JP2011243033A - Expansion plan creation method and device for solid body and frame manufacturing device and method, solid body, manufacturing device and method for solid body, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To create an expansion plan for assembling a solid body by folding the expansion plan according to the polygonal line of the expansion plan without cutting or pasting plane raw materials from one plane.SOLUTION: When a conic type expansion plan is created, a regular N-sided plane corresponding to the number of sides N of a rotary sweep-shaped solid body is used, and the plane is equally divided into N (S100 to S110), and the expansion plan obtained by opening the rotary sweep-shaped solid body in a rotary axial direction is arranged in each division area of the plan (S120). In each division area, a line extending from a side edge corresponding to the ridge of the rotary sweep-shaped solid body to the boundary of the division areas in parallel with the contour line of the rotary sweep-shaped solid body is set to an auxiliary line (S130). In each division area, the side edge corresponding to the ridge of the rotary sweep-shaped solid body is set to the first polygonal line of the expansion plan of the rotary sweep-shaped solid body. As for each contour line of the rotary sweep-shaped solid body, a line made by connecting internal points internally dividing the auxiliary line by a predetermined rate (1:1 in a conic type) is set to the second polygonal line of the expansion plan of the rotary sweep-shaped solid body (S140).

Description

  The present invention relates to a three-dimensional development drawing creation method and development drawing creation apparatus, a formwork manufacturing apparatus and a formwork manufacturing method, a three-dimensional object, a three-dimensional object manufacturing apparatus and method, and a program. More specifically, a mechanism for creating a two-dimensional development view of a three-dimensional solid object, a three-dimensional object having a shape capable of assembling the two-dimensional development drawing of the present invention, and a manufacturing method thereof, and such a shape. Formwork manufacturing apparatus and formwork manufacturing method for manufacturing (designing) a formwork used when manufacturing a three-dimensional object, and a three-dimensional object manufacturing apparatus (particularly a mold) having a shape capable of assembling the two-dimensional development of the present invention The present invention relates to a manufacturing apparatus using a frame and a manufacturing method.

  Various shapes of three-dimensional solid objects are conceivable, and how the three-dimensional object is manufactured depends on the shape itself.

  For example, there are strict restrictions on the shape that can be created simply by folding a flat material (such as paper), and there are not many variations of shapes that can be created.

  On the other hand, the inventor of the present application has proposed a mechanism for creating a developed view of a three-dimensional object from a single flat object (see Non-Patent Documents 1 and 2).

Jun Mitani, “Automatic generation method of 3D origami with a swept swept shape”, Japanese Society of Applied Mathematical Sciences Research Group Joint Presentation (Origami Engineering, Room C (Room 204), March 8) Jun Mitani, “16. Automatic generation method of unfolded drawings of 3D origami containing rotating sweep shapes”, 2009 Japan Society for Graphic Science (Session 4: “Figure and Geometry”, May 9, 2009)

  The mechanism described in Non-Patent Documents 1 and 2 is a three-dimensional shape of a rotational sweep expressed as a trajectory formed by rotating a two-dimensional broken line in 360 / N degree increments (N> 2) around the axis of a three-dimensional space. A development view is created from one plane (such as paper). In realizing this, pleats having an appropriate size are arranged between adjacent constituent surfaces constituting the rotational sweep-shaped solid. A development view of a three-dimensional object having a shape in which a swept three-dimensional solid is a basic shape and a wrinkle is added to the outside is created. By increasing the value of N and representing the broken line used as input with a fine line segment and smoothing it, it is possible to create a developed view of a three-dimensional object having an approximately curved surface.

  The first aspect of the present invention provides a mechanism for creating a developed view of a three-dimensional object based on a rotating sweep shape from a single plane by a method different from the mechanism described in Non-Patent Documents 1 and 2. Objective.

  The second aspect of the present invention aims to provide a three-dimensional object having a shape capable of assembling the two-dimensional development view of the present invention and a method for manufacturing the same.

  Furthermore, a third form of the present invention is a formwork for manufacturing (designing) a formwork used when manufacturing a three-dimensional object having a shape capable of assembling the developed view generated in the first form of the present invention. It is an object of the present invention to provide a manufacturing apparatus and a mold manufacturing method, and a manufacturing apparatus (particularly a manufacturing apparatus using a mold) and a manufacturing method of a three-dimensional object having a shape capable of assembling the two-dimensional development view of the present invention. To do.

  The first embodiment of the present invention relates to a process for creating a three-dimensional development, and specifies the ridge line of a rotational sweep-shaped solid that is a solid object having a rotational sweep shape, and the rotational sweep-shaped solid is based on the rotational sweep-shaped solid. A development view of a three-dimensional object having an external protrusion having a triangular cross section at the ridge portion is created on a single plane.

  “Creating a development view with one plane” means that a three-dimensional object can be assembled by folding a two-dimensional development view according to the folding line.

  Preferably, the plane is evenly divided according to the number of angles of the rotational sweep-shaped solid, and a development view in which the rotational sweep-shaped solid is opened in the rotation axis direction is arranged in each divided area of the plane, and in each of the divided areas, A line extending from the edge corresponding to the ridge line of the rotational sweep solid to the boundary of the divided region in parallel with the contour line of the rotational sweep solid is defined as an auxiliary line.

  Then, in each of the divided areas, the edge corresponding to the ridgeline of the rotational sweep solid is the first fold line of the development diagram of the rotational sweep solid, and an auxiliary line is predetermined for each contour line of the rotational sweep solid. A line formed by connecting the internal dividing points that are internally divided at a certain ratio is defined as a second broken line of the development diagram of the rotational sweep solid.

  The second form of the present invention forms a three-dimensional object by assembling the developed view generated in the first form of the present invention by mountain folding or valley folding according to the folding line.

  The 3rd form of this invention is related with the manufacturing method of the solid object which has a shape which can assemble the expanded view produced | generated by the 1st form of this invention. Specifically, a formwork is formed based on a development view of a three-dimensional object having a triangular shape in cross section at the ridge line portion of the rotation sweep-shaped solid, based on a rotational sweep-shaped solid that is a three-dimensional object having a rotational sweep shape. . And the target solid thing is manufactured using this formwork. For example, the formwork is assembled so as to represent the outer shape of a three-dimensional object having an external protrusion having a triangular cross section at the ridge line portion of the rotational sweep-shaped solid, based on the rotational sweep-shaped solid. Then, a material such as resin or metal is filled in the space formed by the assembled formwork, the filled material is cured, and the formwork is removed after the filled material is cured.

  Note that the mechanism according to the present invention (particularly with respect to the manufacture of a three-dimensional object is the point of forming a formwork) can also be realized by software using an electronic computer (computer). It is also possible to extract the stored recording medium as an invention. The program may be provided by being stored in a computer-readable storage medium, or may be provided by distribution via wired or wireless communication means.

  According to the first embodiment and the second embodiment of the present invention, it is possible to create a development view of a three-dimensional object based on a rotating sweep solid that is a three-dimensional object having a rotating sweep shape from one plane. A three-dimensional object based on a rotational sweep-like solid can be assembled by folding according to the folding line of the developed view created according to the present invention.

  This method creates a developed view of a three-dimensional object having external projections having a triangular cross section at the ridge line portion of a rotational sweep-shaped solid. In the present invention, the element to be placed outside the rotational sweep-shaped solid is a protrusion having a triangular cross section, and the mechanisms described in Non-Patent Documents 1 and 2 are eclipsed, and there is a difference between them. The shape of the object is also different between the two.

  As a result, variations in shapes that can be made simply by folding flat materials (such as paper) without cutting or pasting them can be expanded, and the range of application can be expanded in terms of design and industrial applications.

  Furthermore, according to the 3rd form of this invention, by forming a formwork using the 1st form and forming a solid thing using this formwork, the ridgeline part of a rotation sweep-like solid It is possible to easily manufacture a three-dimensional object having external protrusions having a triangular cross section.

It is a figure explaining the basic method in the case of creating a conical development view. It is a figure explaining another example of the basic technique in the case of creating a conical development view. It is a figure explaining the basic method in the case of creating a cylindrical development view. It is a figure explaining the loss prevention processing applied to a cone type. It is a figure explaining the basic view of a tiling process. It is a figure (N = 3) which shows an example of the basic element of the rotation sweep-like solid arranged by tiling processing. It is a figure (N = 4) which shows an example of the basic element of the rotation sweep-like solid arranged by tiling processing. It is a figure (N = 6) which shows an example of the basic element of the rotation sweep-like solid arranged by tiling processing. It is FIG. (1) explaining the outline | summary of application of a tiling process. It is FIG. (2) explaining the outline | summary of application of a tiling process. It is a figure explaining the example of 1 composition of the development drawing creation device of this embodiment. It is the flowchart which showed an example of the procedure which produces a cone-shaped development view. It is the figure (the 1) showing visually the process in which a development figure is created in the shape of a cone from the solid shape included in a finished product. It is the figure (the 2) showing visually the process in which a development figure is created with a cone shape from the solid shape included in a finished product. It is the figure (the 3) showing visually the process in which a development figure is created with a cone shape from the solid shape included in a finished product. It is a figure which shows the example of a work which can assemble a conical development view. It is the flowchart which showed an example of the procedure which produces a column-shaped development view. It is the figure (the 1) showing visually the process in which a development figure is created with a cylindrical form from the solid shape included in a finished product. It is the figure (the 2) showing visually the process in which a development figure is created in the shape of a cylinder from the solid shape included in a finished product. It is a figure which shows the example of a work which can assemble a cylinder-shaped development view. It is a figure which shows the detail of a cone-shaped 1st work example. It is a figure which shows the detail of the 2nd example of a cone type work. It is a figure which shows the detail of a cone-shaped 3rd work example. It is a figure which shows the detail of the 4th example of a cone-shaped work. It is a figure which shows the detail of a column-type 1st work example. It is a figure which shows the detail of a column-type 2nd work example. It is a figure which shows the detail of a column-type 3rd work example. It is a figure which shows the detail of the column-shaped 4th work example. It is a figure which shows the example of a work to which tiling processing is applied. It is a figure explaining the example of 1 composition of the formwork design device of this embodiment. It is a flowchart which shows an example of the production | generation process sequence of a formwork drawing. It is a figure explaining the example of 1 composition of the solid thing manufacture device of this embodiment. It is a flowchart which shows an example of the solid thing manufacturing process procedure of this embodiment.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The description will be made in the following order.
1. Basic concept (outline, conical type (broken line, almost curved), cylindrical type, loss prevention, tiling treatment)
2. System overview (basic configuration, operation screen, configuration by electronic computer)
3. Drawing drawing method (conical type, cylindrical type)
4). Sample works (conical, cylindrical, tiling)
5). Manufacturing method of solid objects (form design device, form design process, solid object manufacturing device, solid object manufacturing process)

<Basic concept>
[Overview]
The method for creating a development view of the present embodiment relates to a method for automatically generating a development view for producing a three-dimensional shape from a single plane material (paper or the like). This embodiment is intended for a three-dimensional object including an axisymmetric three-dimensional shape generated by a rotation sweep, and as a design method for creating a development view of such a three-dimensional object with a single planar object, rotation It is characterized in that it takes a method of adding a protrusion (referred to as an external protrusion) having a triangular cross section to the ridgeline of the sweep solid QJ.

  Here, when automatically generating a development drawing of origami containing an axisymmetric three-dimensional shape (rotary sweep-like three-dimensional QJ), it is preferable to automatically generate the geometric data of the completed three-dimensional shape and predict the completion. The figure is displayed by CG (CG (Computer Graphics)). The process of creating the development view can be realized by any single configuration or any combination of hardware and software.

  Preferably, when assembling the finished product from the developed view (during processing), the broken lines where the broken lines are concentrated are thinned out so that the material is not destroyed. Preferably, a change instruction from the operator is received on the CG display, and the change is reflected in the development view. While looking at the completed drawing, you can easily design and trial on the computer, and you can easily design a variety of shapes.

  Rotational sweep is a technique for generating an axisymmetric solid shape by rotating a two-dimensional broken line (or curved line) about an axis in a three-dimensional space, and uses existing CG (computer graphics) and CAD (electronic). This is one of the shape generation operations generally used in computer software for computer-aided design. The two-dimensional fold line (or curve) corresponds to the ridgeline of the rotational sweep solid QJ, and the ridgeline is a line that forms the edge of each surface at the boundary of the two surfaces of the rotational sweep solid QJ. .

  The target three-dimensional shape of the rotational sweep (the rotational sweep-shaped solid QJ) is a polyhedron represented as a locus formed by rotating a two-dimensional fold line (or curve) around the axis in 360 / N degree (N> 2) increments. Expressed. Since the value of N is increased and the broken line used as input is expressed by a broken line with fine line segments and smoothed, a curved origami can be created approximately.

  The external protrusion having a triangular cross section is essentially unnecessary for the original three-dimensional shape, and it may not be preferable to protrude to the front side. However, considering that the external protrusion is also a part of the work (design), there is an advantage that the target shape can be expressed with a simple development view. Further, by smoothing the input broken line, there is an advantage that a three-dimensional object having a smooth curved surface can be created with little effort.

  In general, there are severe restrictions on the shape that can be created by simply folding a flat material (such as paper) without cutting or pasting it, and the shapes that can be created do not vary greatly. However, by applying the mechanism of the present embodiment, a new three-dimensional object that includes a three-dimensional shape of a rotational sweep and has an external protrusion having a triangular cross section added to the ridgeline portion of the rotational sweep-shaped three-dimensional object is obtained from a single planar object. Can be assembled. By defining the ridge line with a curve, a shape including a curved surface can be created.

  It is also possible to generate a drawing of a formwork (formwork figure) when manufacturing a three-dimensional object based on a development view generated by applying such a development view generation method. By assembling the formwork generated based on the formwork drawing, filling the inside space with a material such as resin or metal and hardening it, and then removing the formwork (sand mold etc.) Can be easily manufactured as a three-dimensional object having an external projection with a triangular cross section at the ridgeline portion.

  It becomes possible to design shapes with a wide range of applications, both in terms of design and industrial applications. For example, it can be used for the design of gifts, wrapping and new packages. It can also be used for costume decorations (corsages). Furthermore, it can be applied to furniture such as lampshades and product designs that require design. Furthermore, it may be provided as design software to companies that design and manufacture packages, lamp shades, and costume decorations. It can also be provided as a figurine having external projections having a triangular cross section.

  Here, when creating a development drawing or a formwork of a three-dimensional object obtained by a rotation sweep, basically, the target shape is obtained by rotating a broken line (or curve) in increments of 360 / N. The development surface is basically a trapezoid, and in a special case, the upper base becomes a triangle having a length of zero, and a three-dimensional shape can be constituted by a set of these development surfaces.

  Regardless of whether the development plane is a triangle or a quadrangle (or a combination thereof), a development view can be created with a rectangular (rectangular) planar object, which is referred to as a cylinder (or cylinder). On the other hand, when the development surface has a triangle (and may have a trapezoidal shape), a development view can be created with a regular N-square planar object, which is referred to as a conical shape.

  In any case, a basic rotational sweep solid can be arranged in a plurality of layers so as to be in close contact with each other (see FIGS. 10, 11A, 11B, and 11C described later).

  The development drawing creation method of this embodiment is based on a sectional view obtained by cutting the development shape after folding the target shape at a contour plane (horizontal plane) when the axis of the rotation sweep is determined vertically in the three-dimensional space. Thus, a projection having a triangular cross section is added to the apex of the shape of the cut surface. Here, if the dimensions of the protrusions having a triangular cross section are set in any way, a solid having a swept solid QJ having a desired shape from a single flat object and external protrusions having a triangular cross section added to each ridgeline. Decide whether you can create a development view of the object. Hereinafter, this point will be described for each of the conical type and the cylindrical type.

[Cone type: Polyline]
The conical development view is a technique for creating a development view based on a regular N-gonal plane (such as paper). In the case of this example, it is expanded so as to make up for it by arranging an area that forms an external projection of a triangular cross section of an appropriate size in the gap of the development surface that forms a solid object having at least a conical shape that contains the target shape. Realize the figure.

  In order to arrange a triangular cross section having an appropriate size in the gap between the development planes, it is necessary to insert an area of a triangle (triangular cross section area AT) between two basic development planes. The conditions are discussed below.

  FIG. 1 is a diagram for explaining a basic method for creating a conical development view. FIG. 1A is a diagram showing a part of a cone (N pyramid) whose one surface is an isosceles triangle. FIG. 1B is a horizontal sectional view of a part of the cone. Incidentally, FIG. 1 (2) shows the case of N = 4.

  The ridge line OB is provided with an external protrusion having a triangular cross section. The ridge line corresponds to the first fold line in the development view. Let A be the intersection of the perpendicular from the vertex O to the base BB ″ on the first surface S1 and the base BB ″. Similarly, let A ′ be the intersection of the perpendicular from the vertex O to the bottom of the second surface S2 and the bottom. The two vertices on the bottom side of the external protrusion are C and C ', respectively, and the intersection (the middle point of the bases C and C') with the perpendicular from the vertex O to the bottom connecting the vertices C and C 'is D. In FIG. 1B, an angle ∠AO′B formed by the perpendicular line O′A and the ridge line O′B is α. α is “360 ° / N × 1/2 = 180 ° / N”.

  FIG. 1 (3) is a development view of a part of the three-dimensional object shown in FIG. 1 (1). In the following, it is shown that the three-dimensional object shown in FIG. 1A can be assembled from one plane object (such as paper) by appropriately setting the length of the line segment BC. When creating a development view of the rotational sweep-like solid QJ having external projections having a triangular cross section, the triangular cross section area AT is inserted between two adjacent basic development surfaces S1 and S2. This is shown in the development view of FIG.

  Since the rotational sweep-shaped solid QJ is an N pyramid, the plane is divided into N areas, and the basic development planes are evenly arranged in the divided areas. For example, the boundary line of each divided region where the two basic development surfaces S1 and S2 are arranged is defined as OE. The side on the basic development surface S2 side corresponding to the ridge line OB is defined as OB '. A line on the development corresponding to the ridge line (bus line) is a first broken line.

  A portion that forms a triangular cross-sectional area AT with respect to the boundary line OE is arranged in line symmetry. That is, the portion of the triangular cross-sectional area AT is arranged symmetrically with respect to the boundary line OE between the side OB on the basic development surface S1 side and the side OB 'on the basic development surface S2 side. Accordingly, ΔOBC and ΔOB′C ′ are congruent (ΔOBC≡ΔOB′C ′) in both the three-dimensional object and the developed view (referred to as relational expression 1).

  In the three-dimensional object, ΔOBC ′ and ΔOAB are arranged on the same plane, and ΔOBC and ΔOA′B are arranged on the same plane (referred to as relational expression 2). On the other hand, in the developed view, the points A, B, and C are arranged on the same straight line.

  From FIG. 1 (2), CD = BCcos α (represented by relational expression 3). From FIG. 1 (3), since the basic development surface S1 side and the basic development surface S2 side have symmetry with respect to the boundary line OE, the boundary line OE and the straight line CC ′ are perpendicular (OE⊥CC ′), and , ΔAOE and ΔDCE are similar (ΔAOE∽ΔDCE). Therefore, the angle (∠DCE) formed by the straight line DC and the straight line CE is equal to α. Thus, CD = ECcos α (relationship expression 4). From relational expression 3 and relational expression 4, line segment BC and line segment EC have the same length (BC = EC).

  That is, when creating a developed view of a rotating sweep-shaped solid QJ with an external protrusion having a triangular cross section added to the ridgeline and assembling the rotating sweep-shaped solid QJ, BC = EC (B′C in FIG. 1 (3). A line segment formed by connecting the point C (point C ′) such that “= EC ′) to the vertex O side may be set as the second broken line in the development view. Incidentally, as inferred from the developed view (FIG. 1C), the triangle ΔCC′E at the apex of the regular N-gonal planar object is an unnecessary part and may be cut off.

  FIG. 1 (4) is a diagram for explaining a case where the above conditions are generally developed. A horizontal line having a predetermined length is arranged in parallel with the base BB ″ further below the base BB ″ side of the isosceles triangle, and a quadrangle is formed between the base BB ″ of the isosceles triangle. The state is equivalent to expressing the ridgeline of the rotational sweep-like solid QJ by “a broken line having a certain condition”. The term “folded line having a certain condition” is based on the fact that the line needs to be monotonously increasing or monotonically decreasing in the axial direction of the rotating shaft in order to prevent penetration (Non-Patent Document 1, 2) 6.2).

  In this case, it may be considered in the same manner as described above, focusing on the horizontal line passing through the portion where the broken lines intersect. For example, in FIG. 1 (4-1), let a be the intersection of the perpendicular from the vertex O to the newly added horizontal line, b be the vertex of the quadrangle on the horizontal line, and e be the intersection of the horizontal line and the boundary line. Further, the base that forms the external protrusion (see FIG. 1 (4-2)) of the triangular cross section formed by forming a quadrangle with the base BB ″ of the isosceles triangle is cc ′.

  In the developed view, the points a, b, c, and e are arranged on the same straight line. Therefore, by making the line segment bc and the line segment ec the same length (bc = ec), one piece of the conical shape can be obtained. It is possible to create a development view of a rotational sweep-like solid QJ with a regular N-gonal flat object. Incidentally, the triangle Δcc′e at the apex of the regular N-gonal planar object is an unnecessary part and may be cut off.

[Cone type: almost curved]
FIG. 1A is a diagram for explaining another example of the basic method in the case of creating a conical development view. Although the basic method is the same as that described above, a description will be given of how to deal with a case in which the ridgeline of the target three-dimensional object (rotary sweep-shaped solid QJ) is substantially curved. In such a case, the same method may be applied by replacing the above-mentioned horizontal line with a contour line, as estimated from focusing on the horizontal line at the corner of the broken line. As can be seen from the figure, it is possible to express a curved line by expressing the ridgeline as a broken line with fine line segments and smoothing it, so that the horizontal line (contour line) at the corner of the broken line showing the curve The focused process may be applied as described above.

  For example, FIG. 1A (1) shows an overall outline of a three-dimensional object that includes a rotational sweep-like solid QJ whose ridgeline is a curve and in which external protrusions having a triangular cross section are added to the ridgeline. In the figure, a contour line a and a region dividing line b are shown. A line on the development corresponding to the ridge line (bus line) is a first broken line.

  FIG. 1A (2) is a view showing a quarter portion (a portion including the external projection of the arrow X) of the three-dimensional object shown in FIG. 1A (1). FIG. 1A (3) is a view showing a certain layer portion (a portion indicated by an arrow Y) in the ¼ partial view shown in FIG. 1A (2). This figure corresponds to FIG. 1 (4-2). FIG. 1A (4) is an overall development view of the three-dimensional object shown in FIG. 1 (1). FIG. 1A (5) is a development view of a part of the three-dimensional object shown in FIG. 1 (1) (part of FIG. 1A (2)).

  Similar to the description in FIG. 1, when creating a developed view of a rotating sweep solid QJ in which triangular projections are added to a substantially curved ridgeline and assembling the rotating sweep solid QJ, FIG. 5) A line segment formed by connecting points C such that BC = EC may be used as the second broken line in the development view. Incidentally, as inferred from the developed views (FIGS. 1 (4) and (5)), the triangle Δcc′e at the apex portion of the regular N-square planar object is an unnecessary portion and may be cut off.

  As described above, in the case of the conical shape, a regular N-gonal plane object is used, and the regular N-gonal shape corresponding to the vertex O as the center of the development view and the contour line (including the horizontal line) of the rotational sweep-shaped solid QJ is used. A line formed by connecting an internal dividing point that equally bisects the auxiliary line is defined as a line obtained by extending a line segment parallel to the side from the side (line) corresponding to the ridge line to the boundary line of the divided area as a second line. By using the fold line, it is possible to create a development view of the rotational sweep solid QJ having a desired shape. When the ridge line is a straight line, that is, when the rotational sweep solid QJ is indicated by a broken line connecting a plurality of points, the line segment connecting the vertex O and each of the inner dividing points is the second broken line. That's fine. As described above, the line corresponding to the ridge line is the first broken line.

  In FIGS. 1A (4) and 1A (5), the ridgeline is shown as a curve, so it is not shown. However, when the basic shape of the rotating sweep solid QJ is shown as a foldline, the horizontal line passing through the intersection of the foldlines can be extended. You may add the 3rd broken line by connecting the intersection (C, C ', c, c' of Drawing 3 (3)) of an auxiliary line and the 2nd broken line. Although only a quarter portion is shown in FIG. 1, by performing this operation as a whole, the third fold line is composed of, for example, the line segment CC ′ and the line segment cc ′ of FIG. (See FIG. 8C described later). If the third fold line is not added, the ridge line of the solid object that is completed when the development drawing is assembled can be curved, and as a result, the surface of the completed solid object can be curved.

[Cylinder type]
The development view of a cylindrical type (cylindrical type) is a method of creating a development view based on a rectangular (rectangular) plane (paper or the like). In the case of this example, a development view is realized by making up an area having an external projection of a triangular cross section of an appropriate size by placing it in a gap between the development surfaces forming a cylinder containing the target shape. It becomes a pattern which pastes a development view in the shape of a cylinder.

  As with the cone type, in order to place a triangular cross section of an appropriate size in the gap between the development planes, a triangular area (triangular section area AT) is formed between the two basic development planes. Need to get in. The conditions are discussed below.

  FIG. 2 is a diagram for explaining a basic method for creating a cylindrical development view. FIG. 2A is a diagram showing a part of the ridgeline of the rotational sweep-shaped solid QJ. FIG. 2 (2) is a horizontal sectional view of a part of the rotational sweep solid QJ.

  An external protrusion having a triangular cross section is added to the ridgeline Bb. A line on the development corresponding to the ridge line (bus line) is a first broken line. Let A be the intersection of the vertical and horizontal lines from the point O '. An angle related to the central angle of the cross section is α. Α is “360 ° / N × 1/2 = 180 ° / N”, where N is the number of divisions of the region with respect to the rectangle. The two vertices on the bottom side of the external protrusion are C and C ', respectively, and the midpoint of the bases C and C' connecting the vertices C and C 'is D.

  FIG. 2 (3) is a development view of a part of the three-dimensional object shown in FIG. 2 (1). First, paying attention to the lower side of the rectangle, the length of the line segment BC (line segment B′C ′) is set appropriately, and the result is shown in FIG. Indicates that a three-dimensional object can be assembled. When creating a development view of the rotational sweep-shaped solid QJ, the triangular cross-sectional area AT is inserted between the two adjacent basic development surfaces S1 and S2. This is shown in the development view of FIG.

  As in the case of the conical shape, the triangular section area AT is arranged with symmetry with respect to the boundary line of the divided area, so that the midpoint D of the bases C and C ′ is arranged on the boundary line of the divided area. Is done. In the developed view, the points A, B, C, D, and C′B ′ are arranged on the same straight line.

  Here, from FIG. 2 (2), CD = BCcos α (referred to as relational expression 3 ′), and CD: BC = cos α: 1. That is, on the development view, the point C is arranged at a position that divides the line segment DB into cos α: 1.

  The same can be said even when focusing on the upper side of the rectangle. That is, the two vertices on the upper side of the external protrusion are c and c ', respectively, and the midpoint of the upper sides c and c' connecting the vertices c and c 'is d. The midpoint d of the upper sides c and c 'is arranged on the boundary line of the divided area. In the developed view, the points b, c, d, and c'b 'are arranged on the same straight line.

  Here, from FIG. 2 (2), cd = bccosα = BCcosα (referred to as relational expression 3 ″), and cd: bc = cosα: 1. That is, on the developed view, the point c is a line segment db. Is arranged at a position internally dividing cos α: 1.

  By satisfying such a relationship, it is possible to create a developed view of the rotational sweep-like solid QJ with a single rectangular flat object using a cylindrical shape.

  In other words, in the case of a cylindrical type, an extension that extends to the boundary line in parallel with the upper side (lower side) of each divided area of the developed view (rectangle) corresponding to the horizontal line of the rotary sweep-like solid QJ using a rectangular plane object A line segment formed by connecting internal dividing points that are cos α (boundary line side) of a line (corresponding to BD in the figure): 1 (vertex side of the basic development plane) is defined as a second broken line in the development drawing. Thus, it is possible to create a development view of a rotational sweep solid QJ having a desired shape. When the ridgeline is a straight line, that is, when the rotational sweep-like solid QJ is indicated by a broken line connecting a plurality of points, the line segment connecting the aforementioned internal dividing points may be set as the second broken line.

  Although not shown, when the ridgeline of the target three-dimensional object (rotary sweep-shaped solid QJ) is substantially indicated by a curve, the same method may be applied by replacing the above-mentioned horizontal line with a contour line. When the basic shape of the rotational sweep-shaped solid QJ is represented by a broken line, an auxiliary line formed by extending a horizontal line passing through the intersection of the broken lines and the intersection of the second folded line may be connected to add a third broken line. . If the third fold line is not added, the ridgeline of the three-dimensional object that is completed when the development view is assembled can be curved.

[Damage prevention]
FIG. 3 is a diagram for explaining a loss prevention process applied to the conical shape. When assembling (creating) a three-dimensional object from a development created in a conical shape, as shown in FIGS. 3 (1-1) and 3 (2-1), at a point (vertex) where a plurality of broken lines intersect, There is a risk of tearing during processing of the crease and during folding operation.

  As a countermeasure, in this embodiment, when this method is not applied, the line segments are gathered so that the broken lines do not intersect at a portion where the broken lines gather (end point on the boundary side with other divided regions: arrow A in the figure). Is moved a fixed distance in the direction away from the vertex (region boundary).

  As shown in FIGS. 3 (1-2) and 3 (2-2), this loss prevention process may be applied to all the broken lines toward the apex. Or you may process by thinning. For example, as shown in FIG. 3 (1-2), when the number of line segments sharing the same vertex is 3 or more, the end points are moved away from the vertex in each of the third and subsequent line segments except the two. Move a certain distance. Alternatively, as shown in Fig. 3 (2-3), when there are three or more line segments that share the same vertex, the direction in which the endpoints are separated from the vertex in every other line segment (every other in the figure) Move to a certain distance.

  By taking a countermeasure for such loss prevention and outputting a development view on paper or the like, the broken line is not concentrated on the apex portion, and tearing can be prevented.

  Incidentally, the loss prevention treatment may be applied to the cylindrical type, but in many cases, the necessity is poor. When creating a development view with a cylindrical shape, there is no conical apex portion, and in most cases, the folding line is concentrated in one place with one second line corresponding to the ridge line (bus line). Since it is limited to one third broken line corresponding to the broken line and the horizontal line, it may be considered that there is little significance in applying the loss prevention processing described here.

[Tiling process]
4A to 6A are diagrams illustrating the tiling process. Here, FIG. 4 is a diagram for explaining the basic concept of tiling processing. 5 to 5B are diagrams illustrating examples of basic elements of the rotational sweep-shaped solid QJ arranged by the tiling process. 6A to 6A are diagrams illustrating an outline of application of the tiling process.

  It is also possible to create a single planar object in which a plurality of three-dimensional objects having triangular projections on the ridgeline of the rotational sweep-shaped solid QJ are arranged (laid). Such a mechanism is called tiling. However, the tiling process is not applicable to all rotational sweep-like solid QJs, and can be applied only to those that satisfy certain conditions. Hereinafter, a method for creating a development view of a shape (tiling pattern) in which three-dimensional origami having external projections having a triangular cross section is spread will be described.

  In a tiling process applied to three-dimensional origami laying or the like, regular polygons that can be filled (that can be tiling) are regular triangles (1-1) and regular squares (1) as shown in FIG. -2) and regular hexagon (1-3). Making a shape in which three-dimensional origami is placed at each vertex from one piece of paper is called three-dimensional origami laying (tiling process).

  As shown in FIG. 4 (2), the basic idea of the tiling process is to place a three-dimensional origami at the position indicated by the arrow A in the figure so as to connect it to the place indicated by a circle in the figure. It is to arrange origami. That is, three-dimensional objects (for example, three-dimensional folded paper) assembled in a conical development view with N = 6, 4, 3 are arranged. In a conical development, a plane of any size can be filled with the same pattern. Tiling processing cannot be applied to a cylindrical development. In other words, the conditions for realizing this are as follows. First, the developed view of the swept three-dimensional QJ (three-dimensional origami) is conical, and the regular polygons that can be tiled are regular triangles, regular squares, regular sixs. That is three of the squares.

  As a condition that can be realized from the procedure when laying out a plurality of development views, as shown in FIG. 4 (3), the last line segment constituting the bus line forming the ridgeline of the rotating sweep solid QJ is made horizontal. That is the point. In this way, it is possible to tile a developed view of the conical solid origami with N = 6, 4, 3 at the locations indicated by the arrow A shown in FIG.

  Like the example of FIG. 4 (3-1) and FIG. 4 (3-2), the last element of the bus-line which makes a ridgeline should just be horizontal, and the shape of other parts is fundamentally unquestioned. It is not essential that all the three-dimensional origami papers to be tiled have the same shape. However, in order to perform tiling, as can be seen from the development shown in FIG. 6A, the width of the ridges of each solid to be connected (the interval between the first fold line (ridge line) and the second fold line) Need to be the same (this is referred to as a “tiling constraint”). Hereinafter, for the sake of explanation, the input in FIG. 4 (3-1) will be described as an example.

  For the input of FIG. 4 (3-1), a development view of N = 3, 4, 6 is generated in a conical shape. For example, when N = 3, a shape as shown in FIG. 5 can be obtained. When N = 4, a shape as shown in FIG. 5A can be obtained. When N = 6, a shape as shown in FIG. 5B can be obtained. In each figure, (1) is an external view, and (2) is a development view.

  Here, when attention is paid to FIG. 5 when N = 3, the outer periphery of the developed view is a cut line, and since it is unnecessary, it is as shown in FIG. As shown in FIG. 6 (2), N = 3 solid origami (shown in FIG. 5 and FIG. 6 (1)) is placed on each vertex of the regular hexagonal tiling, and the outward folding line is extended. The tiling process is completed by connecting to the broken line of the adjacent development. The reason why the end of the input bus is horizontal is to enable this connection. Arbitrary numbers can be repeatedly arranged, and the shape of other elements other than the last element of the bus bar is not required. For example, the input example of FIG. 4 (3-2) may be used. it can.

  The same applies to the tiling of a regular square or a regular triangle. For example, as shown in FIG. 6A (1), N = 4 three-dimensional origami (see the figure shown in FIG. 5A) is placed on each vertex where a regular square is tiled, and the folding line extending outward is extended and adjacent. The tiling process is completed by connecting to the broken line in the development view. As shown in FIG. 6A (2), N = 6 three-dimensional origami paper (see the figure shown in FIG. 5B) is placed on each apex obtained by tiling equilateral triangles, and the fold line extending outward is extended and adjacently developed. The tiling process is completed by connecting to the broken line.

<System overview>
FIG. 7 is a diagram for explaining a configuration example of the development drawing creation apparatus according to the present embodiment. Here, FIG. 7A is a block diagram showing an example of the configuration of the development drawing creation apparatus of the present embodiment. FIG. 7B is a block diagram illustrating another configuration example (when configured with an electronic computer) of the development drawing creation apparatus 100.

[Basic configuration]
FIG. 7A is a block diagram showing a configuration example of the development drawing creation apparatus of the present embodiment. The developed view creation apparatus 100 of this embodiment includes a three-dimensional shape specifying unit 110, a storage unit 130, a display control unit 150, a developed view creation unit 170, a print control unit 180 (image formation control unit), and a main control unit 190.

  The three-dimensional shape specifying unit 110 specifies the basic shape of the target three-dimensional object. As the three-dimensional shape specifying unit 110, for example, a method of specifying the basic shape of a three-dimensional object from an actual three-dimensional object with a three-dimensional (3D) scanner or the like can be used. When a 3D scanner is used, an object can be scanned with a laser beam to obtain point cloud data having three-dimensional coordinates, and various objects can be efficiently and three-dimensionally modeled and analyzed. . It is also possible to take a method of reading a two-dimensional drawing or photograph of a three-dimensional object with a two-dimensional (2D) scanner and specifying the basic shape of the three-dimensional object from the data. These methods using a scanner device require a scanner device, but have the advantage of not requiring operator input.

  Alternatively, the three-dimensional shape specifying unit 110 may use data of drafting (graphic) software. In this case, there is an advantage that it is not necessary to waste the already created graphic data, a scanner device is unnecessary, and the operator can save the trouble of inputting the basic shape of the three-dimensional object.

  Furthermore, the three-dimensional shape specifying unit 110 may accept an input of a line (specifying coordinates) for specifying a basic shape from an operator on an operation screen using a GUI (Graphical User Interface). There is an advantage that it is possible to create a developed view of a three-dimensional object even when there is no data of a scanner device or drafting (graphic) software, although a special device is not required although an operator's input is troublesome.

  Here, the “target three-dimensional object” in the present embodiment targets a three-dimensional object having a rotational sweep shape. The completed three-dimensional object includes a rotating sweep-shaped solid (basic), and has an external protrusion having a triangular cross section at the ridge line portion of the rotating sweep shape.

  The storage unit 130 stores data (such as three-dimensional three-dimensional data and development view data) used in various processes. The display control unit 150 performs various screen displays using various display devices such as a liquid crystal display device and a CRT display device.

  Based on the basic shape (rotational sweep shape) of the three-dimensional object specified by the three-dimensional shape specifying unit 110, the development drawing creation unit 170 is a three-dimensional object having an external protrusion having a triangular cross section at the ridge line portion of the rotation sweep shape. Create an exploded view.

  The print control unit 180 prints the developed view generated by the developed view creation unit 170 on a flat object (for example, paper) using a printing apparatus. The main control unit 190 controls each functional unit of the development drawing creating apparatus 100.

  In detail, the development drawing creation unit 170 includes a ridge line identification unit 172, a creation method identification unit 174, and a broken line identification unit 178.

  The ridge line specifying unit 172 specifies a ridge line (bus line) of a three-dimensional object having a rotational sweep shape. The broken line specifying unit 178 sets the first line on the development corresponding to the ridge line (bus line) as the first broken line.

  As a method for specifying the ridge line, when the solid shape specifying unit 110 specifies a shape from an actual three-dimensional object, the ridge line of the three-dimensional object is specified from the specified shape data. Further, when the three-dimensional shape specifying unit 110 receives an input of a line and coordinates for specifying the basic shape of the object on the operation screen using the GUI, the development drawing creation unit 170 uses the information on the input lines and coordinates to read the three-dimensional object. Identify the ridgeline.

  The creation method specifying unit 174 has a function of an operation unit, and accepts designation of the number of divisions N of a two-dimensional plane, whether to create a development view in a conical type or a cylindrical type, whether or not a tiling process is performed, etc. To determine the format of the development. For example, when the three-dimensional shape specifying unit 110 specifies a basic shape from an actual three-dimensional object (using a three-dimensional scanner or the like), the creation method specifying unit 174 sets the division number N to the number of faces of the specified basic shape. Align. The basic shape can be made different from the actual three-dimensional object by receiving an input of the number of divisions N different from the number of faces of the basic shape. In addition, the creation method specifying unit 174 receives the designation of the division number N when the solid shape specifying unit 110 receives a line or coordinate input and specifies the basic shape of the three-dimensional object.

  The broken line specifying unit 178 determines a broken line of the developed view according to a predetermined procedure according to the creation method determined by the creating method specifying unit 174. For example, the broken line specifying unit 178 first divides the plane into N pieces, and uniformly arranges the shape of the basic development plane determined by the ridgeline and the division number N in each of the divided areas. After that, the point at which the first line on the development view corresponding to the ridgeline (bus line) of the rotational sweep-shaped solid intersects the second line (side) on the development view corresponding to the contour line (horizontal line) 1 intersection. Further, the broken line specifying unit 178 sets a point that intersects the boundary of the region when the second line is extended to the boundary of the region as the second intersection.

  Then, the broken line specifying unit 178 sets a point that internally divides between the first intersection and the second intersection at a predetermined ratio. As described above, the internal dividing point is a midpoint in the case of a conical shape, and is a point where cos (π / N): 1 in the case of a cylindrical shape. And a 2nd broken line is added so that the internal dividing point about each contour line (horizontal line) may be connected.

  The fold line specifying unit 178 further specifies an intersection between the added second fold line and the extension of the second line, and adds a third fold line so as to connect the intersections.

[Operation screen]
Although not shown in the drawing, the display control unit 150, as will be understood from the description in the basic concept, information on whether to expand in a conical shape or a cylindrical shape (cylindrical shape), the number of divisions N, and a basic rotational sweep shape. An operation screen for accepting an input of a broken line indicating a bus (ridge line) defining a solid is presented. The development drawing creation unit 170 adds various line segments according to the above-described derivation process based on the information received by this operation.

  Further, the display control unit 150 presents a 3D model indicating the state of the finished product. Preferably, the process of assembling a three-dimensional object from the created development view or the reverse process is displayed as an animation. Preferably, a change operation for the 3D model is directly received and reflected in the development view. That is, a change instruction is received on the displayed three-dimensional schematic diagram, and a development view is recreated according to the received information. For example, the change instruction is automatically reflected on the polygonal line input screen, and the same processing is repeated to present a development view or 3D model after the change.

  The development of various three-dimensional objects and their finished products (for example, origami works) can be done with a simple interface in which an actual three-dimensional object is read by a scanner or an operator inputs a broken line with a pointing member such as a mouse on the screen. Can design. Since the folded shape is displayed on the screen by 3DCG technology, trial and error can be performed without folding an actual plane object (paper or the like). Usability is improved by enabling trial and error not only by the change operation from the broken line input but also by the change operation from the 3D model.

[Configuration by electronic computer]
FIG. 7B is a block diagram of another configuration example of the development drawing creation apparatus 100. Here, a more realistic hardware configuration of the control mechanism of the development drawing creation process constructed from a microprocessor or the like that executes software using an electronic computer such as a personal computer is shown.

  That is, in the present embodiment, the mechanism of the development diagram creation apparatus 100 that performs the development diagram creation processing and the control processing related to this processing is not limited to being configured by the hardware processing circuit, but based on the program code that realizes the function. It is realized by software using an electronic computer (computer). Therefore, a program suitable for realizing the mechanism according to the present embodiment by software using an electronic computer (computer) or a computer-readable storage medium storing this program is extracted as an invention. By adopting a mechanism that is executed by software, the processing procedure and the like can be easily changed without changing hardware.

  The series of development drawing creation processes described above can be realized not only by hardware or software alone but also by a combined configuration of both. When executing processing by software, a program showing the processing procedure is installed (installed) in a storage medium in a computer embedded in hardware and executed, or a general-purpose electronic computer capable of executing various types of processing is used. Incorporate and execute the program.

  A program for causing a computer to execute the development drawing creation processing function is distributed through a recording medium such as a CD-ROM. Further, this program may be stored in the FD instead of the CD-ROM. In addition, an MO drive may be provided to store the program in the MO, or the program may be stored in another recording medium such as a nonvolatile semiconductor memory card such as a flash memory. Furthermore, the program constituting the software is not limited to being provided via a recording medium, and may be provided via a wired or wireless communication network. For example, the program may be downloaded and acquired from another server or the like via a network such as the Internet or updated.

  Furthermore, the program is provided as a file describing a program code that realizes the function of performing the development drawing creation process. In this case, the program is not limited to being provided as a batch program file, and the hardware of the system configured by the computer Depending on the hardware configuration, it may be provided as an individual program module.

  For example, the computer system 900 includes a central control unit 910, a storage unit 912, an operation unit 914, and other peripheral members omitted from illustration.

  The central control unit 910 includes a CPU (Central Processing Unit) and a microprocessor. The central control unit 910 is similar to the central control unit 910 that forms the center of an electronic computer whose representative example is a CPU in which functions of computation and control performed by a computer are integrated into an ultra-small integrated circuit.

  The storage unit 912 includes a ROM (Read Only Memory) that is a read-only storage unit, or a RAM or a hard disk device (HDD) that is a memory that can be read / written as needed. The ROM stores a development program for a development drawing creation function. The operation unit 914 is a user interface for accepting an operation by a user with a keyboard, a mouse, or the like.

  The control system of the computer system 900 may be configured such that an external recording medium such as a memory card that is not shown can be inserted and removed, and can be connected to a communication network such as the Internet. For this purpose, the control system includes a memory reading unit 920 that reads information on a portable recording medium and a communication I / F 922 as a communication interface unit with the outside in addition to the central control unit 910 and the storage unit 912. It is good to. By providing the memory reading unit 920, the program can be installed and updated from an external recording medium. By providing the communication I / F 922, the program can be installed or updated via the communication network. The basic development drawing creation mechanism is the same as described above.

  Here, the configuration example in which the function of the development view creation apparatus 100 is realized on software by a computer has been described. However, each unit of the development view creation apparatus 100 for realizing the development view creation processing of the present embodiment. Specific means (including functional blocks) may be hardware, software, communication means, a combination thereof, or other means, and this is obvious to those skilled in the art. Moreover, the functional blocks may be combined and integrated into one functional block. Also, software that causes a computer to execute program processing is installed in a distributed manner according to the combination.

  Although the mechanism performed by software can flexibly cope with parallel processing and continuous processing, the processing time becomes longer as the processing becomes complicated, so that a reduction in processing speed becomes a problem. On the other hand, when constructed with a hardware processing circuit, even if the processing is complicated, a reduction in processing speed is prevented, and an accelerator system is constructed that achieves high speed to obtain high throughput.

<Drawing method for development>
[Cone type]
8 to 8D are diagrams for explaining a procedure for creating a conical development view. Here, FIG. 8 is a flowchart showing an example of a procedure for creating a conical development view. FIG. 8A to FIG. 8C are diagrams visually showing a process in which a development view is created in a conical shape from a basic three-dimensional shape (included in a finished product) (in this example, a rotational sweep-like solid QJ). FIG. 8D is an example of a work that can be created by assembling the development views created in accordance with the procedure for creating a conical development view.

  In the following, a case where the rotational sweep-shaped solid QJ is a structure in which a quadrangular pyramid is placed on a quadrangular prism will be described as an example. However, the present invention is not limited to this and can be applied to any rotational sweep-shaped solid QJ. The following processing is automatically executed according to a predetermined program. The overall operation is controlled by the main control unit 190.

  FIG. 8A (1) shows a basic swept solid QJ (included in the finished product), and FIG. 8A (2) shows a completed sheet made of one sheet according to the procedure of this embodiment. The shape of the three-dimensional object (the one obtained by adding the external protrusion having the triangular cross section to the rotating sweep-shaped solid QJ) is shown. Of the edges that make up the swept solid QJ, the horizontal ones are called “horizontal lines” and the other ones are called “busbars”.

  The three-dimensional shape specifying unit 110 acquires shape data of a rotational sweep-shaped three-dimensional solid QJ (FIG. 8A (1)) that is a development drawing target by using, for example, a scanner or existing data (S100). On the operation screen, the creation method specifying unit 174 accepts an instruction on whether to create a development view with a division number N or a conical or cylindrical shape. Basically follow these instructions, but when the user gives a cone-shaped instruction, if the vertex coordinates do not exist on the rotation axis, a cylindrical shape is applied instead of the cone shape to notify the operator to that effect. To do. Alternatively, a vertex is added on the rotation axis to form a cone shape. In the case of a cylindrical type, it can be applied regardless of the presence or absence of a vertex on the rotation axis. Therefore, when the user's instruction is a cylindrical type, this is followed.

  Next, the creation method specifying unit 174 defines the combination of the bus line M and the horizontal line L among the line segments indicating the shape of the rotational sweep-shaped solid QJ from the data acquired by the solid shape specifying unit 110 and the received instruction information. The surface to be processed (basic development surface) is specified (S102). That is, one surface (FIG. 8A (3)) of the developed view in which the target rotation sweep solid QJ is opened in the direction of the rotation axis C is specified. This is the basic figure in the developed view.

  The bus M forms an edge of the rotational sweep-shaped solid QJ. The bus line M (ridge line) is located at the boundary between two adjacent surfaces to form an edge of each surface, and is associated with the two surfaces. The horizontal line L is a line located on the horizontal plane of the rotational sweep-shaped solid QJ, and corresponds to a crease portion in the plane (basic figure in the developed view). For example, the buses M forming the edge of the surface A are the buses M1 to M4, and the buses M1 and M2 are located at the boundary between the adjacent surfaces A and B. For example, the bus M1 is associated with the identification numbers of the faces A and B as M1 (A, B). The same applies to the other buses M2 to M8. Specifying the bus M (edge line) is known as a “Half Edge structure” in the field of CG (computer graphics). In each drawing, the same reference numerals as those of the bus M and the horizontal line L are used so that the correspondence relationship between the bus M and the horizontal line L in the rotation sweep solid QJ in the basic development plane and the development drawing becomes clear.

  Incidentally, the processing up to this point can be substituted by the input of the broken line Q indicating the generatrix M of the rotational sweep-shaped solid QJ on the operation screen in the development drawing creation unit 170 (the ridge line identification unit 172). For example, as shown in FIG. 8A (4), the rotation axis C of the rotation sweep solid is displayed on the operation screen, and the broken line (basic line M) indicating the basic shape (bus M) of the rotation sweep solid QJ is displayed on the same screen. Alternatively, the input of coordinates P_ @) is accepted. In addition, an instruction is received as to whether the development number is to be created by the division number N or the conical or cylindrical type. The specified polygonal line Q is rotated about the rotation axis C by (360 / N) degrees, and polygons surrounded by ridge lines (which can be made in a three-dimensional space) formed by connecting corresponding vertices are arranged on a plane. By doing this, it is possible to specify the surface that will be the basic figure in the developed view.

  The development drawing creation unit 170 divides a regular N-gonal plane at an interval of 360 ° / N (N = 4 in the example in the figure) from the center (S110, FIG. 8A (5)). The development drawing creation unit 170 arranges a basic figure which is a development drawing in which the target rotation sweep solid QJ is opened in the direction of the rotation axis C in each region (S120, FIG. 8B (1)). Due to symmetry, the same shape of the development is drawn in each area.

  Incidentally, whether the line (side) corresponding to the horizontal line L or the valley of the line corresponding to the bus line M is determined by the shape of the original rotation sweep solid QJ, but in this example, the line corresponding to the horizontal line L is Mountain folding is performed, and a line corresponding to the bus M (first folding line) is a valley. Here, the horizontal line L is shown, but as can be understood from the above description, the “third broken line” including the line corresponding to the horizontal line L is not included for the curved surface (see FIG. 10B (described later)). 3), see FIG. 10C (3)). Considering that the curved line can be approximated by expressing the broken line as a fine line and smoothing it, the decision not to enter it as a broken line is based on whether the angle is shallow (close to 180 degrees) or not. That's fine.

  The developed view creation unit 170 extends the side of the developed view corresponding to the horizontal line L to the boundary B of the region (broken line in the drawing) and sets this as the auxiliary line S (S130, FIG. 8B (2)). The developed view creation unit 170 adds a second broken line T connecting the center O of the developed view and the midpoint of the auxiliary line S based on the logic described above (S140, FIG. 8C (1)). The developed view creation unit 170 adds a line X and a line Y that connect the intersection CR (circle mark in FIG. 8C (2)) of the second broken line T and the auxiliary line S added in step S140 (S150).

  Lines (lines X, auxiliary lines S, horizontal lines L and lines Y, auxiliary lines S, horizontal lines L) formed by connecting and adding the intersection points CR over the entire divided areas are rotationally swept solid QJ This is the third fold line of the developed view. Incidentally, the line X and line Y other than the horizontal line L constituting the third fold line, and the difference between the peaks and valleys of the auxiliary line S are also determined based on the shape of the original rotational sweep solid QJ. For example, in this example in which the line corresponding to the horizontal line L is a mountain fold, the auxiliary line S is a valley fold, and the lines X and Y are a mountain fold. In addition, when making the surface of a solid object into a curved surface by making a ridge line into a curve, it is good to omit the process of step S150 and not to provide a 3rd broken line.

  Incidentally, the auxiliary line S is a virtual line for specifying the second fold line or the third fold line (particularly the line X or line Y constituting the fold line in the third fold line). It is not a thing. On the actual computer (actual program), the second fold line or the third fold line can be specified without using the “auxiliary line S”.

  Basically, a conical development view is completed by the processing so far. In the present embodiment, more preferably, the loss prevention process is performed on the apex portion where the broken line can be concentrated (S160, S162). That is, at the apex part where the broken line is gathered when the loss prevention processing is not applied, the end point of the line segment (all or any of the thinned out objects may be targeted) so that the broken lines do not intersect. Is moved a certain distance away from the vertex.

  In this way, a developed view of a three-dimensional object with an external protrusion having a triangular cross section is created from a plane object having a triangular cross section, and the three-dimensional model is assembled on the basis of the rotation sweep solid QJ. It is done. By printing out the developed drawing on paper or the like after applying the loss prevention process, the broken lines are not concentrated on the apex portion, and tearing at the apex portion can be prevented during assembly work.

  The display control unit 150 displays the developed view generated by the developed view creation unit 170 and the 3D model indicating the state of the finished product based on the developed view on the display device (S174), and changes the 3D model as necessary. Is directly accepted (S176, S178). A development view or a 3D model may be created with a color or pattern. When there is a change instruction, the change information is automatically reflected in the development drawing creation, and the same process is repeated (for example, returning to step S102 to repeat the same processing), the changed development drawing and the 3D model Present.

  The development drawing creation unit 170 further performs tiling processing as necessary (S180, S182). Also at this time, the display control unit 150 displays the developed view generated by the developed view creation unit 170 and the 3D model indicating the state of the finished product based on the developed view on the display device (S184), as necessary. Changes are directly accepted on the 3D model (S186, S188). When there is a change instruction, the change information is automatically reflected, and the same process is repeated (for example, the process returns to step S180 and the same process is repeated). Present the model.

  Further, preferably, the intermediate shape of the 3D model of the finished product can be obtained from the developed view while showing the correspondence between the surface included in the solid and the surface included in the developed view so that the correspondence between the developed view and the three-dimensional shape can be confirmed. It may be displayed as an animation (S190). To realize such animation display, use known techniques such as morphing to interpolate two shapes by animation and smooth animation by applying rigid body transformation based on polygon model. Good.

  In general, when assembling a completed three-dimensional object (paper model) from a development view, it is impossible to imagine a finished product even if only the development view is given, and it is difficult to understand the correspondence between the elements of the development view and the finished product. Therefore, it is difficult to understand “how to assemble” and it may take time to assemble. As an aid to this, in normal paper craft, etc., an “assembly instruction” may be attached together with a development view.

  When a development view is created by a computer or a dedicated development view creation device 100, the correspondence between the planes included in the solid and the planes included in the development view is self-evident, and the display device has a 3D model (solid model). Since both can be displayed, it is possible not only to create a developed view by a computer or the like but also to assist in assembling by effectively utilizing them.

  When the creation of the development drawing is finally completed (S192-YES), the print control unit 180 prints the development drawing on a flat object such as paper by the printing apparatus (S192). By assembling the printed development view, for example, a three-dimensional object as shown in FIG. 8D is completed. Incidentally, when not completed, the main control unit 190 returns to the desired processing step (S192-NO).

[Cylinder type]
9 to 9C are diagrams illustrating a procedure for creating a cylindrical development view. Here, FIG. 9 is a flowchart showing an example of a procedure for creating a cylindrical development view. 9A to 9B are diagrams visually showing a process of creating a development view from a basic solid shape (rotary sweep-like solid QJ in this example). FIG. 9C is an example of a work that can be created by assembling the developed view created by this procedure.

  In the following, a case where the rotational sweep-shaped solid QJ is a structure in which a quadrangular pyramid is placed on a quadrangular prism will be described as an example. However, the present invention is not limited to this and can be applied to any rotational sweep-shaped solid QJ. The following processing is automatically executed according to a predetermined program. The overall operation is controlled by the main control unit 190. Below, it demonstrates paying attention especially to a difference with a cone type. The part without special description may be the same as the conical type.

  FIG. 9A (1) shows a basic rotational sweep-shaped solid QJ, and FIG. 9A (2) shows a completed solid object (rotational sweep-shaped solid QJ) created by one sheet of paper according to the procedure of this embodiment. The shape of the external projection having a triangular cross section is added. As in the conical shape, of the sides constituting the rotational sweep solid QJ, the horizontal one is called the horizontal line, and the other one is called the “bus line”.

  The three-dimensional shape specifying unit 110 acquires three-dimensional data of a rotational sweep-shaped solid QJ (FIG. 9A (1)) that is a development target of the development view (S200). Next, the solid shape specifying unit 110 specifies a surface defined by the combination of the bus line M and the horizontal line L among the line segments indicating the shape of the rotational sweep solid QJ from the acquired data (S202). That is, one surface (FIG. 9A (3)) of the developed view in which the target rotation sweep solid QJ is opened in the direction of the rotation axis C is specified. This is the basic figure in the developed view.

  Incidentally, the processing up to this point can be substituted by the input of the broken line Q indicating the generatrix M of the rotational sweep-like solid QJ by using the operation screen as in the conical shape (FIG. 9A (4)).

  The development drawing creation unit 170 divides the rectangular plane at an interval of 360 ° / N (N = 4 in the example in the figure) from the center (S210, FIG. 9A (5)). The development drawing creation unit 170 arranges a basic figure which is a development drawing in which the target rotation sweep solid QJ is opened in the direction of the rotation axis C in each region (S220, FIG. 9B (1)). Due to symmetry, the same shape of the development is drawn in each area. The size of the external protrusion changes depending on the interval between the development views. Incidentally, the distinction between the horizontal line L and the peaks and valleys of the bus line M is determined by the shape of the original rotational sweep-shaped solid QJ, but in this example, the line corresponding to the horizontal line L is mountain-folded, and the line corresponding to the bus line M is It becomes a valley.

  The developed view creation unit 170 extends the side of the developed view corresponding to the horizontal line L to the boundary B of the region (broken line in the drawing), and uses this as the auxiliary line S (S230, FIG. 9B (2)).

  Based on the logic described above, the development drawing creation unit 170 extends an extension line (auxiliary line S) extending from the vertex of the basic development plane to the boundary line for each of the upper side and the lower side of each divided area of the rectangular planar object. Cos α (boundary line side): 1 (second apex side of the basic development plane) A second broken line T connecting points is added (S240, FIG. 9B (3)).

  The developed view creation unit 170 adds a line Z that connects the intersection CR (circle mark in FIG. 9B (4)) of the second broken line T and the auxiliary line S added in step S240 (S250). A line (the whole of the line Z, the auxiliary line S, and the horizontal line L) formed by connecting and adding the intersection points CR over the entire divided areas becomes the third broken line of the developed view of the rotational sweep-shaped solid QJ. The difference between the peaks and valleys of the line Z other than the horizontal line L constituting the third fold line is also determined based on the shape of the original rotation sweep solid QJ. For example, in this example in which the line corresponding to the horizontal line L is a mountain fold, the auxiliary line S is a valley fold, and the line Z is a mountain fold. When the ridgeline is a curve and the surface of the three-dimensional object is a curved surface, the process of step S250 may be omitted so that the third fold line is not provided.

  In this way, a developed view of the three-dimensional object including the rotation sweep-shaped solid QJ and having the external protrusion having the triangular cross section is created from the rectangular plane object. By assembling the printed development view, for example, a three-dimensional object as shown in FIG. 9C is completed.

  Incidentally, unlike the conical shape, there is no apex portion where the broken line can be concentrated, so there is no need to perform the loss prevention process. Also, there is no application of tiling processing. In addition, it is good to attach a margin part to the edge of the longitudinal direction of a development view.

<Example works>
[Cone type]
FIGS. 10 to 10C are diagrams illustrating details of the cone-shaped work example (first work example to fourth work example). In each figure, the input polygonal line (bus line) is shown in the upper left column (1), the 3D (three-dimensional) model is shown in the upper right column (2), and the developed view is in the lower left (3). The photo of the example is shown in the lower right column (4). For example, a known method such as a wire frame model, a surface model, a solid model, a voxel model, a polygon model (including a mesh model as an example) may be applied to the 3D model.

  In each case, the coordinates of the vertex P_0 are always arranged on the rotation axis C of the rotational sweep solid, and the coordinates P _ @ (@ are formed so as to form a polygonal line Q indicating the generatrix M of the rotational sweep solid. Is a coordinate number). A horizontal line passing through each coordinate P_ @ corresponds to a horizontal line L (an example of a contour line) of a rotating sweep-shaped solid QJ (including a 3D model as well as a finished product).

  The first work example shown in FIG. 10 is a case where the division number N is four. The basic rotating sweep solid is a structure in which the quadrangular pyramids are reversed and are adhered in two layers so that the bottom surfaces are joined to each other. Therefore, the broken line Q indicating the generatrix of the rotational sweep solid is symmetric with respect to the horizontal base line L_0 in which the upper half and the lower half are orthogonal to the rotational axis C of the rotational sweep solid. One is in a mirror image relationship with the other. On the other hand, in addition to the coordinates of the vertex P_0, only the first coordinate P_1 is designated on the horizontal base line L_0. The horizontal base line L_0 corresponds to the horizontal line L of the 3D model (FIG. 10 (2)).

  The second work example shown in FIG. 10A is a case where the division number N is six. The basic rotating sweep solid is a hexagonal column with a top and bottom surfaces horizontal. Accordingly, the broken line Q indicating the generatrix of the rotational sweep solid is on a line parallel to the horizontal base line L_0 passing through the coordinates of the vertex P_0 in addition to the coordinates of the vertex P_0 on the rotational axis C of the rotational sweep solid to form the upper surface. A first coordinate P_1 is specified at a certain distance, and a second coordinate P_2 is specified at a position where the coordinate P_1 is projected onto the horizontal base line L_0. In this example, a third coordinate P_3 is specified at a position further away from the rotation axis C on the horizontal base line L_0 so as to form a skirt portion in the completed solid object. As inferred from the developed view (FIG. 10A (3)), when the coordinate P_3 is not designated, the skirt portion is not formed in the completed three-dimensional object. Incidentally, since the upper surface of the rotational sweep solid is horizontal, the line passing through the center is omitted in the developed view (FIG. 10A (3)).

  The third work example shown in FIG. 10B is a case where the division number N is six. The basic rotational sweep solid is generally hemispherical and has a structure with an open upper surface. Therefore, the broken line Q indicating the generatrix of the rotational sweep solid is designated by the coordinates of the vertex P_0 on the rotational axis C of the rotational sweep solid below the rotational axis C, and the polygonal line Q used as an input is a fine line. A large number (eight in this example) of coordinates P_1 to P_8 are designated so that a spherical shape is smoothly expressed in minutes. The end point coordinate P_8 is designated at a position away from the rotation axis C so as to open the upper surface. Incidentally, since the upper surface of the rotational sweep solid is horizontal, the line passing through the center is omitted in the development view (FIG. 10B (3)). In the developed view (FIG. 10B (2)), the fold line forming the horizontal line connecting the positions corresponding to the coordinates P_1 to P_8 of the 3D model (FIG. 10B (3)) is a curved surface in the finished product (FIG. 10B (4)). The illustration is omitted for the sake of illustration.

  The fourth work example shown in FIG. 10C is a case where the division number N is five. The basic rotating sweep solid is generally bowl-shaped and has a structure with an open bottom surface. Therefore, the polygonal line Q indicating the generatrix of the rotational sweep solid is designated with the coordinates of the vertex P_0 on the rotational axis C of the rotational sweep solid above the rotational axis C, and the polygonal line Q used as an input is a fine line. A large number (12 in this example) of coordinates P_1 to P_12 are designated so as to smoothly express the saddle shape in minutes. The end point coordinate P_12 is designated at a position away from the rotation axis C so as to open the lower surface. Incidentally, in the developed view (FIG. 10C (2)), the fold line forming the horizontal line connecting the positions corresponding to the coordinates P_1 to P_12 of the 3D model (FIG. 10C (3)) is the finished product (FIG. 10C (4)). The illustration is omitted to represent the curved surface.

[Cylinder type]
FIG. 11 to FIG. 11C are diagrams showing details of a columnar work example (first work example to fourth work example). In each figure, the input polygonal line (bus line) is shown in the upper left column (1), the 3D (three-dimensional) model is shown in the upper right column (2), and the development view is in the second stage ( It is shown in the column 3), and a photograph of the work example is shown in the column (4) in the third row.

  Coordinates P_ @ are input so as to form a polygonal line Q indicating the generatrix M of the swept sweep solid. Incidentally, since it is a cylindrical type, unlike the conical type, the coordinates of the vertex P_0 may or may not be arranged on the rotation axis C of the rotational sweep-like solid. A horizontal line passing through each coordinate P_ @ corresponds to a horizontal line L of a rotational sweep-shaped solid QJ (including a 3D model as well as a finished product).

  The first work example shown in FIG. 11 is a case where the division number N is four. The basic rotating sweep solid is a structure in which a quadrangular prism is arranged under a quadrangular pyramid.

  The second work example shown in FIG. 11A is a case where the division number N is four. Similar to the first cone-shaped work example, the basic rotational sweep-shaped solid is a structure in which the quadrangular pyramids are reversed and are adhered in two layers so that the bottom surfaces are joined to each other. Therefore, the broken line Q indicating the generatrix of the rotational sweep solid is symmetric with respect to the horizontal base line L_0 in which the upper half and the lower half are orthogonal to the rotational axis C of the rotational sweep solid. One is in a mirror image relationship with the other. On the other hand, in addition to the coordinates of the vertex P_0, only the first coordinate P_1 is designated on the horizontal base line L_0.

  The third work example shown in FIG. 11B is a case where the division number N is six. The broken line Q indicating the base line of the rotational swept solid that is the base is symmetric with respect to the horizontal base line L_0 in which the upper half and the lower half are orthogonal to the rotational axis C of the swept solid. The coordinates of the vertex P_0 are not arranged, and as a whole, the upper surface and the lower surface (part of the coordinate P_1) of the cylinder whose size is defined by the coordinates P_2 are narrowed down.

  The fourth work example shown in FIG. 11C is a case where the division number N is six. As with the third work example, the broken line Q indicating the generatrix of the basic rotational sweep-shaped solid is symmetric with respect to the horizontal base line L_0 whose upper half and lower half are orthogonal to the rotational axis C of the rotational sweep-shaped solid. ing. The coordinates of the vertex P_0 are not arranged, and as a whole, the upper and lower sides (part of the coordinates P_1) of the sphere whose size is defined by the coordinates P_6 are cut. In other words, a larger number (11 in this example) of coordinates P_1 to P_11 are designated so that the broken line Q used as an input can be smoothly expressed in a spherical shape with fine line segments than in the third work example. The coordinates P_1 and P_11 of the end points are designated at positions away from the rotation axis C so as to open the upper side and the lower side. Incidentally, in the developed view (FIG. 11C (2)), the fold line forming the horizontal line connecting the positions corresponding to the coordinates P_1 to P_11 of the 3D model (FIG. 11C (3)) is in the finished product (FIG. 11C (4)). The illustration is omitted to represent the curved surface.

[tiring]
FIG. 12 is a diagram illustrating an example of a work to which tiling processing is applied. FIG. 12 (1) shows a case where N = 3 solid origami papers are laid and placed on each vertex of a regular hexagonal tile. FIG. 12 (2) shows an arrangement in which N = 4 three-dimensional origami papers are laid down on each vertex where a regular square is tiled. FIG. 12 (3) shows an arrangement in which N = 6 three-dimensional origami papers are laid down on each apex obtained by tiling regular triangles.

<Production method of solid objects>
Next, a mechanism for manufacturing a three-dimensional object based on a development view generated by applying the development drawing generation method of the present embodiment will be described. Basically, a formwork drawing used for manufacturing a three-dimensional object is designed based on a development drawing generated by the development drawing creation apparatus 100, and a formwork is generated based on the design drawing (formwork drawing). Then, the produced mold is assembled so as to represent the outer shape of the three-dimensional object, and the filling is filled in the space formed in the interior to be cured. Hereinafter, it demonstrates in order.

[Form design equipment]
FIG. 13 is a diagram illustrating a configuration example of the formwork designing apparatus according to the present embodiment. A formwork designing apparatus 300 according to the present embodiment designs (manufactures) a formwork drawing using the development drawing creating apparatus 100 according to the present embodiment.

  As shown in the figure, the formwork designing apparatus 300 includes a development drawing creating apparatus 100 and further includes a formwork drawing generating unit 310. As described above, the development drawing creation apparatus 100 creates a development drawing of a three-dimensional object having an external projection having a triangular cross section at the ridge line portion of the rotation sweep solid QJ, based on the rotation sweep solid QJ. Part 170. The form drawing generation unit 310 generates a form drawing based on the development drawing generated by the development drawing creation unit 170. Information of the form drawing generated by the form drawing generation unit 310 is notified to the display control unit 150 and the print control unit 180.

  When generating a formwork drawing from a developed view, basically, it is preferable to divide the formwork at each broken line portion. Of course, this is only an example, and other known methods may be used. In any case, by assembling the formwork generated based on the formwork drawing, a three-dimensional object having an external protrusion having a triangular cross section at the ridgeline portion of the rotational sweep-like solid QJ is based on the rotational sweep-like solid QJ. It suffices if the mold can be manufactured (designed) so that the outer shape can be expressed.

[Form design process]
FIG. 13A is a flowchart illustrating an example of a process for generating a form drawing used for manufacturing a three-dimensional object.

  The development drawing creation apparatus 100 incorporated in the formwork designing apparatus 300 is a development drawing of a three-dimensional object having an external projection having a triangular cross section at the ridge line portion of the rotational sweep type solid QJ according to the procedure shown in FIGS. Are created (S100 to S192, S200 to S292).

  Thereafter, the formwork drawing generation unit 310 generates a formwork drawing based on the development drawing generated by the development drawing creation unit 170 (S310).

  The display control unit 150 displays on the display device the 3D model indicating the form drawing generated by the form drawing generation unit 310 and the state of the finished product (three-dimensional object) based on the form drawing (S374), and is necessary. In response, the change is directly accepted on the 3D model (S376, S378). When there is a change instruction, the change information is automatically reflected in the creation of the form drawing, and the same process is repeated (for example, returning to step S310 and the same processing is repeated). Present a 3D model.

  Preferably, the formwork is assembled while showing the correspondence between the surfaces included in the solid and the formwork (surfaces of each formwork included) so that the correspondence between the formwork and the three-dimensional shape can be confirmed. The intermediate shape until it becomes a finished product may be displayed by animation (S290).

[Three-dimensional object manufacturing equipment and three-dimensional object manufacturing process]
FIG. 13B is a diagram illustrating a configuration example of the three-dimensional object manufacturing apparatus of the present embodiment. FIG. 13C is a flowchart illustrating an example of a three-dimensional object manufacturing process procedure according to this embodiment.

  The three-dimensional object manufacturing apparatus 400 of this embodiment is generated based on the form drawing generated by the form design apparatus 300 that designs (manufactures) the form drawing using the development drawing creation apparatus 100 of this embodiment. A three-dimensional object is manufactured using a mold. Naturally, the manufactured finished product becomes a three-dimensional object based on the rotation sweep-shaped solid QJ and having an external protrusion having a triangular cross section at the ridge line portion of the rotation sweep-shaped solid QJ.

  As illustrated in FIG. 13B, the three-dimensional object manufacturing apparatus 400 includes a mold assembly line 410, a material filling line 420, a material curing line 430, and a mold removal line 440, and manufactures a three-dimensional object by a flow operation. ing. Of course, this is only an example, and a manufacturing method that does not depend on flow work may be used. The formwork designing apparatus 300 and the formwork manufacturing factory 390 are arranged on the front side of the three-dimensional object manufacturing apparatus 400, and a three-dimensional object is formed by these processes.

  The formwork drawing (or its drawing file) generated by the formwork design apparatus 300 is supplied to a formwork manufacturing factory 390 (for example, outsourcing) (S300 to S394). The mold manufacturing factory 390 manufactures the mold according to the mold drawing and delivers it to the three-dimensional object manufacturing factory including the three-dimensional object manufacturing apparatus 400 (S400).

  The formwork assembly line 410 is an example of a formwork assembly part, and the formwork delivered from the formwork manufacturing factory 390 is based on a rotational sweep-shaped solid and has a triangular cross section at the ridgeline portion of the rotational sweep-shaped solid. Assemble so as to represent the outer shape of a three-dimensional object having protrusions (S410: mold assembly process).

  The material filling line 420 is an example of a material filling portion, and fills a space portion formed by the assembled mold with a material such as resin (for example, an ultraviolet curable resin) or metal (S420: material filling step).

  The material curing line 430 is an example of a material curing unit, and cures the filled material by ultraviolet irradiation or heat dissipation (S430: material curing step).

  The formwork removal line 440 is an example of a formwork removal unit, and removes the formwork after the filled material is cured (S440: formwork removal step).

  The three-dimensional object manufactured by such a procedure is a three-dimensional object having a rotation sweep-like three-dimensional solid QJ as its basic shape and a triangular cross-section external projection on its ridgeline part, for example, used as a figurine or a designable weight can do.

  DESCRIPTION OF SYMBOLS 100 ... Development drawing production apparatus, 110 ... Three-dimensional shape specific | specification part, 130 ... Memory | storage part, 150 ... Display control part, 170 ... Development drawing preparation part, 172 ... Ridge line specific part, 174 ... Creation method specific part, 178 ... Fold line specific part DESCRIPTION OF SYMBOLS 180 ... Print control part 190 ... Main control part 300 ... Formwork design apparatus (formwork manufacturing apparatus), 310 ... Formwork drawing generation part, 400 ... Three-dimensional object manufacturing apparatus, 410 ... Formwork assembly line, 420 ... Material filling line, 430 ... Material curing line, 440 ... Formwork removal line, 900 ... Computer system

Claims (14)

Identifies the ridgeline of a three-dimensional object having a rotational sweep shape, and is based on a rotational sweep-shaped solid that is a three-dimensional object having a rotational sweep shape. A development drawing creation unit for creating a development drawing on one plane;
An operation unit for receiving an instruction of the division number N of the plane;
With
The development drawing creation unit has a creation method identification unit and a broken line identification unit,
The creation method identifying unit identifies the shape of the basic plane of the development view to be created based on the relationship between the information received by the operation unit and the ridgeline of the rotational sweep solid,
The broken line specifying part is
Dividing the plane evenly according to the division number N,
The basic plane shape of the identified development view is arranged in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A development drawing creation device, wherein a line formed by connecting the internal dividing points that internally divide between the two at a predetermined ratio is used as a second broken line of the development drawing of the rotational sweep solid. 2. The fold line specifying unit defines a line formed by connecting intersections with the second fold line when the second line is extended as a third fold line of the development diagram of the rotating sweep solid. The development drawing creation apparatus described in 1. The operation unit includes a conical type that creates a development view based on a regular N-gonal plane when the division number is N, and a cylindrical type that creates a development view based on a rectangular plane when the division number is N. Accept the instruction of which to create the development drawing,
When the operation unit receives the cone-shaped instruction, the broken line specifying unit sets a middle point that equally bisects between the first intersection and the second intersection as the inner dividing point. The developed view creation apparatus according to claim 1. The operation unit includes a conical type that creates a development view based on a regular N-gonal plane when the division number is N, and a cylindrical type that creates a development view based on a rectangular plane when the division number is N. Accept the instruction of which to create the development drawing,
When the operation unit receives the cylindrical instruction, the broken line specifying unit sets the inner dividing point to cos α (α = π / N) on the boundary side of the divided region, and a line corresponding to the ridge line The development drawing creating apparatus according to claim 1, wherein the development is specified based on a ratio in which the side is 1. The development drawing creation device according to claim 1, wherein the broken line specifying unit moves an end point on the boundary side of the second broken line with another divided region by a certain distance in a direction away from the region boundary. The development drawing creation unit creates a development drawing of a three-dimensional object in a state in which a plurality of three-dimensional objects having external projections having a triangular cross-section are arranged on the ridgeline of the rotational sweep-like solid on one plane.
Arranging a solid object having external projections of triangular cross section on the ridgeline of the rotational sweep-shaped solid formed by assembling a conical development with 6 divisions, or at each vertex of an equilateral triangle, or
Arranging solid objects having external projections of triangular cross section on the ridgeline of the rotational sweep-shaped solid formed by assembling a development view with a conical shape with a division number of 4 at each vertex of a regular square, or
A three-dimensional object having triangular projections on the ridgeline of the rotational sweep solid formed by assembling a conical development with three divisions is arranged at each vertex of a regular hexagon,
The development drawing production apparatus according to claim 1, wherein in the development drawing for each three-dimensional object, the second folding line extending outward is extended and connected to the second folding line of the development drawing of another adjacent three-dimensional object. A development view of a three-dimensional object that identifies a ridge line of a rotation sweep-shaped solid that is a three-dimensional object having a rotation sweep shape and has an external protrusion having a triangular cross section at the ridge line portion of the rotation sweep-shaped solid based on the rotation sweep-shaped solid. When creating a single plane,
Dividing the plane evenly according to the number of corners of the rotating sweep solid,
Arranging the shape of the basic plane of the development view in which the rotational sweep solid is opened in the direction of the rotation axis in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A development drawing creation method, in which a line formed by connecting internal dividing points that internally divide between the two at a predetermined ratio is defined as a second broken line of the development drawing of the rotational sweep solid. A ridge line identifying step for identifying a ridge line of a rotational sweep solid that is a solid object having a rotational sweep shape;
A development drawing creation step of creating a development drawing of a three-dimensional object having an external projection having a triangular cross section at a ridge line portion of the rotation sweeping solid on a single plane by the development drawing creation unit, based on the rotation sweep solid.
Receiving an instruction of the number N of the divided areas and an instruction to create a development view in a conical type or a cylindrical type,
The development drawing creation step has a creation method identification step and a broken line identification step,
The creation method specifying step is based on the relationship between the number N of divided areas, information on whether a development view is created in a conical or cylindrical shape, and the ridgeline of the rotational sweep solid. Identify the shape of the plane
The broken line specifying step includes:
Dividing the plane evenly according to the number of corners of the rotating sweep solid,
Arranging the shape of the basic plane of the development view in which the rotational sweep solid is opened in the direction of the rotation axis in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended And a line formed by connecting the internal dividing points that internally divide between and a predetermined ratio as the second broken line of the development diagram of the rotational sweep solid,
A program for creating a three-dimensional development view by causing a computer to execute each process. It is a single plane object that shows a fold line for assembling a three-dimensional object having an external protrusion having a triangular cross-section at the ridge line portion of the rotation sweep-shaped solid, based on a rotational sweep-shaped solid that is a three-dimensional object having a rotational sweep shape. It is a three-dimensional object formed by assembling the developed development generated by mountain folding or valley folding according to the folding line,
When the three-dimensional object is developed into one flat object,
The plane is evenly divided according to the number of corners of the rotational sweep solid,
The shape of the basic plane of the development view in which the rotation sweep-shaped solid is opened in the direction of the rotation axis is arranged in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep-shaped solid is the first fold line of the development view of the rotational sweep-shaped solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A solid line formed by connecting the internal dividing points that internally divide between the two at a predetermined ratio is the second broken line of the developed view of the rotational sweep solid. A development view showing a fold line for assembling a three-dimensional object having an external protrusion having a triangular cross-section at the ridge line portion of the three-dimensional rotation sweep-shaped solid, based on a three-dimensional object having a rotational sweep shape. Create with a plane,
In producing a three-dimensional object by assembling the developed development according to the above folding line by mountain folding or valley folding,
Dividing the plane evenly according to the number of corners of the rotating sweep solid,
Arranging the shape of the basic plane of the development view in which the rotational sweep solid is opened in the direction of the rotation axis in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A method of manufacturing a three-dimensional object, wherein a line formed by connecting internal dividing points that internally divide between the two at a predetermined ratio is defined as a second broken line of the development view of the rotational sweep solid. A development drawing creation unit for creating a development drawing of a three-dimensional object having an external protrusion having a triangular cross section at a ridge line portion of the rotation sweep-shaped solid, based on a rotation sweep-shaped solid that is a three-dimensional object having a rotation sweep shape;
An operation unit that receives an instruction of the number of divisions N of the plane and an instruction to create a development view in a conical type or a cylindrical type;
A form drawing generation unit that generates a form drawing based on the development view generated by the development drawing generation unit;
With
The development drawing creation unit has a creation method identification unit and a broken line identification unit,
The creation method identifying unit identifies the shape of the basic plane of the development view to be created based on the relationship between the information received by the operation unit and the ridgeline of the rotational sweep solid,
The broken line specifying part is
Dividing the plane evenly according to the division number N,
The basic plane shape of the identified development view is arranged in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A formwork manufacturing apparatus in which a line formed by connecting internal dividing points that internally divide between the two at a predetermined ratio is used as a second broken line of the development diagram of the rotational sweep solid. A development drawing creation step for creating a development drawing of a three-dimensional object having a triangular protrusion in the cross section at the ridge line portion of the rotation sweep-shaped solid, based on a rotation sweep-shaped solid that is a three-dimensional object having a rotation sweep shape;
An instruction receiving step of receiving an instruction of the division number N of the plane and an instruction to create a development view of a conical type or a cylindrical type;
A form drawing generation step for generating a form drawing based on the development drawing generated in the development drawing creation step;
With
The development drawing creation step has a creation method identification step and a broken line identification step,
The creation method specifying step specifies the shape of the basic plane of the developed view to be created based on the relationship between the information received in the instruction receiving step and the ridgeline of the rotational sweep-shaped solid,
The broken line specifying step includes:
Dividing the plane evenly according to the division number N,
The basic plane shape of the identified development view is arranged in each divided area of the plane,
In each of the divided areas,
The first line corresponding to the ridgeline of the rotational sweep solid is a first fold line of the development view of the rotational sweep solid,
A first intersection where the first line intersects with a second line corresponding to the contour line of the rotational sweep solid and a second intersection where the first line intersects the boundary of the region when the second line is extended A mold manufacturing method in which a line formed by connecting internal dividing points that internally divide between the two at a predetermined ratio is used as a second broken line of the development diagram of the rotational sweep solid. The mold according to claim 11, based on a developed view of a three-dimensional object based on a rotating sweep-shaped solid, which is a three-dimensional object having a rotational sweep shape, and having an external protrusion having a triangular cross section at the ridge line portion of the rotational sweep-shaped solid. An assembly part for assembling a mold formed by a frame manufacturing apparatus so as to represent the outer shape of a three-dimensional object having an external projection having a triangular cross section at a ridge line portion of the rotational sweep solid, based on the rotational sweep solid;
A filling portion for filling a material into a space formed by the assembled formwork;
A curing part for curing the filled material;
A removal section for removing the mold after the filled material is cured;
A three-dimensional object manufacturing apparatus. The mold according to claim 12, based on a development view of a three-dimensional object based on a rotation sweep-shaped solid, which is a three-dimensional object having a rotation sweep shape, and having an external protrusion having a triangular cross section at a ridge line portion of the rotation sweep-shaped solid. Formwork assembling step for assembling a mold formed by a frame manufacturing method so as to represent the outer shape of a three-dimensional object having a triangular cross-section at the ridge line portion of the rotary sweep-shaped solid based on the rotary sweep-shaped solid When,
A filling step of filling the material formed in the space formed by the assembled formwork;
A curing step to cure the filled material;
A removal step of removing the mold after the filled material is cured;
The manufacturing method of the solid object provided with.