する前に、船型板３６に予め開口窓３７を開口しておくことが好ましい。例えば型板２６に、開口窓３７に対応する開口を設けておき、画素ユニットの位置決めと併せて、開口窓３７の開口位置も規定することもできる。そして図１５に示すように、各画素ユニット１００を所定の位置に固定する。各画素ユニット１００の固定には螺合や接着が利用できる。各画素ユニット１００の底面に設けた発光素子５０は、開口窓３７を通じて球状表示部１の内部で配線される。
（画素ユニット１００） The spherical display unit 1 is fixed to the surface of the spherical frame 30 to which the boat-shaped plate 36 is attached, thus obtained. Specifically, the pixel units 100 constituting the spherical display unit 1 are fixed to the boat-shaped plate 36. The pixel units 100 may be fixed to the entire spherical surface, or may be fixed by dividing the spherical surface into the northern and southern hemispheres, or may be fixed to each portion, such as 1/3 or 1/4 of the spherical surface. When fixing the pixel units 100 to the boat-shaped plate 36, a template 26 may be placed on the surface of the boat-shaped plate 36 for each pixel unit 100, as shown in FIG. 14. The template 26 is temporarily placed to position the pixel units 100, and is removed after the placement position of each pixel unit 100 is determined. Cardboard or a plastic plate can be used for such a template 26. It is also preferable to open an opening window 37 in the boat-shaped plate 36 beforehand before fixing the pixel units 100. For example, an opening corresponding to the window 37 can be provided in the template 26, and the opening position of the window 37 can be specified in addition to the positioning of the pixel units. Then, as shown in Fig. 15, each pixel unit 100 is fixed in a predetermined position. Each pixel unit 100 can be fixed by screwing or adhesive. The light-emitting element 50 provided on the bottom surface of each pixel unit 100 is wired inside the spherical display unit 1 through the window 37.
(Pixel unit 100)
　画素ユニット１００は、上述の通り六角柱状や五角柱状の、所定の高さを有する多角柱状である。各画素ユニット１００の模式断面図を図１６に示す。この図に示すように画素ユニット１００は、反射構造体１０と、拡散シート２０と、発光素子５０とを備える。この例では、底面を六角形とした六角柱状の第一画素ユニット１００Ａの例を示している。なお底面を五角形とした五角柱状の第二画素ユニット１００Ｂについても、形状以外の構造は第一画素ユニット１００Ａと共通としている。よって、以下では画素ユニット１００の代表例として、第一画素ユニット１００Ａについて説明する。 As described above, the pixel unit 100 is a polygonal prism having a predetermined height, such as a hexagonal prism or a pentagonal prism. A schematic cross-sectional view of each pixel unit 100 is shown in FIG. 16. As shown in this figure, the pixel unit 100 includes a reflective structure 10, a diffusion sheet 20, and a light-emitting element 50. In this example, a first pixel unit 100A having a hexagonal prism shape with a hexagonal bottom surface is shown. Note that the second pixel unit 100B having a pentagonal prism shape with a pentagonal bottom surface has the same structure as the first pixel unit 100A, except for the shape. Therefore, the first pixel unit 100A will be described below as a representative example of the pixel unit 100.
　反射構造体１０は、外形を六角柱状あるいは五角柱状とし、内部を空洞として一方を開口端としている。 The reflective structure 10 has a hexagonal or pentagonal prism shape, is hollow inside, and has an open end on one side.
　拡散シート２０は、反射構造体１０の開口端を閉塞するように配置された、透光性を有する部材である。この拡散シート２０は、画素発光領域を構成する。この拡散シート２０は、反射板２２で構成される。 The diffusion sheet 20 is a light-transmitting member arranged to close the open end of the reflective structure 10. This diffusion sheet 20 constitutes the pixel light-emitting area. This diffusion sheet 20 is composed of a reflector 22.
　反射板２２には、アクリル板やポリカーボネート、ポリプロピレン、塩化ビニル樹脂、ＰＥＴ樹脂等が好適に利用できる。また反射板２２の厚さは、１ｍｍ～５ｍｍとすることが好ましい。反射板２２の色は、乳白色とし、半透明とすることが好ましい。 Acrylic plate, polycarbonate, polypropylene, polyvinyl chloride resin, PET resin, etc. can be suitably used for the reflector 22. The thickness of the reflector 22 is preferably 1 mm to 5 mm. The color of the reflector 22 is preferably milky white and semi-transparent.
　また拡散シート２０として、反射板２２に拡散フィルム２４を組み合わせて構成してもよい。拡散フィルム２４は、拡散材を塗布した樹脂製のフィルムシートであり、反射板２２の表面に積層して使用される。このような拡散フィルム２４にはポリエステルフィルムが好適に利用できる。また拡散フィルム２４の厚さは、ＬＥＤ光源やアクリル板の厚さに応じて設定され、３８μｍ～１２５μｍとすることが好ましい。ここでは、Tochiman technical paper co. ltd製の、厚さ３８μｍのポリエステルフィルムを用いた。また拡散フィルム２４は樹脂製とする他、紙製としてもよい。また、反射板と拡散フィルムを一枚のシートで構成する場合や、より薄い厚みとすることもできる。 The diffusion sheet 20 may also be constructed by combining a reflector 22 with a diffusion film 24. The diffusion film 24 is a resin film sheet coated with a diffusing material, and is laminated onto the surface of the reflector 22 when used. A polyester film is suitable for use as this type of diffusion film 24. The thickness of the diffusion film 24 is set according to the thickness of the LED light source and the acrylic plate, and is preferably 38 μm to 125 μm. Here, a 38 μm-thick polyester film manufactured by Tochiman technical paper co. ltd is used. The diffusion film 24 may be made of paper instead of resin. The reflector and diffusion film may also be constructed from a single sheet, or may be made even thinner.
　発光素子５０は、反射構造体１０の他方の端縁において、この端縁の中央部分に配置された光学素子である。発光素子５０は、赤色、緑色、青色等の異なる発光色に発光可能なものを利用できる。このような発光素子５０としては、発光ダイオードや半導体レーザ、あるいは有機ＥＬのような半導体発光素子が好適に利用できる。この例では発光素子５０として赤色、緑色、青色に発光可能な発光ダイオード（ＬＥＤ）を用いている。 The light-emitting element 50 is an optical element located in the center of the other edge of the reflective structure 10. The light-emitting element 50 can be one that is capable of emitting different colors such as red, green, and blue. As such a light-emitting element 50, a light-emitting diode, a semiconductor laser, or a semiconductor light-emitting element such as an organic electroluminescence (EL) can be suitably used. In this example, a light-emitting diode (LED) that is capable of emitting red, green, and blue colors is used as the light-emitting element 50.
　この画素ユニット１００を複数台、各画素ユニット１００の角柱状の側面同士を積層して、天面の拡散シート２０で構成される画素発光領域同士を隣接させて、大きな表示領域を構成している。この構成により、発光素子５０の点状光源からの光を拡散シート２０で面状に拡げると共に、拡散シート２０で構成される面発光領域を隣接させることで、従来のＬＥＤディスプレイではＬＥＤ同士の間が非発光のため表示面が不均一となっていた問題を解消できる。すなわち、ＬＥＤ同士の間隔を拡げても、各画素を面状光源とし、かつこれらを近接させたことで、従来のような画素同士の間に存在する非発光領域を低減して、表示領域全体で均一な発光が得られ、結果として使用する発光素子の数を低減しても、均一でドット感の少ない高品質な表示装置を実現できる。また画素ユニット１００を角柱状としたことで、十分な強度を備えさせ、多数の画素ユニット１００を積層しても型崩れしない利点も得られる。
（反射構造体１０） A large display area is formed by stacking a plurality of pixel units 100 with their prismatic side surfaces facing each other, and placing the pixel light-emitting areas formed by the diffusion sheet 20 on the top surface next to each other. With this configuration, the light from the point light source of the light-emitting element 50 is spread in a planar manner by the diffusion sheet 20, and the planar light-emitting areas formed by the diffusion sheet 20 are placed next to each other, thereby solving the problem of the display surface being uneven in the conventional LED display because the areas between the LEDs are not emitting light. That is, even if the distance between the LEDs is increased, the pixels are made planar light sources and are placed close to each other, reducing the non-light-emitting areas between the pixels as in the conventional display area, and uniform light emission is obtained throughout the display area. As a result, a high-quality display device with uniformity and little dot feeling can be realized even if the number of light-emitting elements used is reduced. In addition, the pixel unit 100 is made prismatic, which provides sufficient strength and has the advantage of not losing its shape even when a large number of pixel units 100 are stacked.
(Reflective structure 10)
　反射構造体１０は、外形を六角柱状又は五角柱状とし、正面側に拡散シート２０を配置している。また反射構造体１０の他方の端縁すなわち底は、底面板２５で閉塞している。この底面板２５の中央部分に開口部ＯＰを形成し、この開口部ＯＰから発光素子５０を反射構造体１０の内部に挿入している。また反射構造体１０の内部は、反射性に優れた色や材質とする。例えば内面を白色とすることで、反射構造体１０の内部の反射率を容易に高めることができる。さらに反射構造体１０の側面は、発光素子の光が透過しないことが望ましい。加えて側面の厚さを薄くすることが望ましい。側面が厚いと、反射板２２で閉塞する際に発光面の外周部に陰が生じるためである。 The reflective structure 10 has a hexagonal or pentagonal prism shape, with a diffusion sheet 20 disposed on the front side. The other edge, i.e., the bottom, of the reflective structure 10 is closed with a bottom plate 25. An opening OP is formed in the center of the bottom plate 25, and the light-emitting element 50 is inserted into the reflective structure 10 through this opening OP. The inside of the reflective structure 10 is made of a color and material with excellent reflectivity. For example, by making the inner surface white, the reflectivity of the inside of the reflective structure 10 can be easily increased. Furthermore, it is desirable that the side surface of the reflective structure 10 does not transmit light from the light-emitting element. In addition, it is desirable to make the thickness of the side surface thin. This is because if the side surface is thick, a shadow will be created on the outer periphery of the light-emitting surface when it is closed with the reflector plate 22.
　このように画素ユニット１００の反射構造体を角柱状に構成すると、画素表示領域である六角形状、五角形状の周辺部、特に頂点の部分の光量低下が低減され、色むらが抑制される。このように、画素表示領域が正方形状では四隅において光が均一に照射されないものの、六角形状や五角形状としたことで隅まで一様に照射させることが可能となる。また画素ユニット１００の反射構造体を角柱状としたことで、図１６の垂直断面図に示すように、内部においても立方体等の構造に比べ、より多く側面で光を反射し、画素内の上層部すなわち画素表示領域に光を充填できる効果が得られる。
（傾斜側面） By configuring the reflective structure of the pixel unit 100 in a prismatic shape in this way, the reduction in the amount of light around the periphery of the hexagonal or pentagonal pixel display region, particularly at the vertices, is reduced, and color unevenness is suppressed. In this way, although light is not uniformly irradiated at the four corners of a square pixel display region, the hexagonal or pentagonal shape makes it possible to irradiate the corners uniformly. In addition, by configuring the reflective structure of the pixel unit 100 in a prismatic shape, as shown in the vertical cross-sectional view of Figure 16, more light is reflected from the side surfaces inside the pixel unit 100 than in a structure such as a cube, and the upper layer of the pixel, i.e., the pixel display region, can be filled with light.
(Sloping side)
　このような六角柱状の画素ユニット１００を用いて、平面状でなく球状の表示装置を構成するため、反射構造体は図１７に示すような側面同士が平行な角柱状でなく、図１８に示すように、ハニカム球の外縁に向かって拡がるように傾斜された傾斜側面としている。具体的には、各第一画素ユニット１００Ａの、六角柱状を構成する側面は、平行でなく、前記球状の外縁に向かって拡がるよう傾斜されている。また各第二画素ユニット１００Ｂの、前記五角柱状を構成する側面は、平行でなく、前記球状の外縁に向かって拡がるよう傾斜されている。側面同士が平行な角柱であれば設計が簡単であるものの、図１７に示すように画素ユニット１００Ｘ同士の間に隙間ＧＰが形成されてしまい、ディスプレイの表示品質が低下する。そこで、図１８に示すように側面を傾斜させて傾斜側面とした六角柱状の画素ユニット１００を用いることで、隙間を無くすことができる。 In order to configure a spherical display device instead of a planar display device using such hexagonal prism pixel units 100, the reflective structure is not a prism with parallel sides as shown in FIG. 17, but has inclined side surfaces that are inclined so as to expand toward the outer edge of the honeycomb sphere as shown in FIG. 18. Specifically, the side surfaces of each first pixel unit 100A that configure the hexagonal prism are not parallel, but are inclined so as to expand toward the outer edge of the sphere. Also, the side surfaces of each second pixel unit 100B that configure the pentagonal prism are not parallel, but are inclined so as to expand toward the outer edge of the sphere. If the side surfaces are parallel prisms, the design is simple, but as shown in FIG. 17, a gap GP is formed between the pixel units 100X, which reduces the display quality of the display. Therefore, by using a hexagonal prism pixel unit 100 with inclined side surfaces as shown in FIG. 18, the gap can be eliminated.
　しかしながら、このような傾斜側面を有する六角柱状の画素ユニット１００の設計は容易でない。単に球面を六角形や五角形で近似すること自体は既に知られている。例えばゴールドバーク多面体は、六角形と五角形の組み合わせで、近似的に平面を球状に配置することができる。しかし、単に六角形と五角形の表面上にＬＥＤ等の発光素子５０を貼り付けると、発光素子５０のドット感が強く表れてしまい、均一な面発光を実現できない。 However, designing a hexagonal prism-shaped pixel unit 100 with such inclined side surfaces is not easy. Simply approximating a spherical surface with a hexagon or pentagon is already known. For example, a Goldberg polyhedron is a combination of hexagons and pentagons, and allows the plane to be arranged approximately in a spherical shape. However, simply attaching light-emitting elements 50 such as LEDs to the surfaces of the hexagons and pentagons results in a strong dot-like appearance of the light-emitting elements 50, making it impossible to achieve uniform surface emission.
　これを回避するために、上述した奥行きのある六角柱状の底面に発光素子５０を配置した画素ユニットを複数用意して、これに五角柱状の画素ユニットを組み合わせて、球状に配置すれば、ドット感を低減した均一な面発光が得られる。しかしながら、奥行きのある六角柱状や五角柱状の画素ユニットを、そのまま球状をなす表面に配置しようとすると、図１７に示したように、各画素ユニット１００Ｘの奥行き方向、すなわち球の半径方向において、隣接する画素ユニット１００Ｘ間で隙間ＧＰが生じてしまう。隙間ＧＰは、奥行き方向の外側に向かうに従って広くなる。画素ユニット１００Ｘ間の隙間があると、画素密度が低下して表示部の解像度が低下し、また外観上の見栄えも悪くなる。 To avoid this, multiple pixel units are prepared in which the light-emitting element 50 is arranged on the bottom surface of the above-mentioned deep hexagonal prism, and then these are combined with pentagonal prism-shaped pixel units and arranged in a spherical shape, resulting in uniform surface emission with reduced dotted appearance. However, if an attempt is made to arrange deep hexagonal or pentagonal prism-shaped pixel units as they are on a spherical surface, as shown in FIG. 17, gaps GP will be generated between adjacent pixel units 100X in the depth direction of each pixel unit 100X, i.e., in the radial direction of the sphere. The gaps GP become wider as they move outward in the depth direction. If there are gaps between pixel units 100X, the pixel density will decrease, the resolution of the display will decrease, and the external appearance will also deteriorate.
　このような隙間の発生を回避するためには、六角柱状や五角柱状の各画素ユニットを共通の形状とせず、図１８に示すように、球面の位置毎に、予め隣接する画素ユニット間の隙間を埋めるように個別に設計した画素ユニット１００を準備する必要がある。しかしながら、球が大きくなるほど、あるいは画素ユニットの数を増やすほど、その設計は困難となる。 In order to avoid the occurrence of such gaps, it is necessary to prepare pixel units 100 that are individually designed in advance to fill the gaps between adjacent pixel units for each position on the sphere, rather than making each hexagonal or pentagonal prism-shaped pixel unit into a common shape, as shown in Figure 18. However, the larger the sphere is, or the more pixel units are added, the more difficult the design becomes.
　そこで本実施形態に係る球状表示装置１０００においては、その設計方法を精査し、特定の領域のみを設計すれば、他の部分はそのコピーで対応できることから、大幅な省力化が見込まれることを見出し、本願発明を成すに至った。これにより画素ユニット１００をハニカム状に配列したハニカム球でＬＥＤディスプレイを構成し、画素ごとに均一な面発光を得ることができる。またこのようなハニカム球の設計工数の削減、製造に必要な画素ユニット１００の組み合わせを最適化できる。その結果、ハニカム球の最適な設計、製造方法を提供できる。加えて、ハニカムＬＥＤディスプレイを球体とすることで、全方向から見えるユニークなデザインのディスプレイを構成できる利点が得られる。 Then, the design method of the spherical display device 1000 according to this embodiment was carefully examined, and it was found that if only a specific area is designed, the other parts can be copied, which is expected to significantly reduce the labor required, leading to the invention of the present application. As a result, an LED display can be constructed using honeycomb spheres in which pixel units 100 are arranged in a honeycomb shape, and uniform surface emission can be obtained for each pixel. It is also possible to reduce the design labor required for such honeycomb spheres, and to optimize the combination of pixel units 100 required for manufacturing. As a result, it is possible to provide an optimal design and manufacturing method for honeycomb spheres. In addition, by making the honeycomb LED display into a sphere, it is possible to obtain the advantage of being able to construct a display with a unique design that can be seen from all directions.
　六角柱の底面の六角形の外接円の直径は、８ｃｍ以上、１６ｃｍ以下とすることが好ましい。六角形の一辺の長さは、４ｃｍから８ｃｍまでとすることが好ましい。また六角柱の高さを、六角形の一辺の長さよりも高くすることが好ましい。これにより、均一な面発光を得ることができる。
（駆動回路） The diameter of the circumscribing circle of the hexagon at the base of the hexagonal prism is preferably 8 cm or more and 16 cm or less. The length of one side of the hexagon is preferably 4 cm to 8 cm. The height of the hexagonal prism is preferably greater than the length of one side of the hexagon. This allows for uniform surface emission.
(Drive circuit)
　各発光素子５０は駆動回路により点灯駆動される。図１９に、各画素ユニット１００を点灯駆動する駆動回路のブロック図を示す。この図に示すように、各発光ユニットの発光素子５０は、コントローラ７０に接続されている。コントローラ７０は、外部の画像ソース等から入力された、あるいは予め設定された、表示領域に表示すべき内容、例えば静止画像や動画像、テキストなどの情報を受け、これに応じて発光させる画素の位置や発光色などを決定し、必要な画素に対して制御を行う。例えば所望の輝度や色度で発光させるよう、赤色ＬＥＤ、緑色ＬＥＤ、青色ＬＥＤの駆動電流量や点灯タイミングを調整する。またこのコントローラ７０は、外部の電源から電力供給を受けて、各画素ユニット１００の発光素子５０に対して必要な駆動電力を供給する。 Each light-emitting element 50 is driven to light by a drive circuit. FIG. 19 shows a block diagram of a drive circuit that drives each pixel unit 100 to light. As shown in this diagram, the light-emitting element 50 of each light-emitting unit is connected to a controller 70. The controller 70 receives information on the content to be displayed in the display area, such as still images, moving images, text, etc., input from an external image source or set in advance, and determines the position of the pixels to be lit and the color of light to be emitted accordingly, and controls the necessary pixels. For example, it adjusts the amount of drive current and the lighting timing of the red LED, green LED, and blue LED so that they emit light with the desired brightness and chromaticity. The controller 70 also receives power from an external power source and supplies the necessary drive power to the light-emitting element 50 of each pixel unit 100.
　なお図１９の例では、各画素ユニット１００を点灯駆動する駆動回路を、共通のコントローラ７０で構成し制御しているが、画素ユニット毎に駆動回路を設けてもよい。あるいはまた、図２０の変形例に示すように、コントローラ７０に外部機器と無線通信するための通信回路７２を付加してもよい。通信回路７２は、外部機器から無線操作で発光素子の点灯を制御できるようにするための部材である。この通信回路７２が外部機器からの無線操作を受け付けるためのワイヤレス接続方式には、電波、マイクロ波、光通信等等が利用できる。電波の場合は、短距離無線、無線ＰＡＮ、無線ＬＡＮ等が利用できる。特にＷｉＦｉやＢｌｕｅｔｏｏｔｈ、ＺｉｇＢｅｅ、６ＬｏＷＰＡＮ、Ｓｕｂ－１ＧＨｚ（いずれも商品名）等の規格化された無線通信とすることで、低コストでの実装や導入が可能となる。特にＢｌｕｅｔｏｏｔｈ　Ｌｏｗ　Ｅｎｅｒｇｙ（ＢＬＥ）等の低消費電力に対応した通信方式とすることが好ましい。また、外部機器として、スマートフォンにアプリをインストールした機器を利用することで、手軽に外部からのＬＥＤ点灯の無線操作が可能となる。さらにＬＥＤ照明用の制御信号として一般的なＤＭ×等の規格化された方式を利用する他、専用の制御信号を利用することもできる。 In the example of FIG. 19, the driving circuit for driving the light-emitting elements 100 is configured and controlled by a common controller 70, but a driving circuit may be provided for each pixel unit. Alternatively, as shown in the modified example of FIG. 20, a communication circuit 72 for wireless communication with an external device may be added to the controller 70. The communication circuit 72 is a member for enabling the external device to control the lighting of the light-emitting elements by wireless operation. The wireless connection method for the communication circuit 72 to receive wireless operation from the external device can be radio waves, microwaves, optical communication, etc. In the case of radio waves, short-distance wireless, wireless PAN, wireless LAN, etc. can be used. In particular, standardized wireless communication such as WiFi, Bluetooth, ZigBee, 6LoWPAN, Sub-1GHz (all product names) can be used to implement and introduce the system at low cost. In particular, it is preferable to use a communication method that supports low power consumption such as Bluetooth Low Energy (BLE). Also, by using a device with an app installed on a smartphone as an external device, it is possible to easily control the lighting of the LED wirelessly from outside. Furthermore, in addition to using standardized methods such as the general DMx as a control signal for LED lighting, it is also possible to use a dedicated control signal.
　加えて、外部機器との通信は、発光素子の点灯を操作する他、表示装置からの情報配信を外部機器側で受けるように構成することもできる。例えば表示装置をゲーム機器のモニタとして利用し、外部機器をコントローラとして操作可能に構成してもよい。例えばオセロゲーム（登録商標）やマインスイーパ（登録商標）等に利用することが可能となる。 In addition, communication with an external device can be configured to control the lighting of the light-emitting elements, as well as to allow the external device to receive information distributed from the display device. For example, the display device can be used as a monitor for a gaming device, and the external device can be operated as a controller. For example, it can be used for games such as Othello (registered trademark) and Minesweeper (registered trademark).
　あるいはまた、表示装置を広告用のＰＯＰなどに利用することもできる。この場合、ｉＯＳのｉＢｅａｃｏｎ（登録商標）やＡｎｄｒｏｉｄＯＳのＥｄｄｙｓｔｏｎｅ（登録商標）などのビーコン技術を用いて情報の配信を行うことも可能である。例えば文字や動画を表示装置で表示させる一方、専用のアプリをインストールしたスマホを持つユーザが近付くと、商品紹介ホームページのＵＲＬやクーポンの配信などを自動的に行うことができる。またクーポンを利用したユーザに対して、専用の特典映像を表示させるなどの表示動作を行わせてもよい。 Alternatively, the display device can be used for POP advertising. In this case, it is also possible to distribute information using beacon technology such as iBeacon (registered trademark) for iOS or Eddystone (registered trademark) for Android OS. For example, while text and video are displayed on the display device, when a user with a smartphone that has a dedicated app installed approaches, the URL of a product introduction homepage or a coupon can be automatically distributed. It is also possible to have the display perform a display operation such as showing a special bonus video to a user who has used a coupon.
　さらに各画素ユニット１００とコントローラ７０との接続は、図１９に示すように並列接続とする他、図２０に示すように数珠繋ぎのデイジーチェーン方式とすることもできる。特にデイジーチェーン方式は、多数の画素ユニットを直列に繋ぐことで、接続台数の制限を受け難く容易に接続数を変更できるので、好ましい。
（球状表示装置の製造方法） Furthermore, the connection between each pixel unit 100 and the controller 70 can be a parallel connection as shown in Fig. 19, or a daisy chain system as shown in Fig. 20. The daisy chain system is particularly preferable because it connects a large number of pixel units in series, making it easy to change the number of connections without being subject to restrictions on the number of units that can be connected.
(Method of manufacturing a spherical display device)
　ここで、球状表示装置の一例として、球状表示部１を構成するハニカム球ディスプレイを製造する手順の一例を、図２１のフローチャートに基づいて以下説明する。まずステップＳ２１０１において、正二十面体の一面（正三角形）を等分に分割する。例えば後述する図２５Ａの正二十面体ＲＩにおいて、各面を構成する正三角形面ＥＴＳ（図２５Ｂ）を、単位正三角形ＵＴに分割する。 Here, as an example of a spherical display device, an example of a procedure for manufacturing a honeycomb spherical display constituting the spherical display unit 1 will be described below with reference to the flowchart in FIG. 21. First, in step S2101, one face (equilateral triangle) of a regular icosahedron is divided into equal parts. For example, in the regular icosahedron RI in FIG. 25A described later, the equilateral triangular surfaces ETS (FIG. 25B) constituting each face are divided into unit equilateral triangles UT.
　次にステップＳ２１０２において、分割した正三角形を球面にマッピングする。この時点で、単位正三角形ＵＴから球面に写像された写像単位正三角形の大きさは、球面上の位置によって異なる大きさとなる。 Next, in step S2102, the divided equilateral triangles are mapped onto the sphere. At this point, the size of the mapped unit equilateral triangle mapped onto the sphere from the unit equilateral triangle UT varies depending on the position on the sphere.
　次にステップＳ２１０３において、得られた写像正三角形面のユニットを回転コピーして、ジオデシック多面体を構成する。 Next, in step S2103, the obtained units of the mapped equilateral triangular surfaces are rotated and copied to form a geodesic polyhedron.
　次にステップＳ２１０４において、ジオデシック多面体の写像単位正三角形の面を基に、六角形の面と五角形の面（正二十面体の頂点）を作成する。 Next, in step S2104, hexagonal and pentagonal faces (vertices of a regular icosahedron) are created based on the faces of the equilateral triangles that are mapping units of the geodesic polyhedron.
　次にステップＳ２１０５において、得られた写像正三角形面のユニットを回転コピーして、ハニカム球を作成する。 Next, in step S2105, the obtained unit of the mapped equilateral triangular surface is rotated and copied to create a honeycomb sphere.
　次にステップＳ２１０６において、得られたユニットに発光素子、反射板２２を取り付けできるようハニカム構造を作成する。 Next, in step S2106, a honeycomb structure is created so that the light-emitting element and reflector 22 can be attached to the obtained unit.
　次にステップＳ２１０７において、作成したハニカム構造を回転コピーして、ハニカム球ディスプレイを作成する。以上のようにして、ハニカム球を得ることができる。 Next, in step S2107, the honeycomb structure that was created is rotated and copied to create a honeycomb sphere display. In this way, a honeycomb sphere can be obtained.
　ここで、作成されたハニカム構造のユニットは３つの部分に分解できる。すなわち二等辺三角形を、三角形の中心で１２０度ずつ回転させた、換言すると３つの二等辺三角形に分解できる。さらに各二等辺三角形は、頂点から底辺に下ろした垂線で直角三角形に分割できる。したがって、直角三角形に相当する画素ユニットを設計すれば、残りはコピーによって得ることができる。このように、ジオデシック多面体のクラスＩ、クラスＩＩにおいては、各部分の対称性によって正三角形の１／６の設計で足り、ハニカム球の設計を簡略化できる。正三角形面ＥＴＳは球面全体で２０面あることから、全体としては１／１２０に設計量を削減できる。一方でクラスＩＩＩにおいては線対称でなく回転対称となるため、正三角形の１／３の設計が必要となり、球面全体では１／６０の設計量削減となる（詳細は後述）。以下、ジオデシック多面体のクラスＩ、クラスＩＩを採用する場合の各手順の詳細を順次説明する。
（ハニカム球の設計） Here, the honeycomb structure unit created can be decomposed into three parts. That is, an isosceles triangle can be decomposed into three isosceles triangles, which are rotated 120 degrees at the center of the triangle. Furthermore, each isosceles triangle can be divided into right-angled triangles by a perpendicular line drawn from the vertex to the base. Therefore, if a pixel unit corresponding to a right-angled triangle is designed, the rest can be obtained by copying. In this way, in classes I and II of geodesic polyhedrons, the design of 1/6 of an equilateral triangle is sufficient due to the symmetry of each part, and the design of the honeycomb sphere can be simplified. Since there are 20 equilateral triangular faces ETS on the entire sphere, the overall design amount can be reduced to 1/120. On the other hand, in class III, since it is rotationally symmetric rather than linearly symmetric, it is necessary to design 1/3 of an equilateral triangle, and the design amount of the entire sphere is reduced to 1/60 (details will be described later). Below, the details of each procedure when using classes I and II of geodesic polyhedrons are explained in order.
(Honeycomb sphere design)
　本実施形態に係る球状表示装置１０００の、球状表示部１は、図２２に示すようにハニカム状の画素ユニット１００を複数組み合わせて構成する。このような球状表示部１をハニカム球と呼ぶ。ここではまず、ハニカムの奥行を考えず、球体の表面のみを多角形で近似することを考える。このような球面の近似としては、ジオデシック多面体やゴールドバーグ多面体が知られている。
（ジオデシック多面体） The spherical display section 1 of the spherical display device 1000 according to this embodiment is configured by combining a plurality of honeycomb-shaped pixel units 100 as shown in Fig. 22. Such a spherical display section 1 is called a honeycomb sphere. First, we consider approximating only the surface of the sphere with polygons, without considering the depth of the honeycomb. Known examples of such approximations of a sphere include the geodesic polyhedron and the Goldberg polyhedron.
(geodesic polyhedron)
　ジオデシック多面体は、三角形から成る球体に近い多面体であり、図２３Ａに示すクラスＩ、図２３Ｂに示すクラスＩＩ、図２３Ｃに示すクラスＩＩＩの３種類が知られている。図２３Ａに示すクラスＩのジオデシック多面体はＧ（６，０）であり、図２３Ｂに示すクラスＩＩはＧ（３，３）であり、図２３Ｃに示すクラスＩＩＩはＧ（５，２）である。
（ジオデシック多面体のクラス定義） Geodesic polyhedrons are polyhedrons that are close to spheres and are made up of triangles, and three types are known: Class I shown in Fig. 23A, Class II shown in Fig. 23B, and Class III shown in Fig. 23C. The geodesic polyhedron of Class I shown in Fig. 23A is G(6,0), that of Class II shown in Fig. 23B is G(3,3), and that of Class III shown in Fig. 23C is G(5,2).
(Class definition of a geodesic polyhedron)
　ここでジオデシック多面体のクラス定義について、図２４Ａ～図２４Ｃに基づいて説明する。各図において、微小な三角形が５個集まった五角形をなす部分を頂点ＡＸという。各ジオデシック多面体はＧ（ｍ，ｎ）で表現される。ここで（ｍ、ｎ）は、頂点ＡＸから頂点ＡＸへの線分の分割数である。また周波数ｖはｖ＝ｍ＋ｎである。ここで周波数とは、三角形の頂点から頂点への線分の数のトータルである。周波数は、ジオデシック多面体の緻密度を示しており、周波数が高いと面数が多くなる。さらに三角形の数ＴはＴ＝ｍ2＋ｍｎ＋ｎ2、｛ｍ＞０かつｎ≧０、又はｍ≧０かつｎ＞０｝である。例えば図２４Ａは、クラスＩのＧ（６，０）のジオデシック多面体を示している。また図２４Ｂは、クラスＩＩのＧ（３，３）を、図２４ＣはクラスＩＩＩのＧ（５，２）を、それぞれ示している。 Here, the class definition of a geodesic polyhedron will be explained based on Fig. 24A to Fig. 24C. In each figure, a pentagonal part formed by five tiny triangles is called vertex AX. Each geodesic polyhedron is expressed by G(m,n). Here, (m,n) is the number of divisions of the line segment from vertex AX to vertex AX. Furthermore, the frequency v is v=m+n. Here, the frequency is the total number of line segments from vertex to vertex of a triangle. The frequency indicates the compactness of the geodesic polyhedron, and the higher the frequency, the greater the number of faces. Furthermore, the number of triangles T is T=m 2 +mn+n 2 , {m>0 and n≧0, or m≧0 and n>0}. For example, Fig. 24A shows a geodesic polyhedron of class I, G(6,0). Fig. 24B shows a geodesic polyhedron of class II, G(3,3), and Fig. 24C shows a geodesic polyhedron of class III, G(5,2).
　このようなジオデシック多面体を設計するには、正二十面体の対称性を利用する。図２５Ａに示すように、正二十面体ＲＩは各面を正三角形とする。この正二十面体ＲＩの特性は、正三角形の面の数が２０面、稜線ＲＬが３０本、頂点ＡＸの数が１２個、各面の頂点数が３個、頂点ＡＸに集まる面の数が５面となる。正二十面体ＲＩの一面を構成する正三角形面ＥＴＳを図２５Ｂに示す。図２５Ａの正二十面体ＲＩ及び図２５Ｂの正三角形面ＥＴＳを用いて、図２５Ｃに示すジオデシック多面体に変換する。具体的には正二十面体ＲＩの各面を構成する正三角形面ＥＴＳを、３６等分した微小な正三角形とする。この微小な正三角形を単位正三角形ＵＴと呼ぶ。この単位正三角形ＵＴを元に、３６×２０＝７２０面の微小な正三角形で球体を構成したジオデシック多面体を得る。なお、ジオデシック多面体を構成する微小な正三角形は、単位正三角形ＵＴとは完全に一致せず、微小な正三角形の大きさは部位によって異なる。したがって、ジオデシック多面体を設計するには、本来的には微小な正三角形を個別に設計する必要がある。
（正三角形面ＥＴＳの分割） To design such a geodesic polyhedron, the symmetry of a regular icosahedron is utilized. As shown in FIG. 25A, each face of the regular icosahedron RI is an equilateral triangle. The characteristics of this regular icosahedron RI are that the number of equilateral triangular faces is 20, the number of ridges RL is 30, the number of vertices AX is 12, the number of vertices of each face is 3, and the number of faces that meet at the vertices AX is 5. The equilateral triangular faces ETS constituting one face of the regular icosahedron RI are shown in FIG. 25B. The regular icosahedron RI in FIG. 25A and the equilateral triangular faces ETS in FIG. 25B are used to convert to a geodesic polyhedron shown in FIG. 25C. Specifically, the equilateral triangular faces ETS constituting each face of the regular icosahedron RI are divided into 36 equal parts into minute equilateral triangles. These minute equilateral triangles are called unit equilateral triangles UT. Based on this unit equilateral triangle UT, a geodesic polyhedron is obtained in which a sphere is constituted by minute equilateral triangles of 36×20=720 faces. In addition, the tiny equilateral triangles that make up a geodesic polyhedron do not completely match the unit equilateral triangle UT, and the size of the tiny equilateral triangles varies depending on the part. Therefore, in order to design a geodesic polyhedron, it is essentially necessary to design the tiny equilateral triangles individually.
(Division of equilateral triangular surface ETS)
　ここで、正三角形面ＥＴＳを規則的に単位正三角形ＵＴに分割する分割方法は、ジオデシック多面体のクラスによって異なる。クラスが変わると、ジオデシック多面体、ひいてはハニカム球の配列も変わる。ここで８ｖの場合に、クラスＩの分割例を図２６Ａ、図２６Ｂに、クラスＩＩの分割例を図２６Ｃ～図２６Ｈに、クラスＩＩＩの分割例を図２６Ｉ～図２６Ｊに、それぞれ示す。図２６Ａは、Ｇ（０，８）、Ｔ＝６４のクラスＩを、図２６ＢはＧ（８，０）、Ｔ＝６４のクラスＩを、それぞれ示している。また図２６ＣはＧ（１，７）、Ｔ＝５７のクラスＩＩを、図２６ＤはＧ（７，１）、Ｔ＝５７のクラスＩＩを、図２６ＥはＧ（２，６）、Ｔ＝５２のクラスＩＩを、図２６ＦはＧ（６，２）、Ｔ＝５２のクラスＩＩを、図２６ＧはＧ（３，５）、Ｔ＝４９のクラスＩＩを、図２６ＨはＧ（５，３）、Ｔ＝４９のクラスＩＩを、それぞれ示している。さらに図２６ＩはＧ（４，４）、Ｔ＝４８のクラスＩＩＩを、図２６ＪはＧ（４，４）、Ｔ＝４８のクラスＩＩＩを、それぞれ示している。図２６Ａ、図２６Ｂに示すように、ジオデシック多面体のクラスＩにおいては、正三角形面ＥＴＳの各辺と、分割された単位正三角形ＵＴの一辺とが合致する。また図２６Ｉ、図２６Ｊに示すように、ジオデシック多面体のクラスＩＩにおいては、正三角形面ＥＴＳの各辺と、分割された単位正三角形ＵＴの一辺とは一致していないものの、単位正三角形ＵＴを二分した直角三角形の一辺（底辺）と合致する。したがって、これらクラスＩ、クラスＩＩにおいては、正三角形面ＥＴＳを構成するすべての単位正三角形ＵＴについて個別に設計を行わなくとも、幾何学図形の対称性を利用して正三角形面ＥＴＳの１／６の設計を行えば、他の部分は反転コピーや回転コピーで埋め合わせが可能であり、全体としてハニカム球の設計を簡略化できる。一方でクラスＩＩＩにおいては、図２６Ｃ～図２６Ｈに示すように、正三角形面ＥＴＳの各辺が、単位正三角形ＵＴの辺と一致しておらず、線対称でもないため、正三角形面ＥＴＳの１／３の設計が必要となる。そこで以下では、設計が容易なジオデシック多面体のクラスＩ、クラスＩＩについて主に検討する。
（ゴールドバーク多面体） Here, the division method for regularly dividing the equilateral triangular surface ETS into unit equilateral triangles UT differs depending on the class of the geodesic polyhedron. When the class changes, the arrangement of the geodesic polyhedron and, in turn, the honeycomb spheres also changes. Here, in the case of 8v, division examples of class I are shown in Figures 26A and 26B, division examples of class II are shown in Figures 26C to 26H, and division examples of class III are shown in Figures 26I to 26J. Figure 26A shows class I with G(0,8) and T=64, and Figure 26B shows class I with G(8,0) and T=64. Also, Fig. 26C shows class II of G(1,7), T=57, Fig. 26D shows class II of G(7,1), T=57, Fig. 26E shows class II of G(2,6), T=52, Fig. 26F shows class II of G(6,2), T=52, Fig. 26G shows class II of G(3,5), T=49, Fig. 26H shows class II of G(5,3), T=49. Furthermore, Fig. 26I shows class III of G(4,4), T=48, Fig. 26J shows class III of G(4,4), T=48. As shown in Figs. 26A and 26B, in class I of the geodesic polyhedron, each side of the equilateral triangular surface ETS coincides with one side of the divided unit equilateral triangle UT. As shown in Figures 26I and 26J, in class II of geodesic polyhedrons, each side of the equilateral triangular surface ETS does not coincide with one side of the divided unit equilateral triangle UT, but coincides with one side (base) of the right triangle obtained by bisecting the unit equilateral triangle UT. Therefore, in these classes I and II, it is not necessary to individually design all the unit equilateral triangles UT constituting the equilateral triangular surface ETS. If 1/6 of the equilateral triangular surface ETS is designed by utilizing the symmetry of the geometric figure, the other parts can be filled in by inverted or rotated copies, and the design of the honeycomb sphere as a whole can be simplified. On the other hand, in class III, as shown in Figures 26C to 26H, each side of the equilateral triangular surface ETS does not coincide with the side of the unit equilateral triangle UT, and it is not line-symmetrical, so it is necessary to design 1/3 of the equilateral triangular surface ETS. Therefore, in the following, we will mainly consider classes I and II of geodesic polyhedrons, which are easy to design.
(Goldberg polyhedron)
　次に、ゴールドバーク多面体について説明する。ゴールドバーグ多面体は、六角形と五角形から成る球体に近い多面体であり、図２７Ａ～図２７Ｃに示すクラスＩ、クラスＩＩ、クラスＩＩＩの３種類が知られている。図２７Ａに示すクラスＩは、ＧＰ（４，０）であり、図２７Ｂに示すクラスＩＩはＧＰ（３，３）であり、図２７Ｃに示すクラスＩＩＩはＧＰ（４，１）である。 Next, we will explain Goldberg polyhedrons. Goldberg polyhedrons are polyhedrons that are close to a sphere and are composed of hexagons and pentagons, and three types are known: Class I, Class II, and Class III, as shown in Figures 27A to 27C. Class I, as shown in Figure 27A, is GP(4,0), Class II, as shown in Figure 27B, is GP(3,3), and Class III, as shown in Figure 27C, is GP(4,1).
　このようなゴールドバーク多面体を設計するには、正二十面体の対称性を利用する。上述の通り図２８Ａに示す正二十面体を、図２８Ｂに示すジオデシック多面体に変換する。さらに、このジオデシック多面体から、単位正三角形ＵＴを６個集めた六角形と、５個集めた五角形でもって、図２８Ｃに示すゴールドバーグ多面体を得る。このようにジオデシック多面体を構成する単位正三角形ＵＴを再構成して、六角形や五角形の面を得ている。例えば図２９Ａに示すクラスＩＩ、Ｇ（３，３）のジオデシック多面体は、図２９Ｂに示すクラスＩ、ＧＰ（３，０）のゴールドバーク多面体に対応する。以降では、ゴールドバーグの多面体を利用して、六角形や五角形の面から奥行きのある六角柱状、五角柱状の画素ユニット１００を組み合わせて、ハニカム球を構成する例について説明する。なお、六角柱状や五角柱状は、側面同士が互いに平行でなく、外周面に向かって若干末広がりとなるように傾斜されている。
（画素ブロック） To design such a Goldberg polyhedron, the symmetry of a regular icosahedron is utilized. As described above, the regular icosahedron shown in FIG. 28A is converted into a geodesic polyhedron shown in FIG. 28B. Furthermore, from this geodesic polyhedron, a hexagon consisting of six unit regular triangles UT and a pentagon consisting of five unit regular triangles UT are used to obtain a Goldberg polyhedron shown in FIG. 28C. In this way, the unit regular triangles UT constituting the geodesic polyhedron are reconstructed to obtain hexagonal and pentagonal faces. For example, the geodesic polyhedron of class II, G(3,3) shown in FIG. 29A corresponds to the Goldberg polyhedron of class I, GP(3,0) shown in FIG. 29B. In the following, an example of constructing a honeycomb sphere by combining pixel units 100 in the form of a hexagonal prism or pentagonal prism with depth from hexagonal or pentagonal faces using Goldberg polyhedrons will be described. Note that the side faces of the hexagonal prism or pentagonal prism are not parallel to each other, but are inclined so as to be slightly flared toward the outer periphery.
(Pixel block)
　ゴールドバーグ多面体は上述の通り正二十面体をベースにしており、正二十面体の各面に相当する一面を図３０に示す。この例では、Ｇ（１２，０）のジオデシック多面体から、ＧＰ（４，４）のゴールドバーク多面体を得た例を示している。このようなゴールドバーグ多面体を構成する一面を、画素ブロックＩＢと呼ぶ。ここでは正二十面体の対称性を利用して、球の全体、すなわち２０面分の画素ブロックＩＢを設計するのでなく、図３０に示すような一の画素ブロックＩＢのみを設計し、他の１９面は複製して対応することができる。なお、画素ブロックＩＢ同士の組み合わせにおいて、重複する一部の画素ユニットは適宜削除してよい。 As mentioned above, the Goldberg polyhedron is based on a regular icosahedron, and one surface corresponding to each face of the regular icosahedron is shown in Figure 30. In this example, a Goldberg polyhedron GP(4,4) is obtained from a geodesic polyhedron G(12,0). A surface that constitutes such a Goldberg polyhedron is called a pixel block IB. Here, the symmetry of the regular icosahedron is used to design only one pixel block IB as shown in Figure 30, rather than designing the entire sphere, i.e., pixel blocks IB for 20 faces, and the other 19 faces can be accommodated by duplicating them. Note that when combining pixel blocks IB, some overlapping pixel units may be deleted as appropriate.
　一の画素ブロックＩＢを構成する六角柱状、五角柱状から、正二十面体の対称性を利用して、固有の図形を抽出する。図３０の画素ブロックＩＢは、３１個の画素ユニット１００で構成される。これら３１個の画素ユニット１００の形状は、概ね正三角形状の画素ブロックＩＢが回転対称であり、重心を回転中心として１２０°ずつ回転させると重なることから、画素ブロックＩＢの中心と各頂点とを結ぶ線分でそれぞれ分割した、３つの二等辺三角形ブロックＩＴＢに分解できる。さらに各二等辺三角形ブロックＩＴＢは、左右対称である。このことから、二等辺三角形ブロックＩＴＢを、頂点から底辺の中間に伸ばした垂線で二分割した直角三角形ブロックＲＴＢに分解できる。このようにして得られた直角三角形ブロックＲＴＢについて、画素ユニット１００を設計すれば、残りはこの直角三角形ブロックＲＴＢのデータを変形することで対応できる。すなわち、二等辺三角形ブロックＩＴＢについては、直角三角形ブロックＲＴＢと、これを反転させた反転直角三角形ブロックＲＴＢとを、高さに相当する対辺同士で接合することで得られる。また画素ブロックＩＢについては、二等辺三角形ブロックＩＴＢを、頂点を中心に１２０°ずつ回転させた、計３枚の二等辺三角形ブロックＩＴＢ同士を接合することで得られる。このようにすれば、正三角形状の画素ブロックＩＢの内、これを１／３の二等辺三角形ブロックＩＴＢ二分割し、さらに１／２の直角三角形ブロックＲＴＢに分割した、画素ブロックＩＢの１／６に当たる領域についてのみ、設計すれば足りることになる。また得られた画素ブロックＩＢを２０面分作成すれば、球状表示部１を構成できる。このように、球面全体の１／２０の１／６、すなわち１／１２０の領域についてのみ、画素ユニット１００を設計することで球面を構成でき、従来面倒であった、六角柱状と五角柱状の画素ユニット１００を組み合わせた球状表示装置１０００の設計を、大幅に省力化することが可能となる。以下、球状表示装置１０００の製造方法の詳細を説明する。
（ハニカム球に必要な画素ユニット数）
［実施形態１］ A unique figure is extracted from the hexagonal prism and pentagonal prism constituting one pixel block IB by utilizing the symmetry of a regular icosahedron. The pixel block IB in FIG. 30 is composed of 31 pixel units 100. The shape of these 31 pixel units 100 is rotationally symmetrical with the pixel block IB being roughly equilateral triangular, and overlaps when rotated 120° around the center of gravity. Therefore, it can be decomposed into three isosceles triangular blocks ITB, each divided by a line segment connecting the center of the pixel block IB to each vertex. Furthermore, each isosceles triangular block ITB is bilaterally symmetric. For this reason, the isosceles triangular block ITB can be decomposed into right-angled triangular blocks RTB, which are bisected by a perpendicular line extending from the vertex to the middle of the base. If the pixel unit 100 is designed for the right-angled triangular block RTB obtained in this way, the rest can be handled by modifying the data of this right-angled triangular block RTB. That is, the isosceles triangular block ITB is obtained by joining the opposite sides corresponding to the height of the right-angled triangular block RTB and the inverted right-angled triangular block RTB. The pixel block IB is obtained by joining three isosceles triangular blocks ITB, each rotated 120° around the apex. In this way, it is sufficient to design only the area of the equilateral triangular pixel block IB, which is obtained by dividing the equilateral triangular pixel block IB into two isosceles triangular blocks ITB, which are 1/3 of the pixel block IB, and further dividing the equilateral triangular pixel block IB into two right-angled triangular blocks RTB. The spherical display unit 1 can be constructed by creating 20 faces of the obtained pixel blocks IB. In this way, a spherical surface can be constructed by designing pixel units 100 only for an area of 1/6 of 1/20 of the entire spherical surface, i.e., 1/120, and this makes it possible to significantly reduce the labor required for designing a spherical display device 1000 that combines hexagonal prism-shaped and pentagonal prism-shaped pixel units 100, which was previously troublesome. A manufacturing method for the spherical display device 1000 will be described in detail below.
(Number of pixel units required for a honeycomb sphere)
[Embodiment 1]
　まず、ハニカム球を構成するために必要となる画素ユニット数を説明する。ここでは実施形態１に係る球状表示装置として、Ｇ（１２，０）のジオデシック多面体から、ＧＰ（４，４）のゴールドバーク多面体を得た場合に、必要となる画素ユニット数を説明する。このときの画素ブロックＩＢは、上述した図３０のようになる。換言すると、球全体を設計するのでなく、ゴールドバーク多面体の一面のみを設計すれば足りる。この図において、画素ブロックＩＢの対称性を利用して、固有の図形を抽出する。図３０の画素ブロックＩＢは１２ｖであり、３１個の画素ユニットで構成される。この場合は、図３０においてＩＵ１～ＩＵ１０で示すとおり、１０種類の画素ユニットが使用されている。 First, the number of pixel units required to form a honeycomb sphere will be explained. Here, the number of pixel units required will be explained when a Goldberg polyhedron GP(4,4) is obtained from a geodesic polyhedron G(12,0) as a spherical display device according to embodiment 1. The pixel block IB in this case will be as shown in FIG. 30 above. In other words, it is sufficient to design only one surface of the Goldberg polyhedron, rather than the entire sphere. In this figure, a unique shape is extracted by utilizing the symmetry of the pixel block IB. The pixel block IB in FIG. 30 is 12v, and is composed of 31 pixel units. In this case, 10 types of pixel units are used, as shown by IU1 to IU10 in FIG. 30.
　これら１０種類の画素ユニットが、ゴールドバーク多面体の全体でそれぞれ何個必要になるかを、以下説明する。まずＩＵ１の五角形状の画素ユニット（第二画素ユニット１００Ｂ）は、ゴールドバーク多面体の頂点ＡＸにそれぞれ１個配置するため、頂点ＡＸの数だけ、すなわち１２個必要となる。 The following explains how many of each of these 10 types of pixel units are required for the entire Goldberg polyhedron. First, the pentagonal pixel unit of IU1 (second pixel unit 100B) is placed at each vertex AX of the Goldberg polyhedron, so the number of pentagonal pixel units required is the number of vertices AX, i.e. 12.
　またＩＵ２、３、４、７、８、１０の画素ユニットは、画素ブロックＩＢを構成する３つの二等辺三角形ブロックＩＴＢに、それぞれ１個ずつ存在する。したがって二等辺三角形ブロックＩＴＢ毎に１個であるから、各画素ブロックＩＢでは３個必要となり、６種類×３個＝１８個必要となる。これが画素ブロックＩＢ２０面分必要となるため、１８個×２０面＝３６０個必要となる。 Furthermore, pixel units IU2, 3, 4, 7, 8, and 10 exist in each of the three isosceles triangular blocks ITB that make up pixel block IB, one for each isosceles triangular block ITB, so three are required for each pixel block IB, for a total of 6 types x 3 = 18 units. This is needed for 20 faces of pixel block IB, so 18 units x 20 faces = 360 units are needed.
　さらにまたＩＵ５の画素ユニットは、画素ブロックＩＢの中心に位置するため画素ブロックＩＢ毎に１個となり、２０面分で２０個必要となる。 Furthermore, since the pixel unit of IU5 is located at the center of the pixel block IB, there is one for each pixel block IB, so 20 units are required for 20 faces.
　またＩＵ６の画素ユニットは、二等辺三角形ブロックＩＴＢで２個存在する。ここでＩＵ６の画素ユニットは、正二十面体を構成する稜線ＲＬ上にのみ存在するため、画素ブロックＩＢ同士を組み合わせる際の重複に留意する必要がある。正二十面体を構成する稜線ＲＬの数は、上述の通り３０本であるから、ＩＵ６の画素ユニットは２個×３０本＝６０個が必要となる。 Furthermore, there are two pixel units of IU6 in the isosceles triangular block ITB. Here, since the pixel units of IU6 exist only on the edges RL that make up the regular icosahedron, care must be taken to avoid overlaps when combining pixel blocks IB. As mentioned above, there are 30 edges RL that make up the regular icosahedron, so 2 x 30 = 60 pixel units of IU6 are required.
　同様にＩＵ９の画素ユニットは、稜線ＲＬの中央に存在するので、稜線３０本分、すなわち３０個必要となる。 Similarly, the pixel unit of IU9 is located in the center of edge line RL, so 30 units are required, for 30 edges.
　以上から、球状表示部１を構成するために必要な画素ユニットの数は、１２＋３６０＋２０＋６０＋３０＝４８２となり、トータルで４８２個となる。また、ＩＵ２、ＩＵ３、ＩＵ４、ＩＵ７、ＩＵ８、ＩＵ１０はまとめて作成可能となる。
［実施形態２］ From the above, the number of pixel units required to configure spherical display unit 1 is 12+360+20+60+30=482, which is a total of 482. In addition, IU2, IU3, IU4, IU7, IU8, and IU10 can be created collectively.
[Embodiment 2]
　以上の実施形態１では、Ｇ（１２，０）のジオデシック多面体から、ＧＰ（４，４）のゴールドバーク多面体を得た場合に必要となる画素ユニット数を説明した。画素ユニットの数は、ジオデシック多面体を構成する三角形のサイズ、すなわちゴールドバーク多面体の六角形や五角形の大きさによって変化する。例えば実施形態２に係る球状表示装置として、Ｇ（１８，０）のジオデシック多面体から、ＧＰ（６，６）のゴールドバーク多面体を得る場合を検討する。この画素ブロックＩＢは、図３１に示すようになり、必要となる画素ユニット数は図３０と異なる。正二十面体の特性については図３０と同じで、面の数は２０面、頂点ＡＸの数は１２個、稜線ＲＬの数は３０本、面の頂点数は３個、頂点ＡＸに集まる面の数は５面である。一方で、図３１に示す画素ブロックＩＢを構成する正三角形に含まれる六角柱状の画素ユニットの数は、４６個である。したがって球状表示部１の全体、すなわち２０面分では４６個×２０面＝９２０個となる。なお、図３０の画素ブロックＩＢでは、９種類の画素ユニットが含まれているところ、図３１の画素ブロックＩＢでは１６種類の画素ユニットが含まれている。 In the above embodiment 1, the number of pixel units required when a Goldberg polyhedron of GP(4,4) is obtained from a geodesic polyhedron of G(12,0) has been described. The number of pixel units varies depending on the size of the triangles constituting the geodesic polyhedron, i.e., the size of the hexagons and pentagons of the Goldberg polyhedron. For example, as a spherical display device according to embodiment 2, a case where a Goldberg polyhedron of GP(6,6) is obtained from a geodesic polyhedron of G(18,0) is considered. This pixel block IB is as shown in FIG. 31, and the number of pixel units required is different from that in FIG. 30. The characteristics of the regular icosahedron are the same as those in FIG. 30, with 20 faces, 12 vertices AX, 30 edges RL, 3 vertices on each face, and 5 faces gathering at the vertices AX. On the other hand, the number of hexagonal prism-shaped pixel units included in the equilateral triangle constituting the pixel block IB shown in FIG. 31 is 46. Therefore, for the entire spherical display unit 1, i.e., 20 surfaces, there are 46 pixels x 20 surfaces = 920 pixels. Note that while pixel block IB in FIG. 30 contains 9 types of pixel units, pixel block IB in FIG. 31 contains 16 types of pixel units.
　また五角柱状の画素ユニットの数は、同じくゴールドバーク多面体の各頂点ＡＸである１２の位置に位置することから、１２個となる。さらに稜線ＲＬ上に位置する六角柱状の画素ユニットの数は５個であり、ゴールドバーク多面体では稜線ＲＬが３０本であることから、５個×３０本＝１５０個となる。したがって、９２０＋１２＋１５０＝１０８２となり、全２０種類の画素ユニットが球状表示部１の全体で計１０８２個必要となる。その内訳は、ＩＵ０７が２０個である。またＩＵ０２、ＩＵ０３、ＩＵ０４、ＩＵ０５、ＩＵ０６、ＩＵ０９、ＩＵ１０、ＩＵ１１、ＩＵ１２、ＩＵ１４、ＩＵ１５、ＩＵ１６、ＩＵ１８、ＩＵ１９、ＩＵ２０の１５個の画素ユニットについては、それぞれ二等辺三角形ブロックＩＴＢに１個ずつ、すなわち各画素ブロックＩＢに計３個使用されており、２０面では１５個×３×２０個＝９００個となる。さらにまたＩＵ０１はゴールドバーク多面体の頂点ＡＸにそれぞれ位置するため、１２個必要となる。加えて、ＩＵ０８とＩＵ１３は各稜線ＲＬ上に２個存在し、ゴールドバーク多面体の稜線ＲＬは３０本であるから、２×２個×３０本＝１２０個、一方ＩＵ１６は稜線ＲＬの中間に位置することから、３０個必要となる。
［実施形態３］ The number of pentagonal prism-shaped pixel units is 12, since they are located at 12 positions, which are also the vertices AX of the Goldberg polyhedron. Furthermore, the number of hexagonal prism-shaped pixel units located on the edge line RL is 5, and since the Goldberg polyhedron has 30 edge lines RL, the total number is 5 x 30 = 150. Therefore, the total is 920 + 12 + 150 = 1082, and a total of 1082 pixel units of all 20 types are required for the entire spherical display section 1. This includes 20 IU07s. In addition, for the 15 pixel units IU02, IU03, IU04, IU05, IU06, IU09, IU10, IU11, IU12, IU14, IU15, IU16, IU18, IU19, and IU20, one is used for each isosceles triangular block ITB, i.e., a total of three are used for each pixel block IB, so for 20 faces, 15 units x 3 x 20 units = 900 units are required. Furthermore, since IU01 is located at each vertex AX of the Goldberg polyhedron, 12 units are required. In addition, since two units of IU08 and IU13 exist on each edge line RL, and the Goldberg polyhedron has 30 edges RL, 2 x 2 units x 30 units = 120 units are required, while IU16 is located in the middle of the edges RL, so 30 units are required.
[Embodiment 3]
　さらに実施形態３に係る球状表示装置として、Ｇ（１０，１０）のジオデシック多面体からＧＰ（１０，０）のゴールドバーク多面体に必要となる画素ユニット数を検討する。この画素ブロックＩＢは、図３２に示すようになり、必要となる画素ユニット数は図３０や図３１と異なり、３６個である。したがって球状表示部１の全体、すなわち２０面分では３６個×２０面＝７２０個となる。頂点ＡＸは、１２個、稜線ＲＬは、９個ｘ３０本＝２７０個となる。以上から、球状表示部１を構成するために必要な画素ユニットの数は、７２０＋１２＋２７０＝１００２となり、トータルで１００２個となる。なお図３２の画素ブロックＩＢでは、２２種類の画素ユニットが含まれている。 Furthermore, for the spherical display device according to the third embodiment, the number of pixel units required for the geodesic polyhedron G(10,10) to the Goldberg polyhedron GP(10,0) will be considered. This pixel block IB is as shown in FIG. 32, and the number of pixel units required is 36, which is different from that in FIG. 30 and FIG. 31. Therefore, the total number of pixel units required for the entire spherical display section 1, i.e., 20 faces, is 36 units x 20 faces = 720 units. There are 12 vertices AX, and 9 units x 30 lines RL = 270 units. From the above, the number of pixel units required to configure the spherical display section 1 is 720 + 12 + 270 = 1002, which is a total of 1002 units. Note that the pixel block IB in FIG. 32 contains 22 types of pixel units.
　次に、ジオデシック多面体Ｇ（ｍ，ｎ）の設計方法について、図３３のフローチャートに基づいて説明する。ここでは、三次元設計ＣＡＤ、例えばオートデスク社のＦｕｓｉｏｎ３６０（商品名）を利用して設計を行う。 Next, a method for designing a geodesic polyhedron G(m,n) will be explained based on the flowchart in Figure 33. Here, the design is carried out using a three-dimensional design CAD, for example Fusion 360 (product name) by Autodesk.
　まずステップＳ３３０１において、設計するゴールドバーグ多面体ＧＰ（ｍ，ｎ）を決定する。次にステップＳ３３０２において、ゴールドバーク多面体に基づいて、設計するジオデシック多面体Ｇ（ｍ，ｎ）を決定する。ここでは、ＧＰ（ｍ，ｎ）からＧ（ｍ，ｎ）を構成できるかを確認する。
（等角図の設計） First, in step S3301, a Goldberg polyhedron GP(m,n) to be designed is determined. Next, in step S3302, a geodesic polyhedron G(m,n) to be designed is determined based on the Goldberg polyhedron. Here, it is confirmed whether G(m,n) can be constructed from GP(m,n).
(Isometric design)
　次にステップＳ３３０３において、ジオデシック多面体を構成する単位正三角形ＵＴの一辺の長さＬから、等角図の三角形の一辺を求める。ここでは、次式を使用する。 Next, in step S3303, one side of the triangle in the isometric view is found from the length L of one side of the unit equilateral triangle UT that constitutes the geodesic polyhedron. Here, the following formula is used.
　　（表１）
Ｌ＝ｓｑｒｔ（ｍ＊ｍ＋ｎ＊ｎ＋ｍ＊ｎ）×ａ (Table 1)
L = sqrt(m*m+n*n+m*n) x a
　等角図により、図３４に示すようにすべてのクラスの設計が可能となる。図３４において、等角図の正三角形の一辺＝ａ；高さ＝ｈとする。
ベクトルの長さ｜Ｌ｜＝ｓｑｒｔ（ｘ2＋ｙ2＋ｘｙ）
ｓｑｒｔ（ｘ2＋ｙ2＋２ｘｙｃｏｓ１２０°）
ｃｏｓ１２０°＝０．５ The isometric view allows the design of all classes as shown in Fig. 34. In Fig. 34, one side of the equilateral triangle in the isometric view = a; height = h.
Vector length |L| = sqrt( x2 + y2 + xy)
sqrt( x2 + y2 + 2xycos120°)
cos120°=0.5
　例えばＧ（１２，６）の場合、
Ｌ＝ｓｑｒｔ（１４４ａ2＋３６ａ2＋７２ａ2）
＝ｓｑｒｔ（２５２）ａ
ａ＝Ｌ／ｓｑｒｔ（２５２）
（パラメータの設定） For example, in the case of G(12,6),
L = sqrt( 144a2 + 36a2 + 72a2 )
= sqrt(252)a
a = L / sqrt (252)
(Parameter setting)
　そしてステップＳ３３０４において、パラメータを設定する。ここで設定するジオデシック多面体Ｇ（ｍ，ｎ）の設計に必要なパラメータとしては、以下のようなものが挙げられる。
ジオデシック多面体のｍ：ｇｍ［ｎｏ　ｕｎｉｔ］
ジオデシック多面体のｎ：ｇｎ［ｎｏ　ｕｎｉｔ］
球の直径ｄ［ｍｍ］
球の半径ｒｕ＝ｄ／２［ｍｍ］
正二十面体を成す正三角形の一辺Ｌ＝ｒｕ／０．９５１０５６５１６３［ｍｍ］
等角図の正三角形の一辺ａ＝Ｌ／ｓｑｒｔ（ｇｍ＊ｇｍ＋ｇｎ＊ｇｎ＋ｇｍ＊ｇｎ）［ｍｍ］
等角図の正三角形の高さｈ＝ａ＊ｓｑｒｔ（３）／２［ｍｍ］ Then, in step S3304, parameters are set. The parameters required for designing the geodesic polyhedron G(m, n) to be set here include the following:
m of a geodesic polyhedron: gm [no unit]
n of a geodesic polyhedron: gn [no unit]
Ball diameter d [mm]
Radius of the sphere ru = d/2 [mm]
One side of the equilateral triangle that forms a regular icosahedron L = ru/0.9510565163 [mm]
Side a of an equilateral triangle in an isometric view = L/sqrt(gm*gm+gn*gn+gm*gn) [mm]
Height of equilateral triangle in isometric view h = a * sqrt(3) / 2 [mm]
　このようにして得たパラメータを、三次元設計ＣＡＤに入力する。そして、等角図を作成する。例えば、図３５に示すように正三角形を、原点Ｏに頂点を一致させて描画する。さらに、この正三角形を水平方向に繰り返していく。例えば図３６に示すように、右方向に順次コピーしていく。さらに図３７に示すように、斜辺が一直線状となるように、頂点同士を重ねて積み上げる。そして同様に、この正三角形を水平方向に繰り返していく。例えば図３８に示すように、右方向に順次コピーしていく。さらに、得られた三角形の集合を行単位でコピーしていく。例えば図３９に示すように、三角形を２行分コピーして、斜辺が一直線状となるように積み上げていく。このようにして、図４０に示すような等角図ができあがる。 The parameters obtained in this way are input into a three-dimensional design CAD. An isometric drawing is then created. For example, as shown in Figure 35, an equilateral triangle is drawn with its apex coinciding with the origin O. This equilateral triangle is then repeated horizontally. For example, as shown in Figure 36, it is copied successively to the right. Furthermore, as shown in Figure 37, the apexes are stacked on top of each other so that the hypotenuse forms a straight line. Similarly, this equilateral triangle is then repeated horizontally. For example, as shown in Figure 38, it is copied successively to the right. Furthermore, the set of triangles obtained is copied row by row. For example, as shown in Figure 39, two rows of triangles are copied and stacked so that the hypotenuse forms a straight line. In this way, an isometric drawing such as that shown in Figure 40 is created.
　なお、等角図は上述のように新たに作成する他、テンプレートや書式として予め準備したものを利用してもよい。また、既に作成した等角図データを用いて、正三角形の大きさを変更する等、修正して使用してもよい。
（単位正三角形ＵＴの描画） In addition to creating an isometric drawing from scratch as described above, a template or format that has been prepared in advance may be used. Also, the isometric drawing data that has already been created may be used after modification, such as changing the size of the equilateral triangle.
(Drawing the unit equilateral triangle UT)
　次に、ステップＳ３３０５において、正二十面体を構成する単位正三角形ＵＴを描画する。ここでは、作成済みの等角図データのＸ－Ｙ平面上に、三次元設計ＣＡＤのスケッチ作成機能などを利用して、図４１に示すようにベクトルｍ、ｎの線を引く。そして図４２に示すように正三角形を線で描く。ここでは、一辺が縦軸（Ｘ軸）と一致するように正三角形を配置する。 Next, in step S3305, the unit equilateral triangle UT that constitutes the regular icosahedron is drawn. Here, vectors m and n are drawn on the XY plane of the created isometric drawing data using the sketch creation function of the 3D design CAD, as shown in Figure 41. Then, an equilateral triangle is drawn with lines, as shown in Figure 42. Here, the equilateral triangle is positioned so that one side coincides with the vertical axis (X-axis).
　次に、ステップＳ３３０６において、正三角形内に離散点ＤＰを配置する。ここでは図４２の正三角形に対し、各頂点と中心点を結んだ線分を描いて二等辺三角形を作成し、さらに二等辺角形を、頂点から底辺に下ろした垂線で二等分した直角三角形を得る。そして図４３に示すように、この直角三角形に離散点ＤＰを打つ。各離散点ＤＰは、等角図の頂点毎に打つ。三角形の対称性を利用することで、この直角三角形のパターンを反転、複製すれば、正三角形のすべての領域を設定できる（詳細は後述）。 Next, in step S3306, discrete points DP are placed within the equilateral triangle. Here, for the equilateral triangle in Figure 42, line segments are drawn connecting each vertex and the center point to create an isosceles triangle, and the isosceles triangle is then bisected by a perpendicular line drawn from the vertex to the base to obtain a right-angled triangle. Then, as shown in Figure 43, discrete points DP are placed on this right-angled triangle. Each discrete point DP is placed at each vertex of the isometric drawing. By taking advantage of the symmetry of the triangle, the pattern of this right-angled triangle can be inverted and duplicated to set the entire area of the equilateral triangle (details will be given later).
　さらにステップＳ３３０７において、離散点ＤＰに垂線を引く。ここでは図４３に示す離散点ＤＰを打った三角形を描画したＸ－Ｙ平面に対し、図４４に示すようにＹ－Ｚ平面を表示させる。そして正三角形の中心から垂線を引く。垂線の長さは、ここでは球体の半径（ｒｕ）としているが、これに限られず適当な長さとできる。 Furthermore, in step S3307, a perpendicular line is drawn to the discrete point DP. Here, a YZ plane is displayed as shown in FIG. 44 in comparison with the XY plane on which the triangle with the discrete points DP shown in FIG. 43 is drawn. A perpendicular line is then drawn from the center of the equilateral triangle. Here, the length of the perpendicular line is the radius of the sphere (ru), but it is not limited to this and can be any suitable length.
　さらにステップＳ３３０８において、正三角形の頂点から半径（ｒｕ）の線を引く。ここでは図４５に示すように、正三角形の頂点の一（図において右側）から垂線に線を引き、この線分の長さを半径（ｒｕ）とする。そして垂線と半径（ｒｕ）の線分の交差点を、球体の中心（Ｏ）とする。同様に、三角形の頂点の内、残り２個の頂点からもそれぞれ交差点に半径（ｒｕ）の線分を引く。 Furthermore, in step S3308, a line of radius (ru) is drawn from the vertices of the equilateral triangle. Here, as shown in FIG. 45, a perpendicular line is drawn from one of the vertices of the equilateral triangle (the right side in the figure), and the length of this line segment is set to the radius (ru). The intersection point of the perpendicular line and the line segment of the radius (ru) is set to the center (O) of the sphere. Similarly, line segments of radius (ru) are drawn from each of the remaining two vertices of the triangle to their respective intersection points.
　さらにステップＳ３３０９において、正三角形内の離散点ＤＰから中心（Ｏ）に補助線を引く。ここでは図４６に示すように、各離散点ＤＰからそれぞれ、中心（Ｏ）に補助線を引いていく。Ｆｕｓｉｏｎ３６０（商品名）においては、カーソルが点上に来たとき口になることを確認しながら引く。 Furthermore, in step S3309, auxiliary lines are drawn from the discrete points DP within the equilateral triangle to the center (O). Here, as shown in FIG. 46, auxiliary lines are drawn from each discrete point DP to the center (O). In Fusion360 (product name), the lines are drawn while checking that when the cursor is over the points, it forms a mouth.
　さらにステップＳ３３１０において、中心（Ｏ）から各点線上に実線を引く。ここでは図４７に示すように、中心（Ｏ）からすべての補助線上に実線を引く。ここでは中心（Ｏ）と点は結ばず、途中までの実線となる。また長さは任意となる。Ｆｕｓｉｏｎ３６０（商品名）では、カーソルが中心（Ｏ）では口となり、線上では×となる状態で線を引く。また垂線は選択して「補助線」とした後に線を引く。なお線が重なる箇所は、適宜座標系の表示を回転させるなどして向きを変えて作業を行う。 Furthermore, in step S3310, a solid line is drawn from the center (O) onto each dotted line. Here, as shown in FIG. 47, a solid line is drawn from the center (O) onto all auxiliary lines. Here, the center (O) and the dots are not connected, but the solid line goes partway through. The length can be arbitrary. In Fusion360 (product name), the line is drawn with the cursor becoming a mouth at the center (O) and an x on the line. Perpendicular lines are also selected and set as "auxiliary lines" before the line is drawn. Note that where the lines overlap, the direction is changed by rotating the coordinate system display as appropriate before performing the work.
　さらにステップＳ３３１１において、すべての実線を半径（ｒｕ）とする。ここでは図４８に示すように、中心（Ｏ）から引いたすべての実線を半径（ｒｕ）とする。Ｆｕｓｉｏｎ３６０（商品名）では、実線上にカーソルを合わせると「太い青線」になる。これによって図４８の状態から図４９に示すように、三角形内の各離散点ＤＰが、中心（Ｏ）から半径（ｒｕ）となる。このようにして、図５０に示すように正三角形上の各離散点ＤＰが半径（ｒｕ）の球面上にマッピングされた状態が得られる。 Furthermore, in step S3311, all solid lines are set to a radius (ru). Here, as shown in FIG. 48, all solid lines drawn from the center (O) are set to a radius (ru). In Fusion360 (product name), when the cursor is placed on a solid line, it becomes a "thick blue line." As a result, from the state in FIG. 48, as shown in FIG. 49, each discrete point DP within the triangle becomes a radius (ru) from the center (O). In this way, a state is obtained in which each discrete point DP on an equilateral triangle is mapped onto a sphere of radius (ru), as shown in FIG. 50.
　さらにステップＳ３３１２において、球面上に微小正三角形を作成する。ここでは図５１に示すように、線の先端同士を線で結び、球面上に三角形を作成する。なお図５０において球面状にマッピングする際に放射状となる結果、正三角形の中心から頂点に向かって、微小三角形のサイズが小さくなる。線が引きやすいように、線の重なりがないように、座標系の表示角度などの向きを適宜調整して作業を行う。Ｆｕｓｉｏｎ３６０（商品名）では、線の先端でカーソルが口になることを確認しながら引く。三角形が正しくつながれば「薄い青色」に変わる。例えばｓｋｅｔｃｈ１（座標）は非表示に設定してもよい。このようにして図５２に示すような、直角三角形内の離散点ＤＰから延長された位置に、微小正三角形が得られる。
（直角三角錐の作成） Further, in step S3312, a minute equilateral triangle is created on the sphere. Here, as shown in FIG. 51, the tips of the lines are connected with a line to create a triangle on the sphere. Note that as a result of the radial shape when mapping on a sphere in FIG. 50, the size of the minute triangle becomes smaller from the center of the equilateral triangle to the apex. To make it easier to draw lines and to avoid overlapping of lines, the direction of the display angle of the coordinate system and the like are appropriately adjusted. In Fusion360 (product name), the line is drawn while checking that the cursor becomes a mouth at the tip of the line. If the triangle is connected correctly, it turns to "light blue". For example, sketch1 (coordinate) may be set to hidden. In this way, a minute equilateral triangle is obtained at a position extended from a discrete point DP in a right-angled triangle as shown in FIG. 52.
(Creating a right-angled pyramid)
　さらにステップＳ３３１３において、微小正三角形の面を作成する。ここでは図５３に示すように、パッチにより微小正三角形を埋める面を作成していく。Ｆｕｓｉｏｎ３６０（商品名）では、Ｓｕｒｆａｃｅモードに変更し、Ｃｒｅａｔｅ→Ｐａｔｃｈを選択する。そして表面の三角形をすべてパッチする。この結果、ＰｒｏｆｉｌｅＮＮと表示され、黄土色になる。また側面領域もすべて選択してパッチにより面を作成する。この結果、図５４に示す図形が得られる。このようにして、図５５、図５６に示すような、二等辺三角形を二分した直角三角形状を底面とする三角錐状のブロック、すなわち直角三角錐ＲＴＰが得られる。以降は、この直角三角錐ＲＴＰをコピーして、球面を構成していく。 Furthermore, in step S3313, the surface of a tiny equilateral triangle is created. Here, as shown in Figure 53, a surface that fills the tiny equilateral triangle is created by patching. In Fusion360 (product name), change to Surface mode and select Create → Patch. Then patch all the triangles on the surface. As a result, ProfileNN is displayed and turns ochre. All the side areas are also selected and surfaces are created by patching. As a result, the shape shown in Figure 54 is obtained. In this way, a triangular pyramid block with a right-angled triangular base formed by bisecting an isosceles triangle, that is, a right-angled triangular pyramid RTP, is obtained, as shown in Figures 55 and 56. Thereafter, this right-angled triangular pyramid RTP is copied to construct a spherical surface.
　まずステップＳ３３１４において、直角三角錐ＲＴＰから二等辺三角錐ＩＴＰを得る。具体的には、直角三角錐ＲＴＰを反転コピーして接合する。例えばＦｕｓｉｏｎ３６０（商品名）で直角三角錐ＲＴＰをドラッグしてすべて選択し、Ｓｕｒｆａｃｅモード→Ｃｒｅａｔｅ→ＭｉｒｒｏｒによりＭｉｒｒｏｒＰｌａｎｅを表示させ、側面を選択してＯＫをクリックする。このようにして図５７に示すように、底面を二等辺三角形状とするブロック、すなわち二等辺三角錐ＩＴＰが得られる。
（正三角錐ＥＴＰ） First, in step S3314, an isosceles triangular pyramid ITP is obtained from a right-angled triangular pyramid RTP. Specifically, the right-angled triangular pyramid RTP is inverted and copied and joined. For example, in Fusion360 (product name), drag the right-angled triangular pyramid RTP to select all of them, display the MirrorPlane by Surface mode → Create → Mirror, select the side, and click OK. In this way, as shown in FIG. 57, a block with an isosceles triangular base, that is, an isosceles triangular pyramid ITP, is obtained.
(Regular triangular pyramid ETP)
　次にステップＳ３３１５において、二等辺三角錐ＩＴＰから正三角錐ＥＴＰを得る。具体的には二等辺三角錐ＩＴＰを１２０°ずつ回転コピーして３つの二等辺三角錐ＩＴＰを接合する。例えばＦｕｓｉｏｎ３６０（商品名）では、二等辺三角錐ＩＴＰをドラッグしてすべて選択し、Ｓｕｒｆａｃｅモード→Ｃｒｅａｔｅ→Ｐａｔｔｅｒｎ→Ｃｉｒｃｕｌａｒ　Ｐａｔｔｅｒｎを選択し、Ａ×ｉｓで中心の線（垂線）をクリックし、Ｑｕａｎｔｉｔｙを３とする。このようにして図５８に示すように、底面を正三角形状とするブロック、すなわち正三角錐ＥＴＰが得られる。このようにして得られた正三角錐ＥＴＰを図５９に示す。ジオデシック多面体の２０面を構成する一面分となる。この状態では、パッチで面を作成した状態であり、中身は空洞である。 Next, in step S3315, a regular triangular pyramid ETP is obtained from the isosceles triangular pyramid ITP. Specifically, the isosceles triangular pyramid ITP is rotated and copied by 120° each time, and three isosceles triangular pyramid ITPs are joined. For example, in Fusion360 (product name), drag to select all the isosceles triangular pyramid ITPs, select Surface mode → Create → Pattern → Circular Pattern, click the center line (perpendicular line) with A×is, and set Quantity to 3. In this way, as shown in Figure 58, a block with an equilateral triangular base, that is, a regular triangular pyramid ETP, is obtained. The regular triangular pyramid ETP obtained in this way is shown in Figure 59. It is one of the 20 faces that make up the geodesic polyhedron. In this state, the face is created with a patch, and the inside is hollow.
　次にステップＳ３３１６において、境界面を非表示とする。例えばＦｕｓｉｏｎ３６０（商品名）で、正三角錐ＥＴＰの内部の境界面を選択してすべて非表示にする。具体的にはブラウザ→Ｂｏｄｉｅｓ→境界面のｂｏｄｙを選択して非表示とする。このようにして図６０の正三角錐ＥＴＰが得られる。 Next, in step S3316, the boundary surfaces are hidden. For example, in Fusion360 (product name), all of the boundary surfaces inside the regular triangular pyramid ETP are selected and hidden. Specifically, go to Browser -> Bodies -> select the body of the boundary surface and hide it. In this way, the regular triangular pyramid ETP in Figure 60 is obtained.
　さらにステップＳ３３１７において、スティッチによりボディを作成する。例えばＦｕｓｉｏｎ３６０（商品名）では、Ｓｕｒｆａｃｅモード→Ｍｏｄｉｆｙ→Ｓｔｉｔｃｈで、すべての面を選択する。選択はドラッグで行い、選択できると青色になる。未選択がある場合は、ブラウザ→Ｂｏｄｉｅｓから選択する。このようにして図６１のように正三角錐ＥＴＰが選択された状態となる。ここまでで、図６２に示すような、スティッチにより１個のＢｏｄｙ（固体）が作成された。 Furthermore, in step S3317, a body is created by stitching. For example, in Fusion360 (product name), select all faces by going to Surface mode -> Modify -> Stitch. Selection is done by dragging, and when selected it turns blue. If there are any unselected faces, select them from Browser -> Bodies. In this way, a regular triangular pyramid ETP is selected as shown in Figure 61. At this point, one Body (solid) has been created by stitching, as shown in Figure 62.
　次にステップＳ３３１８において、回転コピーを行う。例えばＦｕｓｉｏｎ３６０（商品名）では、Ｃｒｅａｔｅ→ｐａｔｔｅｒｎ→Ｃｉｒｃｕｌａｒ　ｐａｔｔｅｒｎにより、Ａ×ｉｓで軸を選択し、さらにボディ１個を選択する。ここではＡｎｇｌｅ：７２、Ｑｕａｎｔｉｔｙ：２とし、図６３に示すように回転コピーを実行し、図５９の正三角錐ＥＴＰの２面分を作成する。 Next, in step S3318, a rotational copy is performed. For example, in Fusion360 (product name), an axis is selected with A×is by selecting Create→pattern→Circular pattern, and one body is then selected. Here, Angle: 72, Quantity: 2, and a rotational copy is performed as shown in Figure 63, creating two faces of the regular triangular pyramid ETP in Figure 59.
　さらにステップＳ３３１９において、回転コピーを継続する。例えばＦｕｓｉｏｎ３６０（商品名）で、同様にＣｒｅａｔｅ→ｐａｔｔｅｒｎ→Ｃｉｒｃｕｌａｒ　ｐａｔｔｅｒｎを選択し、Ａ×ｉｓで軸を選択し、さらにボディ１個を選択し、Ａｎｇｌｅ：７２、Ｑｕａｎｔｉｔｙ：２とし、図６４に示すように回転コピーを実行し、図６２の正三角錐ＥＴＰの３面分を作成する。 Furthermore, in step S3319, the rotation copy is continued. For example, in Fusion360 (product name), similarly, Create → pattern → Circular pattern is selected, an axis is selected with A×is, one body is further selected, Angle: 72, Quantity: 2 are set, and the rotation copy is executed as shown in FIG. 64, and the three faces of the regular triangular pyramid ETP in FIG. 62 are created.
　同様にステップＳ３３２０において、回転コピーをさらに継続する。例えばＦｕｓｉｏｎ３６０（商品名）で、同様にＣｒｅａｔｅ→ｐａｔｔｅｒｎ→Ｃｉｒｃｕｌａｒ　ｐａｔｔｅｒｎを選択し、Ａ×ｉｓで軸を選択し、さらにボディ１個を選択し、Ａｎｇｌｅ：７２、Ｑｕａｎｔｉｔｙ：２とし、図６５に示すように回転コピーを実行して、図６２の正三角錐ＥＴＰの４面分を作成する。 Similarly, in step S3320, the rotation copy is continued. For example, in Fusion360 (product name), similarly, select Create → pattern → Circular pattern, select the axis with A×is, further select one body, set Angle: 72, Quantity: 2, and execute the rotation copy as shown in Figure 65 to create the four faces of the regular triangular pyramid ETP in Figure 62.
　さらにステップＳ３３２１において、同様の回転コピーを繰り返す。例えばＦｕｓｉｏｎ３６０（商品名）で、Ｃｒｅａｔｅ→ｐａｔｔｅｒｎ→Ｃｉｒｃｕｌａｒ　ｐａｔｔｅｒｎでＡ×ｉｓ：軸を選択し、ボディ４個を選択し、ＡｎｇｕｌａｒＳｐａｃｉｎｇ：Ｆｕｌｌ、Ｑｕａｎｔｉｔｙ：５として、図６６に示すブロックを得る。
（ジオデシック多面体） Further, in step S3321, the same rotational copy is repeated. For example, in Fusion360 (product name), Axis: axis is selected in Create->pattern->Circular pattern, four bodies are selected, AngularSpacing: Full, Quantity: 5 are set, and the block shown in FIG.
(geodesic polyhedron)
　そしてステップＳ３３２２において、ボディの結合を行う。例えばＦｕｓｉｏｎ３６０（商品名）で、Ｓｏｌｉｄモードから、Ｍｏｄｉｆｙ→Ｃｏｍｂｉｎｅですべてのボディ（２０個）を選択して、結合し、図Ｘのブロックを得る。このようにして、図６８に示すジオデシック多面体が得られる。なおこの段階では、画素ユニットの高さは未だ設計されていない。
（五角形・六角形のスケッチ作成） Then, in step S3322, the bodies are combined. For example, in Fusion360 (product name), all the bodies (20 bodies) are selected and combined in Solid mode by Modify→Combine to obtain the block shown in Figure X. In this way, the geodesic polyhedron shown in Figure 68 is obtained. Note that at this stage, the height of the pixel unit has not yet been designed.
(Sketching pentagons and hexagons)
　ここで、ジオデシック多面体からゴールドバーク多面体を作成する（設計方法の詳細については後述）。ここでは、得られたジオデシック多面体の三角形を再構成し、五角形・六角形の面を作成して、上述した図２８Ａから図２８Ｂに示したようなゴールドバーク多面体を構成することを考える。このため、まず五角形や六角形のスケッチを作成する。例えばＦｕｓｉｏｎ３６０（商品名）で、Ｃｒｅａｔｅ→Ｓｋｅｔｃｈ（×－Ｙ平面）を選択し、五角形・六角形を線で結ぶ→一面分の表面を設計する。図６９に示すように、ジオデシック多面体の三角形を線で結び五角形・六角形を作成する。さらに図７０に示すように、線を引きながら、Ｂｏｄｙを非表示にして五角形・六角形の線を確認する。 Now, we will create a Goldberg polyhedron from the geodesic polyhedron (details of the design method will be described later). Here, we will reconstruct the triangles of the obtained geodesic polyhedron and create pentagonal and hexagonal faces to construct a Goldberg polyhedron as shown in Figures 28A and 28B above. For this, first create a sketch of the pentagon or hexagon. For example, in Fusion360 (product name), select Create → Sketch (x-Y plane), connect the pentagons and hexagons with lines → design the surface for one face. As shown in Figure 69, connect the triangles of the geodesic polyhedron with lines to create pentagons and hexagons. Furthermore, as shown in Figure 70, while drawing the lines, hide the Body to check the lines of the pentagons and hexagons.
　さらにＰａｔｃｈで面を作成する。例えばＦｕｓｉｏｎ３６０（商品名）で、ＳｕｒｆａｃｅモードからＣｒｅａｔｅ→Ｐａｔｃｈで、図７１に示すように五角形・六角形の外周の線を順にクリックして面を作成する。このようにして、図７２で示すようなゴールドバーク多面体の一面分を作成する。
（ハニカム球の設計） Furthermore, create a surface with Patch. For example, in Fusion360 (product name), in Surface mode, select Create → Patch, and create a surface by clicking the lines around the periphery of the pentagon and hexagon in order as shown in Figure 71. In this way, one face of the Goldberg polyhedron as shown in Figure 72 is created.
(Honeycomb sphere design)
　さらに、得られたゴールドバーク多面体に基づいてハニカム球の設計を行う。ここでは、図７３に示すような、六角形と五角形の画素ユニットで構成されたハニカム球を設計する。このハニカム球を構成する一セクションＳＣの展開図を図７４に示す。ここでハニカム球を分解した展開図を理解するため、図７５のように球体の面を複数の正三角形で構成した正二十面体を考える。正二十面体の特性として、正三角形の面の数が２０面、稜線ＲＬの数が３０本、頂点ＡＸの数が１２個、各面の頂点ＡＸの数が３個、頂点ＡＸに集まる面の数が５面である。このようなハニカム球の各面を３Ｄプリンタで造形することを考える。ここで、２０面の正三角形は、図７６に示すように展開できる。この図においては、図７７に示す４つの正三角形の組を５つ集合したものと捉えることができる。ここで４つの正三角形の組を一セクションＳＣと呼ぶ。この一セクションＳＣを構成するハニカム球の展開図が、上述した図７４に該当する。 Furthermore, a honeycomb sphere is designed based on the obtained Goldberg polyhedron. Here, a honeycomb sphere composed of hexagonal and pentagonal pixel units as shown in FIG. 73 is designed. A development of one section SC constituting this honeycomb sphere is shown in FIG. 74. In order to understand the development of the honeycomb sphere, a regular icosahedron is considered, in which the surfaces of the sphere are composed of multiple equilateral triangles, as shown in FIG. 75. The characteristics of a regular icosahedron are that it has 20 equilateral triangular faces, 30 edge lines RL, 12 vertices AX, 3 vertices AX on each face, and 5 faces that meet at the vertices AX. Consider forming each surface of such a honeycomb sphere with a 3D printer. Here, the 20 equilateral triangles can be developed as shown in FIG. 76. In this figure, it can be considered as a set of five sets of four equilateral triangles as shown in FIG. 77. Here, a set of four equilateral triangles is called one section SC. The development of the honeycomb sphere constituting one section SC corresponds to FIG. 74 mentioned above.
　また図７７に示す一セクションＳＣは、図７８に示すように正三角形と、稜線ＲＬと、頂点ＡＸにそれぞれ分解できる。ここでは正三角形を、３つの第一画素ブロックＩＢ１と１つの第二画素ブロックＩＢ２に分類する。なお、稜線ＲＬ同士や正三角形同士を接合する際に頂点ＡＸの重複を避けるため、必要に応じて頂点ＡＸを付加、あるいは省略する。また図７７の稜線ＲＬは、図７４に示すハニカム球の稜線ＲＬに対応する。 Furthermore, one section SC shown in FIG. 77 can be decomposed into an equilateral triangle, an edge line RL, and a vertex AX, as shown in FIG. 78. Here, the equilateral triangle is classified into three first pixel blocks IB1 and one second pixel block IB2. Note that to avoid overlapping vertices AX when joining edge lines RL or equilateral triangles, vertices AX are added or omitted as necessary. Furthermore, the edge line RL in FIG. 77 corresponds to the edge line RL of the honeycomb sphere shown in FIG. 74.
　なお、このようにハニカム球を正二十面体で近似することは、ハニカム球の設計の他、得られたハニカム球で表示装置の表示部を構成した際に、表示部に表示される画像を表現する際にも利用できる。例えばハニカム球を図７５の正二十面体で近似した場合の展開図を、図７９に示す。この展開図に、画像等を表示させることで、ハニカム球の全面に表示する画像等を一画面で近似的に表現することができる。
（ハニカム球の制作に必要な画素ユニット） In addition to designing honeycomb spheres, approximating a honeycomb sphere with a regular icosahedron can be used to represent images to be displayed on a display unit of a display device when the display unit of a display device is constructed using the honeycomb sphere obtained. For example, Fig. 79 shows a development of a honeycomb sphere approximating the honeycomb sphere with the regular icosahedron of Fig. 75. By displaying an image on this development, an image to be displayed on the entire surface of the honeycomb sphere can be approximately represented on one screen.
(Pixel units required to create a honeycomb sphere)
　次に、ハニカム球の製作に必要な面データについて説明する。ここでは半径１２５ｃｍのゴールドバーグ多面体ＧＰ（１０，０）を作成するために必要な三角形の画素ブロックＩＢを設計するためのデータである面データについて説明する。このハニカム球の画素ユニットの総数は１００２個であり、この内、頂点ＡＸは１２個、一面を構成する画素ユニットは３６個であり、２０面で総計７２０個となる。また稜線ＲＬは一本あたり画素ユニット数が９個であり、３０本で計２７０個となる。さらに画素ユニットを組み合わせた画素ブロックＩＢは、図８０に示すようになる。この図に示す画素ブロックＩＢは、正三角形と稜線ＲＬと頂点ＡＸを含んだ状態を示している。画素ブロックＩＢは、これら正三角形と稜線ＲＬと頂点ＡＸの組み合わせによって、図８１に示す、三角形の斜辺に相当する２つの稜線ＲＬを含んだ第一画素ブロックＩＢ１と、図８２に示す稜線ＲＬを含まない第二画素ブロックＩＢ２の２種類が準備される。なお図８０に示す画素ブロックＩＢは、一辺を１３１４ｍｍ、外接円を１８ｃｍ～１０ｃｍ、奥行き（高さ）を１０ｃｍとしている。
（画素ブロックＩＢ） Next, the surface data required for manufacturing a honeycomb sphere will be described. Here, the surface data, which is data for designing a triangular pixel block IB required for creating a Goldberg polyhedron GP(10,0) with a radius of 125 cm, will be described. The total number of pixel units in this honeycomb sphere is 1002, of which 12 vertices AX and 36 pixel units constituting one surface, totaling 720 for 20 surfaces. Each edge line RL has 9 pixel units, and there are 30 edges, totaling 270. Furthermore, the pixel block IB, which is a combination of pixel units, is as shown in FIG. 80. The pixel block IB shown in this figure shows a state including an equilateral triangle, an edge line RL, and an apex AX. Two types of pixel blocks IB are prepared by combining these equilateral triangles, edge lines RL, and apexes AX: a first pixel block IB1 shown in FIG. 81, which includes two edge lines RL corresponding to the hypotenuse of the triangle, and a second pixel block IB2 shown in FIG. 82, which does not include an edge line RL. The pixel block IB shown in FIG. 80 has a side of 1314 mm, a circumscribing circle of 18 cm to 10 cm, and a depth (height) of 10 cm.
(Pixel block IB)
　上述の通り、ハニカム状の画素ユニット数は１００２個となる。ここでは図８３に示すように、六角形の画素ユニットが２１種類、五角形の画素ユニットが１種類の、計２２種類の画素ユニットが必要となる。この内、頂点ＡＸは五角形の画素ユニットが１２個、面は７２０個（内訳は画素ユニット１、２、３、４、５、６、７、８、９、１０、１１、１２（１２個）×３×２０面）、稜線ＲＬは２７０個（内訳は画素ユニット１３、１４、１５、１６、１７、１８、１９、２０、２１（９個）×３０本）となる。これら２２種類の画素ユニットで図８３のハニカム球の一面となる画素ブロックＩＢを構成するところ、図８３に示す画素ブロックＩＢを正三角形と捉えたとき、この正三角形は図８４に示すように、正三角形の中心と各頂点ＡＸとを結ぶ線分で３つの二等辺三角形に分割することができる。図８３の画素ユニットの内で、この二等辺三角形に相当する画素ユニットを図８５に示す。図８５に示す二等辺三角形の領域には、二等辺三角形の他、稜線ＲＬに該当する画素ユニットも含まれる。具体的には、画素ユニット１３、１４、１５、１６、１７、１８、１９、２０、２１の９種類が、稜線ＲＬに該当する。
（第一画素ブロックＩＢ１） As described above, the number of pixel units in the honeycomb shape is 1002. Here, as shown in FIG. 83, a total of 22 types of pixel units are required, including 21 types of hexagonal pixel units and one type of pentagonal pixel unit. Of these, the vertices AX have 12 pentagonal pixel units, the faces have 720 (including pixel units 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (12 units) x 3 x 20 faces), and the ridges RL have 270 (including pixel units 13, 14, 15, 16, 17, 18, 19, 20, 21 (9 units) x 30 lines). These 22 types of pixel units constitute the pixel block IB that forms one surface of the honeycomb sphere in FIG. 83. When the pixel block IB shown in FIG. 83 is regarded as an equilateral triangle, this equilateral triangle can be divided into three isosceles triangles by line segments connecting the center of the equilateral triangle to each vertex AX, as shown in FIG. 84. Among the pixel units in Fig. 83, pixel units corresponding to this isosceles triangle are shown in Fig. 85. In addition to the isosceles triangle, the isosceles triangular area shown in Fig. 85 also includes pixel units that correspond to the edge line RL. Specifically, nine types of pixel units 13, 14, 15, 16, 17, 18, 19, 20, and 21 correspond to the edge line RL.
(First pixel block IB1)
　さらに、画素ブロックＩＢの内、図８１に示した第一画素ブロックＩＢ１と、図８２に示す第二画素ブロックＩＢ２の２種類について詳述する。まず第一画素ブロックＩＢ１は、図８６に示すように正三角形に相当する画素ユニットＩＵ１、２、３、４、５、６、７、８、９、１０、１１、１２の１２種類がそれぞれ３個、計３６個使用されている。また２つの稜線ＲＬ（図８６において左右の斜辺）に相当する画素ユニット１３、１４、１５、１６、１７、１８、１９、２０、２１の９種類がそれぞれ２個、計１８個使用されている。すなわち、第一画素ブロックＩＢ１では３６個＋１８個の計５４個の画素ユニットが使用されている。図７６に示したとおり、第一画素ブロックＩＢ１は正二十面体で１５個使用されている。したがって、正二十面体で近似したハニカム球全体では、５４個／第一画素ブロックＩＢ１×１５第一画素ブロックＩＢ１＝８１０個の画素ユニットが必要となる。
（第二画素ブロックＩＢ２） Further, two types of pixel blocks IB, the first pixel block IB1 shown in FIG. 81 and the second pixel block IB2 shown in FIG. 82, will be described in detail. First, the first pixel block IB1 uses 36 pixel units of 12 types, IU1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, which correspond to an equilateral triangle, as shown in FIG. 86. In addition, 2 pixel units of 9 types, IU13, 14, 15, 16, 17, 18, 19, 20, and 21, which correspond to two edge lines RL (the left and right oblique sides in FIG. 86), are used, for a total of 18 pixel units. That is, the first pixel block IB1 uses 36 pixel units + 18 pixel units, for a total of 54 pixel units. As shown in FIG. 76, the first pixel block IB1 is a regular icosahedron and 15 pixel units are used. Therefore, in the entire honeycomb sphere approximated by a regular icosahedron, 54 pixel units/first pixel block IB1×15 first pixel blocks IB1=810 pixel units are required.
(Second pixel block IB2)
　一方、第二画素ブロックＩＢ２を図８７に示す。この図に示すように、第二画素ブロックＩＢ２は正三角形に相当する画素ユニットＩＵ１、２、３、４、５、６、７、８、９、１０、１１、１２の１２種類をそれぞれ３個、計３６個が使用されている。また第二画素ブロックＩＢ２は、図８７に示す通り経線を含まない。したがって第二画素ブロックＩＢ２あたりの画素ユニット数は３６個となる。また図７６に示したとおり、第二画素ブロックＩＢ２は正二十面体で５個使用されている。したがって、ハニカム球全体では、３６個／第二画素ブロックＩＢ２×５第二画素ブロックＩＢ２＝１８０個の画素ユニットが必要となる。 On the other hand, the second pixel block IB2 is shown in Figure 87. As shown in this figure, the second pixel block IB2 uses 3 of each of the 12 types of pixel units IU1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, which correspond to equilateral triangles, for a total of 36. Furthermore, as shown in Figure 87, the second pixel block IB2 does not include meridians. Therefore, the number of pixel units per second pixel block IB2 is 36. Furthermore, as shown in Figure 76, the second pixel block IB2 is a regular icosahedron and five are used. Therefore, the entire honeycomb sphere requires 36 pixel units/second pixel block IB2 x 5 second pixel blocks IB2 = 180 pixel units.
　以上の８１０個＋１８０個＝９９０個の画素ユニットは、いずれも六角形状のハニカム形状の画素ユニットである。これらに加えて、図７６に示したとおり正二十面体では頂点ＡＸが１２個必要となる。頂点ＡＸは五角形状の第二画素ユニット１００Ｂである。本明細書では便宜上、五角形状の画素ユニットもハニカム状の画素ユニットに含めて表現することがある。以上の通り、ハニカム球を構成するために必要な画素ユニット数は、９９０個＋１２個＝１００２個である。またハニカム球のゴールドバーク多面体を図７５、図７６の正二十面体で近似した場合の、正三角形状の面の数は２０個であるから、各面あたり、すなわち画素ブロックＩＢあたりの画素ユニットは１２種類が３個、計３６個であり、２０面で計７２０個となる。なお画素ユニットＩＵ１～１２は、各面で３個、２０面で３×２０＝６０で、それぞれ６０個必要となる。また稜線ＲＬは９種類が２個であり、図８１、図８６の例では第二画素ブロックＩＢ２に含めているので、正二十面体では１５個となり、１８個×１５個＝２７０個となる。また画素ユニットＩＵ１３～２１は、各面で２個、１５個で２×１５＝３０で、それぞれ３０個必要となる。
（ゴールドバーグ多面体の設計） The above 810+180=990 pixel units are all hexagonal honeycomb pixel units. In addition, as shown in FIG. 76, a regular icosahedron requires 12 vertices AX. The vertices AX are the pentagonal second pixel units 100B. For convenience, in this specification, the pentagonal pixel units may be included in the honeycomb pixel units. As described above, the number of pixel units required to configure a honeycomb sphere is 990+12=1002. In addition, when the Goldberg polyhedron of the honeycomb sphere is approximated by the regular icosahedron of FIG. 75 and FIG. 76, the number of equilateral triangular faces is 20, so that there are 3 pixel units of 12 types per face, i.e., 36 pixel units per pixel block IB, for a total of 720 pixel units for the 20 faces. Note that 3 pixel units IU1-12 are required for each face, and 3×20=60 pixel units for the 20 faces, for a total of 60 pixel units of each pixel unit. 81 and 86, these are included in the second pixel block IB2, so there are 15 in the regular icosahedron, for a total of 18 × 15 = 270. Furthermore, there are two pixel units IU13-21 on each face, so 15 are needed on each face (2 × 15 = 30), for a total of 30 of each.
(Design of Goldberg polyhedrons)
　次に、ジオデシック多面体からゴールドバーク多面体を設計する手順の詳細を、図８８のフローチャートに基づいて説明する。ここでも、三次元設計ＣＡＤとしてＦｕｓｉｏｎ３６０を用いて設計を行う例を説明する。 Next, the procedure for designing a Goldberg polyhedron from a geodesic polyhedron will be explained in detail with reference to the flowchart in Figure 88. Here too, an example of design using Fusion 360 as the 3D design CAD will be explained.
　まずステップＳ８８０１において、面の再構成を行う。ここでは図８９に示すジオデシック多面体を構成する三角形の面から、三角形と五角形・六角形を作成する。図８９は、ジオデシック多面体を示しており、このジオデシック多面体の一面分について、図９０に示すように三角形の辺を囲み、図９１に示すようにゴールドバーク多面体を構成する３０の各面毎に、五角形・六角形のパッチを作成する。 First, in step S8801, the surfaces are reconstructed. Here, triangles, pentagons, and hexagons are created from the triangular faces that make up the geodesic polyhedron shown in Figure 89. Figure 89 shows a geodesic polyhedron, and for one face of this geodesic polyhedron, the edges of the triangle are enclosed as shown in Figure 90, and pentagonal and hexagonal patches are created for each of the 30 faces that make up the Goldberg polyhedron as shown in Figure 91.
　次にステップＳ８８０２において、図９２に示すような直角三角形ブロックＲＴＢを設計する。ここではまず、すべてのサーフェイスを球の中心に対し、Ｓｏｌｉｄ→ロフト・スティッチを行う。ここでは図９３に示すようにゴールドバーグ多面体の３０面すべての面を選択してスティッチを行う。次に図９４に示すように、すべての面に対して球の中心にロフトを適用する。さらに図９５、図９６に示すように、Ｓｏｌｉｄ→ロフト（ＮＥＷ　Ｂｏｄｙ）を選択する。 Next, in step S8802, a right-angled triangular block RTB is designed as shown in Figure 92. First, Solid → Loft Stitch is performed on all surfaces to the center of the sphere. All 30 faces of the Goldberg polyhedron are selected and stitched as shown in Figure 93. Next, loft is applied to all faces to the center of the sphere as shown in Figure 94. Furthermore, Solid → Loft (NEW Body) is selected as shown in Figures 95 and 96.
　次に外側に曲線を引き、オフセットで指定の長さで曲線を引く。ここでは図９７に示すように、外の線をＡＲＣ曲線で最初に引く。ここでは半径（ｒｕ）を１０ｍｍとしている。この結果、図９８のような形状が得られる。なお画素ユニットの厚さ（例えばＦＲＰ樹脂の部分の厚み）は不要であるから、後でシェルなどを用いてくりぬく。次に図９９に示すように、スケッチ作成を行う。ここでは図１００に示すように、断面視において、ゴールドバーク多面体に外接する円を基準に設計するため、円弧よりも最大で１０ｍｍ程度、ゴールドバーク多面体を構成する面の高さが薄くなる。 Next, draw a curve on the outside, then offset it to a specified length. Here, as shown in Figure 97, the outer line is first drawn with an ARC curve. Here, the radius (ru) is set to 10 mm. As a result, the shape shown in Figure 98 is obtained. Note that the thickness of the pixel unit (for example the thickness of the FRP resin part) is not necessary, so it will be hollowed out later using a shell or similar. Next, create a sketch as shown in Figure 99. Here, as shown in Figure 100, the design is based on the circle circumscribing the Goldberg polyhedron in cross section, so the height of the faces that make up the Goldberg polyhedron is up to 10 mm thinner than the arc.
　さらにＳｏｌｉｄモード→Ｒｅｖｏｌｖｅ（ｃｕｔ）で球体の内側を設計する。ここでは図９９の内面を、図１０１に示すように削除する。そして図１０２に示すように、Ｓｏｌｉｄ→Ｒｅｖｏｌｖｅ→Ｉｎｔｅｒｓｅｃｔで、反射板２２を置く厚さを設定する。ここでは反射板２２として、３ｍｍ厚のアクリル板を設定する。また画素ユニットの厚み（あとでシェルでくりぬく）、画素ユニットの内側（あとでシェルでくりぬく）、底面の厚みを設定する。 Furthermore, design the inside of the sphere in Solid mode → Revolve (cut). Here, the inner surface of Figure 99 is deleted as shown in Figure 101. Then, as shown in Figure 102, set the thickness of the reflector 22 with Solid → Revolve → Intersect. Here, set a 3 mm thick acrylic plate as the reflector 22. Also set the thickness of the pixel unit (to be hollowed out with a shell later), the inside of the pixel unit (to be hollowed out with a shell later), and the thickness of the bottom surface.
　さらに図１０３に示すように、Ｓｕｒｆａｃｅ→Ｒｅｖｏｌｖｅで内層の線を選択する。これにより図１０４に示すような図形が得られる。さらにＳｕｒｆａｃｅ→Ｓｐｌｉｔ　Ｂｏｄｙで、図１０５に示すように裏側から面を選択し、図１０６に示すようにＳｐｌｉｔｔｉｎｇ　Ｔｏｏｌｓで半球の内側・外側を選択する。そして図１０７に示すように不要な半球を非表示（ｉｎｖｉｓｉｂｌｅ）とする。ここではブラウザで不要な半径を非表示とする。この結果、図１０８に示す図形が得られる。 Furthermore, as shown in Figure 103, select the inner layer lines with Surface → Revolve. This will result in the shape shown in Figure 104. Next, select the faces from the back side with Surface → Split Body, as shown in Figure 105, and select the inside and outside of the hemisphere with Splitting Tools, as shown in Figure 106. Then make the unnecessary hemisphere invisible (invisible), as shown in Figure 107. Here, the unnecessary radii are hidden in the browser. As a result, the shape shown in Figure 108 will be obtained.
　次に、図１０９に示すように一層ごとにｉｓｏｌａｔｅで表示する。ここでは、ブラウザで一層目からｉｓｏｌａｔｅする。具体的には上から見た表面を全選択してｉｓｏｌａｔｅし、１層ずつ処理して、終了後に非表示とする。またＳｈｅｌｌ→表面を全選択→裏面を全選択→２ｍｍとし、反射板２２の厚み部分、反射板２２を置く部分、本体部分を表示させる。この状態では、、図１１０に示すように上下反転させると向きが判別できなくなるので、上下を区別するマーク等、何らかの指標を付加することが好ましい。以上の処理によって、図９２、図１１１の斜視図に示すような直角三角形ブロックＲＴＢを設計できる。 Next, as shown in Figure 109, each layer is displayed with isolate. Here, isolate is performed from the first layer in the browser. Specifically, all the surfaces viewed from above are selected and isolated, and each layer is processed one by one, and hidden after completion. Also, select Shell → all the surfaces → all the back surfaces → 2 mm, and display the thickness of the reflector 22, the area where the reflector 22 is placed, and the main body. In this state, if it is turned upside down as shown in Figure 110, the orientation cannot be determined, so it is preferable to add some kind of indicator, such as a mark to distinguish between upside and down. By the above processing, it is possible to design a right-angled triangular block RTB as shown in the perspective views of Figures 92 and 111.
　さらに図８８のステップＳ８８０３において、直角三角形ブロックＲＴＢから二等辺三角形ブロックＩＴＢを設計する。ここでは、図９２の直角三角形ブロックＲＴＢを反転コピーして、図１１２に示す二等辺三角形相当を得る。
（反射板２２の製造方法） Furthermore, in step S8803 in Fig. 88, an isosceles triangular block ITB is designed from the right-angled triangular block RTB. Here, the right-angled triangular block RTB in Fig. 92 is inverted and copied to obtain an isosceles triangle equivalent to that shown in Fig. 112.
(Method of manufacturing the reflector 22)
　次に、反射板２２を作成する手順を、図１１３のフローチャートに基づいて説明する。ここでは反射構造体１０の開口部に配置する反射板２２を近似的に作成する。この反射板２２の材質には、アクリル板を使用する。 Next, the procedure for creating the reflector 22 will be described based on the flowchart in Figure 113. Here, the reflector 22 to be placed in the opening of the reflecting structure 10 is approximately created. An acrylic plate is used as the material for this reflector 22.
　まずステップＳ１１３０１において、反射構造体１０を表示させる。ここでは図１１４に示すように、対象となる反射構造体１０のみを表示させる。例えばブラウザ→ｂｏｄｙの一覧より表示させる。 First, in step S11301, the reflective structure 10 is displayed. Here, as shown in FIG. 114, only the target reflective structure 10 is displayed. For example, it is displayed from the browser → body list.
　次にステップＳ１１３０２において、反射板２２の外形図を作成する。すなわち反射板２２を取り付ける画素ユニットの開口部に、スケッチを作成して外形図を描く。例えば×－Ｙ平面にスケッチを作成する。そして図１１５に示すように、反射構造体１０の開口部分を線（Ｌｉｎｅ）で囲む。 Next, in step S11302, an outline drawing of the reflector 22 is created. That is, a sketch is created of the opening of the pixel unit where the reflector 22 is to be attached, and the outline drawing is drawn. For example, a sketch is created on the x-y plane. Then, as shown in FIG. 115, the opening of the reflecting structure 10 is surrounded by a line.
　次にステップＳ１１３０３において、外形図に基づいて面を作成する。ここでは、外形図から面を作成して反射板２２とする。面がほぼ平面の場合は、まずＰｒｏｊｅｃｔにより×－Ｙ平面に投影する。例えば、図１１６に示すように、Ｃｒｅａｔｅ→Ｐｒｏｊｅｃｔ／Ｉｎｃｌｕｄｅ→Ｐｒｏｊｅｃｔで、外形線を選択（６本）し、×－Ｙ平面上に投影させる。そしてＰａｔｃｈにより厚さのない平面を作成する。例えばＳｕｒｆａｃｅモードで、Ｃｒｅａｔｅ→Ｐａｔｃｈにより、図１１７に示すように、開口部の領域を選択してＳｕｒｆａｃｅ（面）を作成する。さらにＥ×ｔｒｕｄｅにより面の厚みを作成する。例えば図１１８に示すように、Ｓｏｌｉｄモードで、Ｃｒｅａｔｅ→Ｅ×ｔｒｕｄｅで、反射板２２に相当する厚み（例えば２ｍｍ）の面を、押し出しにより作成する。 Next, in step S11303, a surface is created based on the outline drawing. Here, a surface is created from the outline drawing to create the reflector 22. If the surface is nearly flat, first project it onto the x-Y plane using Project. For example, as shown in FIG. 116, select the outline lines (six lines) using Create → Project/Include → Project and project them onto the x-Y plane. Then create a plane with no thickness using Patch. For example, in Surface mode, select the opening area and create a Surface (surface) using Create → Patch as shown in FIG. 117. Then create the thickness of the surface using Extrude. For example, as shown in FIG. 118, in Solid mode, create a surface by extrusion with Create → Extrude to create a surface with a thickness equivalent to the reflector 22 (for example, 2 mm).
　次にステップＳ１１３０４において、アライメントにより平面に移動させて、面を水平に配置する。例えばＳｕｒｆａｃｅモードで、Ｍｏｄｉｆｙ→Ａｌｉｇｎ（アライメント）を実行する。Ｆｒｏｍ：では面の裏側を選択し、Ｔｏ：でＯｒｉｇｉｎ：×－Ｙ平面を選択して「ＯＫ」とする。これにより図１１９に示すように、傾いた面が、平面に配置される。 Next, in step S11304, the surface is moved onto a plane by alignment, and positioned horizontally. For example, in Surface mode, execute Modify → Align. In From:, select the back side of the surface, and in To:, select the Origin: x-Y plane, and click "OK." This positions the tilted surface on a plane, as shown in Figure 119.
　次にステップＳ１１３０５において、外形線を作成する。ここでは面を×－Ｙ平面にプロジェクションして近似的な外形図を作成する。例えば図１２０に示すように、×－Ｙ平面にスケッチを作成し、アライメントにより平面に配置した面の裏側に線（Ｌｉｎｅ）で引く。そして外形線のプロジェクション（投影）を行う。面が完全に×－Ｙ平面に接地していないときは、×－Ｙ平面へのプロジェクションにより近似する。例えばＣｒｅａｔｅ→Ｓｋｅｔｃｈ、Ｃｒｅａｔｅ→Ｐｒｏｊｅｃｔ／Ｉｎｃｌｕｄｅ→Ｐｒｏｊｅｃｔで、外形線の頂点をクリックすると、ピンク色の点になる。そして図１２１に示すように、ピンク色の各点を線（Ｌｉｎｅ）で結ぶ。さらに面を移動させる。ここでは原点を×－Ｙ平面に移動させる。例えばＭｏｄｉｆｙ→Ｍｏｖｅ／Ｃｏｐｙで、図１２２に示すように原点位置に移動する（Ｃｒｅａｔｅ　Ｃｏｐｙをクリックする）。さらに垂直方向の拘束を行う。ここでは図１２３に示すように垂直方向に拘束（ｃｏｎｓｔｒａｉｎｔ）をかけて、線を×軸に合わせる。例えば×軸、Ｙ軸に接しない程度に移動させ、元の外形図を削除する。またＳｋｅｔｃｈに識別名を付加する（例えばｓ１～ｓ１４　ｌａｓｅｒなどとする）。 Next, in step S11305, the outline is created. Here, the surface is projected onto the x-Y plane to create an approximate outline drawing. For example, as shown in Figure 120, a sketch is created on the x-Y plane, and a line is drawn on the back side of the surface that was placed on the plane by alignment. Then, the outline is projected. If the surface is not completely on the x-Y plane, it is approximated by projecting onto the x-Y plane. For example, by clicking the vertices of the outline using Create → Sketch or Create → Project/Include → Project, they become pink points. Then, as shown in Figure 121, each pink point is connected with a line. The surface is then moved. Here, the origin is moved to the x-Y plane. For example, by using Modify → Move/Copy, it is moved to the origin position as shown in Figure 122 (click Create Copy). Then, a vertical constraint is applied. Here, as shown in Figure 123, a vertical constraint is applied to align the line with the x-axis. For example, move it so that it does not touch the x-axis or y-axis, and delete the original outline drawing. Also, add an identification name to the sketch (for example, s1 to s14 laser).
　次にステップＳ１１３０６において、Ｄ×Ｆファイルとして保存する。例えば図１２４に示すように、ブラウザのＳｋｅｔｃｈを右クリックし、Ｓａｖｅ　ａｓ　Ｄ×Ｆを選択する。ここで、対象となる外形図以外が表示されていないか確認しておく。そしてＥａｇｌｅを起動し、プロジェクトを作成し、ボードを作成（ｂｒｄ）し、ファイル→ｉｍｐｏｒｔ→ｄ×ｆを選択する。 Next, in step S11306, save it as a DxF file. For example, as shown in Figure 124, right-click on Sketch in the browser and select Save as DxF. At this point, make sure that nothing other than the target outline drawing is displayed. Then start Eagle, create a project, create a board (brd), and select File → Import → dxf.
　最後にステップＳ１１３０７において、レーザ加工機にて加工を行う。ここでは作成データをレーザ加工機に入力し、Ｄ×Ｆファイルの外形線に沿ってアクリル板を切削する。まずＤ×Ｆファイルを確認する。例えば図１２５に示すように、Ｌａｙｅｒ：２０Ｄｉｍｅｎｓｉｏｎ（黄線）、中は黒色であることを確認する。次にＤ×Ｆファイルの書き出しを行う。例えばＦｉｌｅ→Ｅ×ｐｏｒｔ→Ｄ×Ｆで、チェックボックスをＯＦＦしてＯＫをクリックする。そしてレーザ加工機にＤ×Ｆファイルを読み込ませる。まずレーザ加工機の電源をＯＦＦした状態で、アクリル板をセットし、レーザの高さ調整する。そしてレーザ加工プログラムを起動する。Ｄ×Ｆファイルを読み込ませて、使用する機材（例えばアクリル板２ｍｍ）を選択する。また加工原点を指定する。そしてレーザ加工機の電源をＯＮし、レーザ加工を開始させる。レーザ加工の終了後は、レーザ加工機の電源をＯＦＦする。以上のようにして、反射板２２を作成する。
（ハニカム球の製造方法） Finally, in step S11307, processing is performed by a laser processing machine. Here, the creation data is input to the laser processing machine, and the acrylic plate is cut along the outline of the DxF file. First, check the DxF file. For example, as shown in FIG. 125, confirm that Layer: 20 Dimension (yellow line) and the inside is black. Next, write out the DxF file. For example, go to File → Export → DxF, turn off the check box, and click OK. Then, have the laser processing machine read the DxF file. First, with the power of the laser processing machine turned off, set the acrylic plate and adjust the height of the laser. Then, start the laser processing program. Read the DxF file and select the equipment to be used (for example, acrylic plate 2 mm). Also, specify the processing origin. Then, turn on the power of the laser processing machine and start laser processing. After the laser processing is completed, turn off the power of the laser processing machine. In this manner, the reflector 22 is created.
(Manufacturing method of honeycomb ball)
　次にハニカム球を組み立てる手順について、図１２６のフローチャートに基づいて説明する。ここでは、図１２７に示すように画素ブロックＩＢを三分割して作成する例を説明する。まずステップＳ１２６０１において、図１２８に示すように三分割された画素分割ブロックＩＳＢ１～３を予め設計する。詳細な手順は、上述の通りである。次にステップＳ１２６０２において、設計に基づき画素分割ブロックをそれぞれ作成する。作成には、例えば３Ｄプリンタが好適に利用できる。また材質としては、ＡＢＳ、ＡＳＡ、ＰＬＡ、ＰＣ、ＰＰ、ＰＥＴＧ、ＴＰＵのプラスチック、植物や木材等の生物由来の生分解性プラスチック、ガラス繊維や炭素繊維を含む強化プラスチック等が利用できる。具体的には、図８５のように画素ユニットＩＵ１～１２を接合した二等辺三角形ブロックＩＴＢを３つ作成し、これを接合して正三角形ブロックＥＴＢを作成し、図１２７のようにそれぞれを連結して、図８７のような第二画素ブロックＩＢ２を５個作成する。連結には、ねじ止めやプラスチック用接着剤を利用できる。ねじ止めの場合は、画素ユニット同士を連結する際に、後から画素ユニット間の隙間を微調整できる利点が得られる。 Next, the procedure for assembling a honeycomb sphere will be described based on the flowchart in FIG. 126. Here, an example will be described in which a pixel block IB is divided into three parts and created as shown in FIG. 127. First, in step S12601, pixel division blocks ISB1 to ISB3 divided into three parts are designed in advance as shown in FIG. 128. The detailed procedure is as described above. Next, in step S12602, each pixel division block is created based on the design. For example, a 3D printer can be suitably used for creation. In addition, as materials, ABS, ASA, PLA, PC, PP, PETG, TPU plastics, biodegradable plastics derived from living organisms such as plants and wood, reinforced plastics containing glass fibers and carbon fibers, etc. can be used. Specifically, three isosceles triangular blocks ITB are created by joining pixel units IU1 to IU12 as shown in FIG. 85, and these are joined to create an equilateral triangular block ETB, which are then connected as shown in FIG. 127 to create five second pixel blocks IB2 as shown in FIG. 87. The connections can be made using screws or plastic adhesive. When using screws, the advantage is that the gaps between the pixel units can be fine-tuned later when connecting the pixel units together.
　一方で、別途正三角形ブロックＥＴＢに対し、画素ユニットＩＵ１３～２１を接合した稜線ブロックを付加した図８６のような第一画素ブロックＩＢ１を１５個作成する。ここでも、３つの二等辺三角形ブロックＩＴＢを作成して接合し、図１２９に示すような第一画素ブロックＩＢ１を得る。 Separately, 15 first pixel blocks IB1 as shown in Figure 86 are created by adding edge blocks to which pixel units IU13 to IU21 are joined to the equilateral triangular block ETB. Again, three isosceles triangular blocks ITB are created and joined to obtain the first pixel block IB1 as shown in Figure 129.
　そしてステップＳ１２６０３において、ハニカム球を構成する各画素ユニットの底面にそれぞれ、発光素子５０を付加し、配線等を行う。 Then, in step S12603, a light-emitting element 50 is added to the bottom surface of each pixel unit that makes up the honeycomb sphere, and wiring is performed.
　最後にステップＳ１２６０４において第一画素ブロックＩＢ１と第二画素ブロックＩＢ２を接着する。また頂点ＡＸとして、第二画素ユニット１００Ｂを付加する。頂点ＡＸは、別部材として造形し、第一画素ブロックＩＢ１や第二画素ブロックＩＢ２と接着してもよいし、あるいは第一画素ブロックＩＢ１や第二画素ブロックＩＢ２を３Ｄプリンタ等で造形する際に、付加してもよい。このようにしてハニカム球、すなわち球状に形成された球状表示部１を得ることができる。 Finally, in step S12604, the first pixel block IB1 and the second pixel block IB2 are bonded together. The second pixel unit 100B is added as the vertex AX. The vertex AX may be formed as a separate member and bonded to the first pixel block IB1 and the second pixel block IB2, or may be added when the first pixel block IB1 and the second pixel block IB2 are formed using a 3D printer or the like. In this way, a honeycomb sphere, i.e., a spherical display unit 1 formed in a spherical shape, can be obtained.
　なお、画素ブロックＩＢの設計に際しては、底面が平面状に近くなるように設計することが好ましい。これによって３Ｄプリンタで造形する際にサポート材の使用量を低減し、さらに造形物の低背化による積層数を低減し、造形のコスト削減と高速化を図ることが可能となる。また画素ブロックＩＢそのものを３Ｄプリンタで造形する必要はなく、例えば画素ブロックを複数の分割ブロックに分割してもよい。これによって、造形対象の底面の形状を平面上に近付け易くできる。 When designing the pixel block IB, it is preferable to design it so that the bottom surface is as close to flat as possible. This reduces the amount of support material used when modeling with a 3D printer, and also reduces the number of layers by making the model shorter, making it possible to reduce modeling costs and speed up modeling. In addition, the pixel block IB itself does not need to be modeled with a 3D printer; for example, the pixel block may be divided into multiple divided blocks. This makes it easier to approximate the shape of the bottom surface of the modeling object to a flat surface.
　また画素ブロックの設計に基づいて、画素ブロックを２０面分作成し、これら２０面分の画素ブロックを組み合わせて、球状表示部を構成している。ここで画素ブロックの作成は、必ずしも画素ブロック全体を作成する必要はなく、画素ブロックを複数の部分に分割して、これらを個別に作成した上で組み合わせてもよい。例えば正三角形状の画素ブロックを、３つの二等辺三角形ブロックに分割して、それぞれ作成した二等辺三角形ブロックを１２０°ずつ回転させて組み合わせることで画素ブロックを構成してもよい。あるいは６つの直角三角形ブロックに分割して、これらを組み合わせて正三角形状の画素ブロックを構成してもよい。そして、これら２０面分の画素ブロックを組み合わせて、正二十面体を構築する要領で球状表示部を構成する。この工程も、必ずしも画素ブロック単位で球状表示部を構成する必要はなく、同様に任意の単位や大きさに適宜分割して、分割されたパーツ同士を組み上げて構成できることは言うまでもない。ここでいう画素ブロックを２０面分作成し、組み合わせるとは、あくまでも球状表示部１を構築するために必要となるパーツの総分量を示しているに過ぎず、画素ブロック単位での作成や組み立てを要求するものでない。 Also, based on the design of the pixel block, 20 pixel blocks are created, and these 20 pixel blocks are combined to form the spherical display unit. Here, it is not necessary to create the entire pixel block, but the pixel block may be divided into multiple parts, which may be created individually and then combined. For example, an equilateral triangular pixel block may be divided into three isosceles triangular blocks, and each of the isosceles triangular blocks may be rotated 120° and combined to form a pixel block. Alternatively, it may be divided into six right-angled triangular blocks, and these may be combined to form an equilateral triangular pixel block. These 20 pixel blocks are then combined to form the spherical display unit in a manner similar to constructing a regular icosahedron. This process does not necessarily require the spherical display unit to be formed in pixel block units, and it goes without saying that it can be similarly divided into any unit or size, and the divided parts can be assembled to form the spherical display unit. Here, creating and combining 20 pixel blocks merely indicates the total amount of parts required to construct the spherical display unit 1, and does not require creation or assembly in pixel block units.
　以上の例では、ジオデシック多面体やゴールドバーク多面体からハニカム球を設計する際の単位として、図２５Ａに示した正二十面体ＲＩの一面に相当する画素ブロック、すなわち図２５Ｂの正三角形面ＥＴＳを基準に行い、正三角形面ＥＴＳをコピーすることでハニカム球の全体を設計している。ただし、このような設計に基づいて実際にハニカム球を製造する段階では、必ずしも設計時と同じ基準、すなわち正三角形面ＥＴＳに相当する正三角形面ＥＴＳを単位として製造する必要はない。例えば、正三角形面ＥＴＳをさらに分割した直角三角形ブロック単位で行う。特に３Ｄプリンタで造形する場合は、製造可能なサイズの制約を受ける上、曲面が多いと使用するサポート材も増え、造形時間も長くなる。したがって、選択した製造方法に適したサイズや形状に、ハニカム球や正三角形面ＥＴＳを分割して設計することが好ましい。このように本実施形態においては、ハニカム球の設計時に分割する単位と、製造時に分割する単位とを一致させる必要はなく、設計や製造にそれぞれ適した分割の単位を選択できる。 In the above example, the unit for designing a honeycomb sphere from a geodesic polyhedron or a Goldberg polyhedron is a pixel block equivalent to one face of the regular icosahedron RI shown in FIG. 25A, i.e., the equilateral triangular surface ETS in FIG. 25B, which is the basis, and the entire honeycomb sphere is designed by copying the equilateral triangular surface ETS. However, when actually manufacturing a honeycomb sphere based on such a design, it is not necessarily necessary to manufacture it using the same basis as at the time of design, i.e., the equilateral triangular surface ETS equivalent to the equilateral triangular surface ETS as a unit. For example, it is performed in units of right-angled triangular blocks obtained by further dividing the equilateral triangular surface ETS. In particular, when molding with a 3D printer, there are restrictions on the size that can be manufactured, and if there are many curved surfaces, the support material used increases and the molding time increases. Therefore, it is preferable to design the honeycomb sphere or the equilateral triangular surface ETS by dividing it into a size and shape suitable for the selected manufacturing method. In this way, in this embodiment, it is not necessary to match the unit for dividing the honeycomb sphere when designing it with the unit for dividing it when manufacturing it, and it is possible to select the unit for dividing that is suitable for design and manufacturing, respectively.
　その一方で、設計時の画素ブロックの構成単位と造形時の単位とを一致させてもよい。例えば画素ブロックを複数の分割ブロックに分割して造形し、造形された複数の分割ブロックを接合して各画素ブロックを構成してもよい。このようにすることで、設計時の分割と造形時の分割を一致させることができ、設計時のデータを造形時のデータに転用できる利点が得られる。
（ジオデシック多面体のクラスＩＩＩ） On the other hand, the constituent units of the pixel block at the time of design may be made to match the units at the time of modeling. For example, the pixel block may be divided into a plurality of divided blocks and modeled, and each pixel block may be configured by joining the plurality of modeled divided blocks. In this way, the division at the time of design and the division at the time of modeling can be made to match, and there is an advantage that the data at the time of design can be converted into data at the time of modeling.
(Class III of geodesic polyhedra)
　また以上の例では、ジオデシック多面体のクラスＩ又はクラスＩＩに基づいてゴールドバーク多面体のハニカム球を設計する手順について説明した。ただジオデシック多面体のクラスＩＩＩに基づいてハニカム球を設計することもできる。例えばジオデシック多面体のクラスＩに基づいて、図２５Ａに示した正二十面体ＲＩの一面に相当する画素ブロックを設計することを考える。この場合は、正三角形面ＥＴＳの各辺と、分割された単位正三角形ＵＴの一辺とが合致する。したがって図２５Ｂの正三角形面ＥＴＳを、図１３０に示すように各頂点から対向する底辺に下ろした垂線を分割線ＤＬとして６つの直角三角形領域ＲＴＡに六等分すると、各直角三角形領域ＲＴＡに含まれる単位正三角形ＵＴのパターンは同一又は鏡像となる。したがって、一個分の直角三角形領域ＲＴＡに相当する部分の画素ブロックを設計すれば、対称性によって他の部分はコピーによって埋めることができる。例えば図１３０に示すＧ（８，０）のジオデシック多面体の場合は、正三角形面ＥＴＳの各頂点から下ろした垂線で六等分した直角三角形ブロックにあたる画素ブロックを設計すれば、他の部分は反転コピーや回転コピーで足りる。 In the above examples, the procedure for designing a honeycomb sphere of a Goldberg polyhedron based on class I or class II of a geodesic polyhedron has been described. However, a honeycomb sphere can also be designed based on class III of a geodesic polyhedron. For example, consider designing a pixel block corresponding to one face of a regular icosahedron RI shown in FIG. 25A based on class I of a geodesic polyhedron. In this case, each side of the equilateral triangular surface ETS matches one side of the divided unit equilateral triangle UT. Therefore, if the equilateral triangular surface ETS in FIG. 25B is divided into six equal right-angled triangular areas RTA with perpendicular lines drawn from each vertex to the opposing base as division lines DL as shown in FIG. 130, the pattern of the unit equilateral triangle UT included in each right-angled triangular area RTA will be the same or a mirror image. Therefore, if a pixel block of a portion corresponding to one right-angled triangular area RTA is designed, the other portions can be filled by copying due to symmetry. For example, in the case of the geodesic polyhedron G(8,0) shown in Figure 130, if you design pixel blocks that correspond to right-angled triangular blocks divided into six equal parts by perpendicular lines drawn from each vertex of the equilateral triangular surface ETS, the other parts can be copied by inverting or rotating them.
　またジオデシック多面体のクラスＩＩに基づいて、同様に画素ブロックを設計する場合も、同様に対応できる。例えばＧ（３，３）のジオデシック多面体の場合は、図１３１に示すように正三角形面ＥＴＳの各頂点から下ろした垂線で六等分した直角三角形ブロックにあたる画素ブロックを設計すれば、他の部分は反転コピーや回転コピーで足りる。なおジオデシック多面体のクラスＩＩにおいては、正三角形面ＥＴＳの各辺と、分割された単位正三角形ＵＴの一辺とは一致していないものの、単位正三角形ＵＴを二分した直角三角形領域ＲＴＡの一辺（底辺）と合致する。また、正三角形面ＥＴＳを六分割する分割線ＤＬは、単位正三角形ＵＴの辺と合致する。 The same can be done when designing pixel blocks based on class II geodesic polyhedrons. For example, in the case of a geodesic polyhedron G(3,3), if pixel blocks are designed that correspond to right-angled triangular blocks divided into six equal parts by perpendicular lines drawn from each vertex of the equilateral triangular surface ETS as shown in Figure 131, then the other parts can be copied by inverting or rotating them. In class II geodesic polyhedrons, although each side of the equilateral triangular surface ETS does not coincide with one side of the divided unit equilateral triangle UT, it does coincide with one side (base) of the right-angled triangular area RTA obtained by bisecting the unit equilateral triangle UT. In addition, the division line DL that divides the equilateral triangular surface ETS into six parts coincides with a side of the unit equilateral triangle UT.
　一方で、ジオデシック多面体のクラスＩＩＩに基づいて正二十面体ＲＩの正三角形面ＥＴＳを分割する例を、図１３２、図１３３、図１３４に示す。これらの図において、図１３２はＧ（４，３）、図１３３はＧ（５，２）、図１３４はＧ（６，２）の、クラスＩＩＩのジオデシック多面体をそれぞれ示している。これらの図に示すように、クラスＩＩＩのジオデシック多面体では、正三角形面ＥＴＳを同様に各頂点から対向する底辺に下ろした垂線で六分割すると、正三角形面ＥＴＳの各辺や分割線ＤＬのいずれも、単位正三角形ＵＴの辺とは合致せず、また線対称でもなく、回転対称となる。この結果、正三角形面ＥＴＳを構成する直角三角形領域はＲＴＡ１、ＲＴＡ２の２種類が必要となる。換言すると、これら２種類の直角正三角形領域ＲＴＡ１、ＲＴＡ２を合わせた二等辺三角形領域を３つ組み合わせた構成となる。したがって、正三角形面ＥＴＳの１／６にあたる直角正三角形領域をＲＴＡ１、ＲＴＡ２の２つ分、あるいは正三角形面ＥＴＳを二等辺三角形に三等分した領域、つまり正三角形面ＥＴＳの１／３の領域を設計すれば、残りはコピーによって埋めることが可能となる。以上をまとめると、ジオデシック多面体のクラスＩ、クラスＩＩでは、正三角形面ＥＴＳの１／６の設計で足りる一方、ジオデシック多面体のクラスＩＩＩでは、正三角形面ＥＴＳの１／３の設計が必要となる。またクラスＩＩＩでは、北極や南極の位置がずれたり、稜線が複雑な形状になる等の問題もある。したがって、上述したクラスＩやクラスＩＩのジオデシック多面体を用いることが好ましい。 On the other hand, examples of dividing the equilateral triangular surface ETS of a regular icosahedron RI based on the class III of geodesic polyhedrons are shown in Figs. 132, 133, and 134. In these figures, Fig. 132 shows a class III geodesic polyhedron of G(4,3), Fig. 133 shows G(5,2), and Fig. 134 shows G(6,2). As shown in these figures, in a class III geodesic polyhedron, when the equilateral triangular surface ETS is similarly divided into six parts by perpendicular lines drawn from each vertex to the opposing base, none of the sides of the equilateral triangular surface ETS or the division lines DL match the sides of the unit equilateral triangle UT, and the surface is not linearly symmetric, but rotationally symmetric. As a result, two types of right-angled triangular regions RTA1 and RTA2 are required to constitute the equilateral triangular surface ETS. In other words, the surface is a combination of three isosceles triangular regions that combine these two types of right-angled equilateral triangular regions RTA1 and RTA2. Therefore, if you design two right-angled equilateral triangular regions, RTA1 and RTA2, which are 1/6 of the equilateral triangular surface ETS, or the region obtained by dividing the equilateral triangular surface ETS into three isosceles triangles, that is, 1/3 of the equilateral triangular surface ETS, you can fill in the rest by copying. In summary, for geodesic polyhedrons of class I and class II, it is sufficient to design 1/6 of the equilateral triangular surface ETS, while for geodesic polyhedrons of class III, it is necessary to design 1/3 of the equilateral triangular surface ETS. In addition, class III has problems such as the north and south poles being misaligned and the ridges having complex shapes. Therefore, it is preferable to use geodesic polyhedrons of class I or class II described above.
　本発明の球状表示装置、球状表示装置の製造方法及び設計方法によれば、大画面の文字や画像の表示ディスプレイ、インテリジェント照明等として好適に利用できる。 The spherical display device, manufacturing method and design method of the spherical display device of the present invention can be suitably used as a large-screen display for displaying characters and images, intelligent lighting, etc.
１０００…球状表示装置
１００、１００Ｘ…画素ユニット
１００Ａ…第一画素ユニット；１００Ｂ…第二画素ユニット
１…球状表示部
２…電源装置
４…台座部；４Ｂ…吊下体
１０…反射構造体
２０…拡散シート
２２…反射板
２４…拡散フィルム
２５…底面板；２５ａ…第一底面板；２５ｂ…第二底面板
２６…型板
３０…球状フレーム
３１…緯線部；３１ａ…第一緯線部；３１ｂ…第二緯線部；３１ｃ…第三緯線部
３２…経線部
３３…極点
３４…補強管
３５…補強軸
３６…船型板
３７…開口窓
４０…支持金具
４１…曲面板
４２…シャフト
４３…横板
４４…経線板
５０…発光素子（ＬＥＤ）
５０Ａ…第一発光素子：５０Ｂ…第二発光素子
７０…コントローラ
７２…通信回路
ＵＴ…単位正三角形
ＡＸ…ゴールドバーク多面体の頂点
ＲＬ…稜線
ＩＢ…画素ブロック；ＩＢ１…第一画素ブロック；ＩＢ２…第二画素ブロック
ＩＳＢ１～３…画素分割ブロック
ＥＴＢ…正三角形ブロック
ＩＴＢ…二等辺三角形ブロック
ＲＴＢ…直角三角形ブロック
ＤＰ…離散点
ＲＴＰ…直角三角錐
ＩＴＰ…二等辺三角錐
ＥＴＰ…正三角錐
ＳＣ…一セクション
ＲＩ…正二十面体
ＥＴＳ…正三角形面
ＵＴ…単位正三角形
ＤＬ…分割線
ＲＴＡ、ＲＴＡ１、ＲＴＡ２…直角三角形領域 1000...Spherical display device 100, 100X...Pixel unit 100A...First pixel unit; 100B...Second pixel unit 1...Spherical display unit 2...Power supply unit 4...Pedestal unit; 4B...Suspended body 10...Reflective structure 20...Diffusion sheet 22...Reflector 24...Diffusion film 25...Bottom plate; 25a...First bottom plate; 25b...Second bottom plate 26...Form plate 30...Spherical frame 31...Latitude line portion; 31a...First latitude line portion; 31b...Second latitude line portion; 31c...Third latitude line portion 32...Meridian line portion 33...Pole 34...Reinforcing tube 35...Reinforcing shaft 36...Boat-shaped plate 37...Opening window 40...Support bracket 41...Curved plate 42...Shaft 43...Horizontal plate 44...Meridian plate 50...Light-emitting element (LED)
50A...First light-emitting element: 50B...Second light-emitting element 70...Controller 72...Communication circuit UT...Unit equilateral triangle AX...Vertex RL of Goldberg polyhedron...Edge line IB...Pixel block; IB1...First pixel block; IB2...Second pixel block ISB1-3...Pixel division block ETB...Equilateral triangle block ITB...Isosceles triangle block RTB...Right-angled triangle block DP...Discrete point RTP...Right-angled pyramid ITP...Isosceles pyramid ETP...Equilateral pyramid SC...One section RI...Regular icosahedron ETS...Equilateral triangular surface UT...Unit equilateral triangle DL...Division line RTA, RTA1, RTA2...Right-angled triangular region

Claims (19)

  1. 　複数の画素ユニットである六角柱状の第一画素ユニットと、五角柱状の第二画素ユニットを隣接して配置した球状の表示装置の製造方法であって、
    　前記球状の表示装置を構成する前記第一画素ユニット及び第二画素ユニットの数と、前記球状の表示装置の直径又は半径と、前記第一画素ユニット及び第二画素ユニットの高さの少なくともいずれかを含むパラメータを設定する工程と、
    　前記表示装置の直径又は半径に基づき、前記球状の表示装置に内接する正二十面体を構成する各正三角形面に対し、前記設定された第一画素ユニット及び第二画素ユニットの数に基づいて、前記球状の表面を多角形で近似したゴールドバーク多面体を構成する六角形の面と五角形の面を、それぞれ単位正三角形の組み合わせで構成するよう、単位正三角形を確定する工程と、
    　前記正三角形面を、各頂点から対向する辺に下ろした垂線で六等分した直角三角形と対応する直角三角形ブロックを、前記単位正三角形を組み合わせた六角形と五角形を底面とし、前記設定された高さを有する第一画素ユニット及び第二画素ユニットを複数組み合わせて設計する工程と、
    　前記直角三角ブロックを反転させた反転直角三角形ブロックと、前記直角三角形ブロックとを組み合わせた二等辺三角形ブロックを設計する工程と、
    　前記二等辺三角形ブロックを１２０°回転させた第一回転二等辺三角形ブロックと、前記第一回転二等辺三角形ブロックをさらに１２０°回転させた第二回転二等辺三角形ブロックと、前記二等辺三角形ブロックとを組み合わせた、前記正二十面体を構成する各正三角形面の一面に相当する画素ブロックを設計する工程と、
    　前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程と、
    を含む球状表示装置の製造方法。     A method for manufacturing a spherical display device having a plurality of pixel units, a first pixel unit having a hexagonal prism shape and a second pixel unit having a pentagonal prism shape, disposed adjacent to each other, comprising the steps of:
    setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit;
    determining unit equilateral triangles for each equilateral triangular surface constituting a regular icosahedron inscribed in the spherical display device based on a diameter or radius of the display device, based on the set numbers of first pixel units and second pixel units, so that the hexagonal and pentagonal surfaces constituting a Goldberg polyhedron approximating the spherical surface with a polygon are each composed of a combination of unit equilateral triangles;
    a step of designing right-angled triangle blocks corresponding to right-angled triangles obtained by dividing the equilateral triangular surface into six equal parts by perpendicular lines drawn from each vertex to an opposing side, the right-angled triangle blocks having bases of hexagons and pentagons formed by combining the unit equilateral triangles, by combining a plurality of first pixel units and second pixel units having the set height;
    A step of designing an isosceles triangular block by combining an inverted right-angled triangular block obtained by inverting the right-angled triangular block and the right-angled triangular block;
    a step of designing pixel blocks corresponding to one of the equilateral triangular faces constituting the regular icosahedron, the pixel blocks being a combination of a first rotated isosceles triangle block obtained by rotating the isosceles triangle block by 120°, a second rotated isosceles triangle block obtained by further rotating the first rotated isosceles triangle block by 120°, and the isosceles triangle block;
    creating 20 pixel blocks based on the design of the pixel blocks, and combining the 20 pixel blocks to configure a spherical display unit of a spherical display device;
    A method for manufacturing a spherical display device comprising the steps of:
  2. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記第一画素ユニットの大きさが一定でない球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    A method for manufacturing a spherical display device, in which the first pixel units are not uniform in size.
  3. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記単位正三角形が、ゴールドバーク多面体のクラスＩ又はクラスＩＩのいずれかに基づいて分割された三角形である球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    The method for manufacturing a spherical display device, wherein the unit equilateral triangle is a triangle divided based on either Class I or Class II of the Goldberg polyhedron.
  4. 　請求項３に記載の球状表示装置の製造方法であって、
    　前記パラメータを設定する工程が、前記ゴールドバーク多面体のＧＰ（ｍ，ｎ）の設定を含む球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 3, comprising the steps of:
    The method for manufacturing a spherical display device, wherein the step of setting parameters includes setting GP(m,n) of the Goldberg polyhedron.
  5. 　請求項４に記載の球状表示装置の製造方法であって、
    　前記パラメータを設定する工程が、
    　　前記単位正三角形の一辺の長さＬから、等角図の三角形の一辺の長さを、数１から求める工程を含む球状表示装置の製造方法。
    ［数１］
    　Ｌ＝ｓｑｒｔ（ｍ＊ｍ＋ｎ＊ｎ＋ｍ＊ｎ）×ａ     A method for manufacturing a spherical display device according to claim 4, comprising the steps of:
    The step of setting the parameters comprises:
    A method for manufacturing a spherical display device, comprising a step of calculating the length of one side of an isometric triangle from the length L of one side of the unit equilateral triangle using Equation 1.
    [Equation 1]
    L = sqrt(m*m+n*n+m*n) x a
  6. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記パラメータを設定する工程が、
    　　前記単位正三角形の一辺Ｌと、
    　　等角図の正三角形の一辺ａと、
    　　等角図の正三角形の高さｈ
    の設定の少なくとも何れかを含む球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    The step of setting the parameters comprises:
    One side L of the unit equilateral triangle;
    One side a of an equilateral triangle in isometric view,
    The height h of an equilateral triangle in isometric view
    A method for manufacturing a spherical display device, comprising at least one of the settings above.
  7. 　請求項６に記載の球状表示装置の製造方法であって、
    　前記パラメータを設定する工程が、
    　　前記球状の表示装置の半径ｒｕに基づき、前記単位正三角形の一辺Ｌを、数２に基づき演算し、
    　　等角図の正三角形の一辺ａを、数３に基づき演算し、
    　　等角図の正三角形の高さｈを、数４に基づき演算する
    ことの少なくとも何れかを含む球状表示装置の製造方法。
    ［数２］
    　Ｌ＝ｒｕ／０．９５１０５６５１６３
    ［数３］
    　ａ＝Ｌ／ｓｑｒｔ（ｍ＊ｍ＋ｎ＊ｎ＋ｍｎ）
    ［数４］
    　ｈ＝ａ＊ｓｑｒｔ（３）／２     A method for manufacturing a spherical display device according to claim 6, comprising the steps of:
    The step of setting the parameters comprises:
    Based on the radius ru of the spherical display device, one side L of the unit equilateral triangle is calculated based on Equation 2,
    Calculate the side a of the equilateral triangle in the isometric view based on Equation 3,
    and calculating a height h of the equilateral triangle in the isometric view based on Equation 4.
    [Equation 2]
    L = ru / 0.9510565163
    [Equation 3]
    a = L / sqrt (m * m + n * n + mn)
    [Equation 4]
    h = a * sqrt (3) / 2
  8. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程において、前記画素ブロックを作成する工程が、３Ｄプリンタを用いた堆積印刷にて行われる球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    A method for manufacturing a spherical display device, comprising the steps of: creating 20 pixel blocks based on a design of the pixel blocks; and combining the 20 pixel blocks to form a spherical display portion of the spherical display device, wherein the step of creating the pixel blocks is performed by deposition printing using a 3D printer.
  9. 　請求項８に記載の球状表示装置の製造方法であって、
    　前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、前記画素ブロックを、複数の分割ブロックに分割し、前記複数の分割ブロックを接合して各画素ブロックを構成する工程を含む球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 8, comprising the steps of:
    A method for manufacturing a spherical display device, comprising the steps of: creating 20 pixel blocks based on a design of the pixel block; and combining the 20 pixel blocks to form a spherical display portion of the spherical display device, the method including the steps of: dividing the pixel block into a plurality of divided blocks; and joining the plurality of divided blocks to form each pixel block.
  10. 　請求項９に記載の球状表示装置の製造方法であって、
    　前記分割ブロックが、前記画素ブロックの三角形状の各辺を底辺とする二等辺三角形状に分割されてなる球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 9, comprising the steps of:
    A method for manufacturing a spherical display device, in which the divided blocks are each divided into an isosceles triangle having a base on each side of the triangular shape of the pixel block.
  11. 　請求項９又は１０に記載の球状表示装置の製造方法であって、
    　前記３Ｄプリンタで堆積印刷される前記分割ブロック又はその一部の底面が、平面に近い形状である球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 9 or 10, comprising the steps of:
    A method for manufacturing a spherical display device, in which the bottom surface of the divided block or a part thereof printed by the 3D printer has a shape close to a plane.
  12. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、当該画素ブロックを構成する前記第一画素ユニット及び第二画素ユニットにそれぞれ、底面板に発光素子を配置する工程を含む球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    A method for manufacturing a spherical display device, comprising the steps of: creating 20 pixel blocks based on a design of the pixel block; and combining the 20 pixel blocks to form a spherical display portion of the spherical display device, the method including the steps of arranging a light-emitting element on a bottom plate of each of the first pixel units and second pixel units that form the pixel block.
  13. 　請求項１２に記載の球状表示装置の製造方法であって、さらに、
    　球状フレームを構成する工程を含み、
    　前記画素ブロックの設計に基づき、当該画素ブロックを２０面分作成し、当該２０面分の画素ブロックを組み合わせて球状表示装置の球状表示部を構成する工程が、
    　　前記球状フレームの表面に、各画素ブロックを固定し、
    　　各画素ブロックの発光素子を電気的に配線する工程を含む球状表示装置の製造方法。     The method for manufacturing a spherical display device according to claim 12, further comprising:
    Constructing a spherical frame,
    a step of creating 20 pixel blocks based on the design of the pixel blocks, and assembling the 20 pixel blocks to configure a spherical display unit of a spherical display device,
    Fixing each pixel block to a surface of the spherical frame;
    A method for manufacturing a spherical display device, comprising a step of electrically wiring light emitting elements of each pixel block.
  14. 　請求項１に記載の球状表示装置の製造方法であって、
    　前記球状表示部が、半球状又は１／３球、２／３球のいずれかに形成されてなる球状表示装置の製造方法。     A method for manufacturing a spherical display device according to claim 1, comprising the steps of:
    The method for manufacturing a spherical display device, wherein the spherical display portion is formed into any one of a hemisphere, a 1/3 sphere, and a 2/3 sphere.
  15. 　複数の画素ユニットである六角柱状の第一画素ユニットと、五角柱状の第二画素ユニットを隣接して配置した球状の表示装置の設計方法であって、
    　前記球状の表示装置を構成する前記第一画素ユニット及び第二画素ユニットの数と、前記球状の表示装置の直径又は半径と、前記第一画素ユニット及び第二画素ユニットの高さの少なくともいずれかを含むパラメータを設定する工程と、
    　前記表示装置の直径又は半径に基づき、前記球状の表示装置に内接する正二十面体を構成する各正三角形面に対し、前記設定された第一画素ユニット及び第二画素ユニットの数に基づいて、前記球状の表面を多角形で近似したゴールドバーク多面体を構成する六角形の面と五角形の面を、それぞれ単位正三角形の組み合わせで構成するよう、単位正三角形を確定する工程と、
    　前記正三角形面を、各頂点から対向する辺に下ろした垂線で六等分した直角三角形と対応する直角三角形ブロックを、前記単位正三角形を組み合わせた六角形と五角形を底面とし、前記設定された高さを有する第一画素ユニット及び第二画素ユニットを複数組み合わせて設計する工程と、
    　前記直角三角ブロックを反転させた反転直角三角形ブロックと、前記直角三角形ブロックとを組み合わせた二等辺三角形ブロックを設計する工程と、
    　前記二等辺三角形ブロックを１２０°回転させた第一回転二等辺三角形ブロックと、前記第一回転二等辺三角形ブロックをさらに１２０°回転させた第二回転二等辺三角形ブロックと、前記二等辺三角形ブロックとを組み合わせた、前記正二十面体を構成する各正三角形面の一面に相当する画素ブロックを設計する工程と、
    を含む球状表示装置の設計方法。     A method for designing a spherical display device in which a plurality of pixel units, a first pixel unit having a hexagonal prism shape and a second pixel unit having a pentagonal prism shape, are arranged adjacent to each other, comprising the steps of:
    setting parameters including at least one of the number of the first pixel units and the second pixel units constituting the spherical display device, the diameter or radius of the spherical display device, and the height of the first pixel unit and the second pixel unit;
    determining unit equilateral triangles for each equilateral triangular surface constituting a regular icosahedron inscribed in the spherical display device based on a diameter or radius of the display device, based on the set numbers of first pixel units and second pixel units, so that the hexagonal and pentagonal surfaces constituting a Goldberg polyhedron approximating the spherical surface with a polygon are each composed of a combination of unit equilateral triangles;
    a step of designing right-angled triangle blocks corresponding to right-angled triangles obtained by dividing the equilateral triangular surface into six equal parts by perpendicular lines drawn from each vertex to an opposing side, the right-angled triangle blocks having bases of hexagons and pentagons formed by combining the unit equilateral triangles, by combining a plurality of first pixel units and second pixel units having the set height;
    A step of designing an isosceles triangular block by combining an inverted right-angled triangular block obtained by inverting the right-angled triangular block and the right-angled triangular block;
    a step of designing pixel blocks corresponding to one of the equilateral triangular faces constituting the regular icosahedron, the pixel blocks being a combination of a first rotated isosceles triangle block obtained by rotating the isosceles triangle block by 120°, a second rotated isosceles triangle block obtained by further rotating the first rotated isosceles triangle block by 120°, and the isosceles triangle block;
    A method for designing a spherical display device comprising:
  16. 　複数の画素ユニットを隣接して配置した球状の表示装置であって、
    　それぞれが六角柱状で、各六角柱状の端面を閉塞する第一底面板に第一発光素子を配置した、複数の第一画素ユニットと、
    　それぞれが五角柱状で、各五角柱状の端面を閉塞する第二底面板に第二発光素子を配置した、複数の第二画素ユニットと、
    で構成された、球状表示部と、
    　前記第一発光素子及び第二発光素子を点灯駆動させる点灯駆動回路と、
    　前記球状表示部を支持する球状フレームと、
    を備え、
    　各第一画素ユニットの、前記六角柱状を構成する側面は、前記球状の外縁に向かって拡がるよう傾斜されており、
    　各第二画素ユニットの、前記五角柱状を構成する側面は、前記球状の外縁に向かって拡がるよう傾斜されてなる球状表示装置。     A spherical display device having a plurality of pixel units arranged adjacent to each other,
    A plurality of first pixel units each having a hexagonal prism shape, each pixel unit including a first light emitting element disposed on a first bottom plate that closes an end surface of each hexagonal prism;
    A plurality of second pixel units each having a pentagonal prism shape, each pixel unit including a second light emitting element disposed on a second bottom plate that closes an end surface of each pentagonal prism;
    A spherical display unit comprising:
    a lighting drive circuit for driving the first light emitting element and the second light emitting element to light;
    a spherical frame supporting the spherical display unit;
    Equipped with
    A side surface of each of the first pixel units constituting the hexagonal prism is inclined so as to expand toward an outer edge of the sphere,
    A spherical display device in which the side surfaces of each second pixel unit constituting the pentagonal prism are inclined so as to widen toward the outer edge of the sphere.
  17. 　請求項１６に記載の球状表示装置であって、
    　前記球状フレームが、
    　　環状の緯線部と、
    　　前記緯線部上において、該緯線部と交差すると共に、赤道上で互いに離間され、上下を各極点で固定した、環状の複数の経線部と
    を備える球状表示装置。     17. A spherical display device according to claim 16,
    The spherical frame is
    An annular latitude portion;
    a plurality of annular meridian sections which intersect the latitude line section on the latitude line section, are spaced apart from each other on the equator, and have upper and lower ends fixed at respective poles.
  18. 　請求項１６に記載の球状表示装置であって、
    　前記第一発光素子及び第二発光素子が、その発光色を可変としてなる球状表示装置。     17. A spherical display device according to claim 16,
    The spherical display device is configured so that the first light-emitting element and the second light-emitting element have variable light emission colors.
  19. 　請求項１６に記載の球状表示装置であって、
    　前記球状表示部が、半球状又は１／３球、２／３球のいずれかに形成されてなる球状表示装置。     17. A spherical display device according to claim 16,
    The spherical display device is configured such that the spherical display portion is formed in any one of a hemisphere, a 1/3 sphere, and a 2/3 sphere.
PCT/JP2023/038240 2022-10-27 2023-10-24 Spherical display device, and manufacturing method and designing method for spherical display device WO2024090393A1 (en)

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