JPS60205775A - Method and device for shape generation - Google Patents

Abstract

PURPOSE:To perform consistently the formative work processing from shape expression to shape generation by setting a triangle having a desired shape and dividing this triangle to four triangles and repeating this operation to form a dense polyhedron. CONSTITUTION:A triangle T10 having a desired shape is set, and points P21- P23 of this triangle are used as dividing vertexes to form a triangle T20, which is obtained by connecting these three points, and three triangles T21-T23 which are obtained in areas where the triangle T20 is eliminated from the triangle T10. This operation is repeated to constitute a dense polyhedron. Dividing points are inputted by setting a light pen to optional position on a display device or by a digitizer. Data related to the generated shape can be used for operations of NC machine tools as it is.

Description

[Detailed description of the invention]

Technical Field] The present invention is based on CAD (Computer Aided
Dcsiu+l, NCI manufactured I geometry machines, etc., are related to devices that create a desired three-dimensional shape or modify the shape. [Back ■1 Technology I When expressing a predetermined shape in CAD, machine tools, etc., wire frame shape description, surface shape description, and solid model shape description are known as shape description methods. .Here, the wireframe shape description is
By using dense point sequences or schools of fish and line elements,
Express the desired shape. The 1-7S shape description is achieved by performing interpolation processing based on function approximation between the points after the point sequence or fish school is 4!1 and IC. C
1. It expresses the desired shape. Also solid - [
Dell shape description expresses a shape by stacking simple shapes (primitives) like building blocks. The main function of each of the conventional shape descriptions described above is to represent the shape of an entity. [Problems with the prior art] First, the above-mentioned prior art lacks flexibility in expression when expressing three-dimensional shapes, so it cannot fully utilize its functions. lC1 Shape expression is one aspect of modeling processing, and shape creation is also one aspect of modeling processing, but there is a problem that modeling processing cannot be performed between the two as one member. For example, even when using the solid model described above, it is possible to express a part of a three-dimensional shape by combining simple shapes, but by its very nature, it is not possible to express a free and detailed shape. This naturally means that it is difficult for one person to perform the modeling process from shape expression to shape creation. [Objective of the Invention 1 The present invention focuses on the problems of the conventional queen The aim is to provide a single shape creation device that can be freely accessed during the entire process from setting up models to manufacturing.
This is a hit. [Summary of the Invention J To achieve this purpose, Kinoe 1J first sets a triangle of a desired shape (first stage triangle), and divides this first stage triangle into four triangles (second stage triangle). ),
Each of the second-stage triangles is again divided into four parts, these operations are repeated to form a large number of triangles, and a dense polyhedron is formed by the continuation of these large numbers of triangles. If you display this shape creation process on the display, you can see the shape creation progress &! This is CAD, and the data regarding the created shape can be used as is to operate the NC machine tool. [Embodiment of the Invention] FIG. 1 is an overall diagram of a system showing an embodiment of the present invention. First, input the positional information about the shape you are about to create, and the positional information of the shape you are about to draw using the keyboard 1. Rai 1 to Ben 2 are set up. And keyboard 1. An arithmetic circuit 3 that performs a predetermined screening process based on a human signal from an input means such as a light ben 2 is built-in. A display 4 is installed to display the shape created in this way.

[Printers 1 to 5 print out the shapes, and an external storage device @6 stores the shapes as predetermined signals such as magnetic signals and optical signals.
There is also a Next, the principle of the present invention will be explained. The present invention first sets a triangle of a desired shape (first stage triangle), divides this first stage triangle into four triangles (second stage triangle), and divides each of the second stage triangles into four again. Decompose and repeat these division operations to form a large number of triangles, and by continuation of these large numbers of triangles - (
'It forms a dense polyhedron. These division processes are sequentially illustrated in FIGS. 2 to 13. FIG. 2 shows a first stage triangle. First, in the initial stage of forming a dense polyhedron, a triangle T10 having a desired shape is set. This triangle TIO is called the first stage triangle. This first stage triangle T104; L, Jt'jJki P 11 , P 12
. Move PI3 and sides R11, R12, and R13 to the right. Based on this second stage triangle T10, the triangle is successively divided into four parts. For convenience of explanation, the first stage triangle 110 is projected onto the projection plane 10 in FIG. 2, and 10 points of the projected triangle are designated as PI.
1 a, PI 2a, l"'l 3a. Generally, for example, point Pi 2. Pi 3. PI 3a. Set a dividing point in the space near either the left or right of the flat curve surrounded by PI 2a. However, considering the simplicity of the explanation of CLt here, (in this back surface, 〆j21-installation GJ, this point I) 21 is designated as the first division 111.Similarly, point P
13. Pi 1. l'l 'IF], set point P22 in the plane surrounded by P'13a, and set this point P22 as the second
Split l mouth and I? aP11. Pi2. Pi 2a
, Set point 1〕23 in the plane surrounded by Plla'',
This point P23 is defined as the third division vertex. In addition, each vertex P1
1, PI2. 1st to 3rd division loss points from PI3 P21°R2
2. The method or means for adding R23 will be described later. These 1.2.3 division loss points P21. By connecting P22°R23, a central triangle T20 is established. A peripheral triangle [21 is set by one side of the central triangle T20 and the point pH, a peripheral triangle T22 is set by the other side of the central triangle]°20 and the point P12, and
An equilateral triangle T23 is set using the remaining sides of the central triangle T20 and the point P13. In other words, first, after setting the first stage triangle 110,
By arbitrarily setting three points and connecting these three points to each other, a -C1 central triangle is created, and by one point among those three points and any side of the central triangle, Create three peripheral triangles outside the central triangle. A state in which the first stage triangle 110 is divided into four triangles is shown in FIG. 3, and a plan view of A is shown in FIG. 4. In this way, the basis for creating a dense polyhedron is created based on one diagonal U, and IE-. Next, in FIG. 3, if the intersections of C1 vertices 1) 22.1) 23 and the projection plane 'IO are P22a and P23a, then JtaP23. I)22. P22a. P 2: ゛1' surrounded by 3a, Ij within the song 1〕3
1, i21, and this point 31 is taken as a new first division point 111. Similarly, point 1-)22. l' 11.
l) 11 a, 1) Point 1 in the plane surrounded by 22ar
' 32 is set, and this point 1332 is set as a new second division 1.
ci +: a, mata point 1) 1'1. +323, P2
3a, set point P33 in the plane surrounded by Pll a,
This +:ti l)33 is taken as a new third division vertex. FIG. 5 shows the peripheral triangle T21 divided into four triangles. '1, 2.3 division vertex 1) 31 in Figure 3
. By connecting R32, 1) 33, a central triangle T'30 of T, #i is set. 1 of this central triangle 130
Another peripheral triangle T 31 is set by one side and the point Pil, another peripheral triangle T 32 is set by the other side of the central triangle 1' 30 and the vertex P23, and the remaining sides of the central triangle T30 and vertex 1]33, another peripheral triangle T33 is set. Thus °C second stage triangle which is one of the triangles]
"21 can be divided again into four triangles. Figure 15 shows one peripheral triangle T21 numbered in Figure 4.
For only T22., the triangle is shown broken down into four parts, but for other surrounding triangles T22. Similarly, T"23 and the central triangle T20 can each be divided into four triangles. FIG. 6 shows the other peripheral triangles T22.1-23 and the central triangle 120 each divided into four. The central triangle and peripheral triangles when the first stage triangle is divided into four are called the second stage triangle, and the central triangle and peripheral triangle when the second stage triangle is divided into four parts respectively. is called the third stage triangle, and the division is repeated in the same manner up to the nth stage triangle.In this way, based on the first stage triangle T'I O'
By sequentially dividing the triangle into four triangles and repeating this dividing operation a predetermined number of times, a dense polyhedron can be constructed. ``The more culms there are, the higher the number of 1-stages, the higher the capacitance or m-density of the 1c polyhedron that is created.'' 7 shows a central triangle T20, peripheral triangles 1-21. T22. Separate T23 (shown as IC-b)
It is. In this Fig. 7, three peripheral triangles 121°'1-
22.123 in the counterclockwise order (numbers 1, 2.3 in the example) (J L/), then the identification number (in the example, the numbers 120) to the central pentagon 120. 4
(= J L). Also, for each side of the second stage triangle -r20. Attach the same.By changing 1° in this way, the first stage triangle 'I 20.l'2'1.l 22,1'23
, it has the advantage that the topological structure can be determined by &1, similarly to the planar graph. In addition, an identification number is provided for each side of the first-stage triangle. Focusing on a two-step triangle, the identification number for each side is set so that the sum of the identification number of one vertex and the identification number of the opposite side of that vertex is 4. When divided into step triangles, each third step triangle is given an identification number.As shown in Figure 7, identification numbers 1 to 4 are used for the second step triangle. , in the third stage triangle, starting from identification number 5, first, the identification numbers (5 to 8
) is attached, and then similarly, the peripheral triangle -r22,1
23. In the order of central triangles 1 to 20, four identification codes (=1) are added to each. The same applies to the identification numbers 41 after the fourth stage triangle. FIG. 9 shows the third stage This example shows the case where the triangle 1°31 is divided into four parts. In the above example, as the division is performed, the surface formed by If we take the vertex upward in the figure, the surface created will be convex 1 [11].Also, we can freely create combinations U of concave and convex surfaces, such as some parts being concave and other parts convex. Go to Figure 10. Figure 13 shows the case where the projection /j shape changes when the ``l pUr41 triangle is divided. In the case of 21 sections 1 to 9, the first stage triangle 1' 10 is divided into several stages 1) 11. In this case, the projected /j triangle is the first stage triangle 1- There are 10, 11, and C, but Figure 10~
In the case of the 1331st head, the first stage ■li triangle 1-10 is 4
When divided into two, the projected shape is different from the first stage triangle T10, and expands and contracts in the horizontal direction. Figure 10 shows the 11th angle Iiii', +, E-gon 'l'
Divide 10 into 4 parts /: If the shape of the rest is 1
It is a flat-in-1 diagram of Figure 10, No. 1114, of Figure 1. FIG. 12 shows that when the first stage triangle +10 is divided into four parts, the entire shape is shrunk and covered, and FIG. 13 is a plan view of FIG. 12. In the case of FIGS. 10 to 13 above, the first to third division loss points are set at positions other than the side surfaces of the triangular prism shown in FIG. 2. In other words, the first to third division beat points may be provided at arbitrary positions. Figures 10 to 13 are examples of dividing the first stage triangle into second stage triangles, and the division into nth stage triangles.
In the same way, the shape can be arbitrarily shrunk. FIG. 14 is a block diagram showing an embodiment of the present invention, which is included in the operating means 3 shown in FIG. In the figure, the first stage triangle setting means BO sets a first stage triangle T10 which is a triangle having a desired shape. The first division loss point setting means B1 is a first stage triangle 1-10.
The first division loss point is provided in a plane that includes any two vertices of the triangle T10 and any point other than the plane of the first stage triangle T10. Further, the second division loss point setting means B2 selects two vertices of the first stage vertices according to other combinations μ and the first division loss point setting means B2.
There is C of b in which the second division stone point is stepped in a plane that includes any point other than the plane of the step triangle TIO, and the third division seed point setting means B3 is set at the vertex of the 111th tfi5 triangle-110. Among them, the remaining combination U includes the two 1 (j points) and the imaginary (f) other than the plane of the first stage triangle 1-10. 7C1 The central triangle setting means B4 sets the central triangle by connecting the first division loss point, the second division 16 points, and the third division Ifj point, and the peripheral triangle setting means B5 is
One side of the central triangle and the first stage triangle [Jfj of 10
At the point J: set three surrounding triangles. The storage means B7 stores information on the results of dividing each triangle. Further, the division repeating means 86 sets one point of the first to third divisions for each of the central triangle and the peripheral triangle, Set new surrounding triangles and add them to −
Step 11 is repeated on the triangle formed in C, and each triangle is divided into four triangles υ1. Next, an example of means for determining the dividing vertices required in this embodiment will be explained. 15 to 35 are diagrams illustrating the principle of determining the dividing vertices, and FIGS. 15 to 24 schematically illustrate the principle of determining the dividing vertices two-dimensionally. It is. In addition, up to FIG. 35, the bold line portions indicate newly appearing portions in the figures. FIG. 15 shows the first stage settings necessary for determining the dividing vertices. In other words, it is a diagram showing a first point 11° provided at an arbitrary position. Note that the first point 11, the second point 12, and the first
It is assumed that the straight line 1 and the second straight line 2 exist on the same plane. In other words, we are trying to create a dividing vertex at a desired position between the first point 11 and the second point 12, where the first point 11 is point P11 in FIG. 12 is considered to be the point P13 in FIG. To set these, for example, ', display 4
Point 11 of M51 is set by placing Ben 2 on Lie 1 at an arbitrary position above. Next, in the same manner, a second point 12 is set at an arbitrary position other than the first point 11. Furthermore, the first point passing through the first point 11
A line aL1 is set, and the direction of this I'1FLLL1 is set by the keyboard '1.Also, a second line I!; Set the direction of L2 in the same way. Take the intersection of Direct In L 1 and 1-2, ?13. 41J3.1-Explanation C is the point digit lt or -'IF
Keyboard 1. Information related to the direction of the horn of A. It is not possible to use the light pen 2 (input C, but is of course limited to 1), but to use other manual means such as a digitizer. The basic triangles and isosceles triangles made from the situation shown in Figure 15 have a small 1.l knee b. Connect the first fish 11 and the second point 12, and call this line segment 13. , this line segment 13 is a string.Here, line segment L3
is called a string because it creates a part of the desired shape (contour line) between the first throat λ11 and the second point 12.
This is because if the contour line is considered as a circular arc, the line segment L3 corresponds to a chord. This line segment L3 corresponds to side R12 in FIG. Three lines L1. L2. The triangle surrounded by L3 is
Let's call it the basic triangle. Of the three sides of this U-hontadorigon, the short side is the side formed by the straight line L1 in the above two examples, and the short side is the side formed by the straight line L1. , is a line segment connecting points 11 and 13. Create an isosceles triangle with this short side equal to 7 so that it overlaps the basic triangle. In other words, the length from the intersection 13 to the first point 11 is 173
1 and set above the second fU line L2 from the intersection 13. This point is indicated as 21. Therefore, the other equilateral side of the isosceles triangle is the line segment connecting point 21 and intersection 13 in FIG. Draw the line segment connecting the first point 11 and point 21 by 1-4 degrees. FIG. 17 is an explanatory diagram of the 'A case in which the necessary constant α is determined when finding the third point.1 Here, the third point is the point r− in FIG. ' This corresponds to the 22nd mag split reconnaissance point. 13 and J9ζ1 'I also have a 5. ), point ゛1
The line segment connecting 1 and 1:, ζ21, etc. has five characters (indicates the river rock that is caught! Jb, and here is the following). The constant tX is structured as follows: a=(area of Δ(21)(11)(13))/(Δ(1
2)(1+)(22) surface beat), 13, Δ(21)(+1)<13) is the point 2'12
Point 111 points 13 't'' Ill indicate a triangle,
For the following, we adopt the representation method of N1rj1 for the 51 triangles. Figure 18 shows 31 when finding the inner center of the above isosceles triangle.
This is a clear diagram. Generally, the incenter of a triangle is the intersection of the bisectors of each interior angle, and the three bisectors intersect at one point. Let L6 be the bisector of the interior angle extending to point 21 of the isosceles triangle. Let the intersection of these trisectors 1iL5.16, that is, the inner center of the isosceles triangle, be the point 23. Further, the midpoint between the point 11 and the inner center 23 is set as a point 24, and the midpoint between the point 21 and the inner center 23 is set as a point 25. FIG. 19 is an explanatory diagram for finding the inner center of the basic triangle. The bisector of the interior angle J3 at point 11 of the basic triangle is the straight line L
7, the bisector of the interior angle of the basic triangle 12 is the i-line L8, and the intersection of these bisectors L7 and L8, that is, the interior center of the basic triangle, is the point 14. FIG. 20 is an explanatory diagram when determining the unbalance amount S. Upper nj! In order to determine the third point, a parameter β is also required in addition to the parameter α, and in order to determine this parameter β, it is necessary to determine the unbalance ms. The unbalance amount S is based on the difference between the attributes of the basic triangle and the attributes of the isosceles triangle. (a) To set the balance 16S, first overlap Figures 18 and 19. That's right, three equal parts! *Extend L7 and L8, set perpendicular line L9 at point 24, and set perpendicular line L9 at point 25.
L 10@ established. Perpendicular line [9 and trisection 1. Let the triangle surrounded by jl L8 and the first straight line [-1 be Sl, and! I! Line L 1.0, bisector L'7 and second straight F
It L 2 and J, (take 82 triangles as asked)
Ru. The unbalanced ms can be claimed as follows. 5 = (S17) if 100 rj) - (S 2 (F) im (
n) However, unbalanced fil
Turn S into a sea urchin °C-b. ＼ Figure 21 is an explanatory diagram for calculating the distance 11111d from the inner center 14 of the basic triangle to the third point that we are currently trying to find. Draw a straight line connecting the inner center 14 of the basic triangle and the intersection 13.
What should I do? This straight line LII is a bisector of the interior angle that intersects the intersection point 13 of the basic triangle. The third fly that we are trying to find now is displayed as point 33, and this third point 33 is fjFr.
There are things that exist in the soil of lLll. Conversely, there is a point where the bisector L11 and the shape to be filled intersect, and this intersecting point is called the third point 33. I am trying to do. and,
The distance between the third point 33 and the inner center 14 of the basic triangle is defined as d. This distance 1111d can be determined as follows. d-β(α·S)/γ This parameter β will be called a position control parameter. Note that the parameter γ is calculated from the first point 11 to the second point 11.
This is the length up to point 12. Figure 22.23 shows the third straight line [
FIG. Here, the third straight line 113 is a tangent to the shape contour line extending to the third point 33. In other words, the first point 11 and the second point
When a contour line of a desired shape is created between the point 22 and the point 22, the tangent of the contour line to the third point 33 is the third straight line 1.13. Conversely, the third direct Fi113 is
This is a straight line necessary to create a new third point between the third point 33 and the first point 11. This third straight line 1
It's my turn to make 3, and I go to the next one. Let the straight line passing through the first point '11 and IU33 be 1-9,
A straight line passing through the second point 12 and r:i33 is L'I O
Toshi, direct Fi! The bisector of the intersection angle of 110 and 19 is 1-
Take 12. This trisection PjA112 is shown in FIG. In the plane of the basic triangle, bisector 12 and 0
113 lines intersect with each other and pass through the third point 33. The angle 0 can be expressed as follows. 0..δ.(α.S)/A This parameter δ is called the tangent control parameter, and Δ is the area of the j:4-tree diagonal. This J 4'1/,: jl FAI-'I
3 is the third white line L 13 (゛). (, OI
You can set the position of the point corresponding to 1]32 in Figure 3 where the 41st point is lit. Figure 24 shows 1-J, sea urchin C1 new! This is an explanatory diagram when calculating the 33rd point. 1 In other words, the third point 33 is the second point 12 shown in FIG.
The third i-line L13 is considered as a substitute for the second straight line 12 shown in FIG. 28, and the operations explained in FIGS. 15 to 21 are repeatedly executed. Point 21a corresponds to point 21 shown in FIG. 16, and point 13a corresponds to point 13 shown in FIG. 15. Therefore, Δ(11)(33)(13a) is a new basic triangle, and Δ(11)(21a)(13a) is a new isosceles triangle. Then, by performing an operation similar to that shown in FIG. 22.23, a new third straight line can be drawn. Here, we will explain up to Figure 23 and explain IC 3.
If this point is taken from the division 111 point P22 in FIG. 2, the third point of the new IC becomes the division apex P32 in FIG. Also, between the second point 12 and the third point 33,
A similar operation is performed to determine another new third point and another new third straight line. In this way, a large number of dividing vertices are set between the first point 11 and the second point 12. Then, (
An fJ dense polygon can be formed. Also, according to the above l1jj filling, to make changes to the created dense polyhedron, each buff meter can be changed, and this parameter - ( is the first I , the second Sada +2 (tl, that is, Sada P-11,1:
)12.113>'s 4CI neck ``1st ``IL'' 1 direction, 2nd ii'4 line [2 1j direction, constants β, δ are i
15 Ru. An example of changing the parameters using this J is ¥112
Snake) From Figure 27, there is C. . Figure 25 is -1 rose makeup l), 1st 1° 1
Line (-1 jl direction and ε (12 n'j line 1-92)
In this case, the locus of the divided vertex can be changed to any J, which is the same as the small I. In the figure, the locus C is The 1'1 line is 11,
This is the locus of 111 division points that fall when the second straight line is L2, and is considered to be one cross section of a dense polyhedron. Here, the first straight line is set to Llb without changing the first point 11, the second point 12, the position control 11 parameter β, and the tangent control + parameter δ. , when the second straight line reaches 1-2b, the locus C becomes the chain double-dashed line cb
Then the trajectory changes. The feature when the direction of the 1st 2 straight lines Ll and L2 is changed is that the convex part of the trajectory becomes the bisector L1
1, there are ML transfer words up and down. J, that is, the first direct I! When 1lL1 is rotated in the time crystal 1 direction (in this case, the second straight line L2 is rotated in the anti-UN1 direction), the two points are 1ml! As can be seen by comparing the trajectory cb of it with the shape C, the convex part of the trajectory cb is the bisector L11
11 moved to F7J. First straight line and reverse 1, counter time n
1jJ in one direction (in this case, the second straight line L2 is the clock 1
direction), the convex part of the trajectory after the change is:
, move 11[ above the equal dividing line L11. In this case, the 1.2nd straight line L1. It is necessary to avoid a situation in which both straight lines 11 and 12 become parallel to each other as a result of each rotation of L2. This is the first point 11 or the second point
This is to cover the trajectory so that it does not have an inflection point at point 12 of -3. Next, the first yjλ11/,:
G;L At the second point 12 (, if the locus can have an inflection point, there is a special restriction on its rotational state between the first straight line FJLI and the second straight line L2) There is no need to step (). FIG. 26 shows how the shape is changed when only the position control parameter β among the above parameters is changed. As the position control parameter β is changed, the degree of bulge of the entire shape, that is, the curvature of the trajectory changes.Figure 26 shows that the position control parameter β is set to a positive value, and once the trajectory C is determined. , shows the change in the trajectory of GJ when the position control parameter β is changed to the ship Sl.In this way, when the parameter β is changed to a negative octopus, the trajectory when /j (, C is , compared to locus C, its bulge is smaller (it is closer to chord L3).In other words, when positional control + parameter β is set to 0, the shape becomes the inner center of the basic triangle. 14.If we change the parameter β to it's octopus, the trajectory will curve closer to the b intersection 13 than the inner center 14, and the larger the β, the closer it will be to the intersection 13. If the parameter β is set to a negative value, the locus will shrink so that it is closer to the string L3 than the inner center 14, and the larger the absolute value of the parameter β, Close to string L3 (=J < J
: Shrink the sea urchin. In other words, the trajectory C approaches a straight line. In the name of position control parameter β, “position” means fJ
II is the position that intersects the bisector L11 of the trajectory created, and when the position control parameter β is changed,
The crossover position is changed. Therefore, for other parts of the locus formed by the mouth, only the curvature of the locus changes. Furthermore, if the trajectory created before changing the position control parameter β is within the basic triangle, even if the position control parameter β is changed afterwards, the trajectory created by n1 will be within the basic triangle. It never sticks out. FIG. 27 shows how the locus can be changed when only the tangent control parameter δ among the above parameters is changed. When the contact FIla, ++ control parameter δ is changed, the point (-'? (1) is k: Jj G
J rum 1 (1) Jjvj Jj J, and 20th
) r, 'a corresponds to +: +1 > C3 (,
The bulge of the shape can be changed. That is, the locus C is determined to be -1,1 between the 1st i 1 1 and the 2nd i 12, and IC is taken. in this case,
The third straight line L゛13 is at the third point 333 of -f [)
C71j of the tangent line of locus 0 and 1111b. Ishi C1
Third! , ', i33 and 30th) i'i t! it
For the next 11.7 fish after I-'I 3 is determined, the direction of this tangent 1- + 3 and the first iil flll L,
'Depending on the direction of I (, + of ε'11:, i11 and the third
A new point is determined between 33 and 33, and the trajectory is gradually determined. However, the fact that the tangent control parameter δ is changed (the tangent (third iin Fed I-1)
) change the direction of (J)
Changing the 1B line control υ11 basimeter δ (this is the same as changing the direction of the second line IL2 when creating the shape for the first time, and in Figure 25 - [Think in the same way as explained above) However, in this case, since the first straight line L1 does not change, the position in the middle of the shape (third point 33)
There is a discontinuity in Specifically, by changing the tangent control parameter δ to the third point 33, the third white line L13 is changed directly, for example, in the direction of t!if L 13 d.
Jj between the third point 33 and the first point 11, the trajectory changes to a two-dot chain FilC<J. In other words, by changing the tangent control parameter δ, J:T-C1 third i
When iMFilL13 is rotated in the a1h direction, the Ω1 shape expands to the right in the figure at the bottom of the bisector L11. This tangent control parameter δ is dangerous because it increases the self-improvement of the shape creation operation. Further, the position control parameter β and the tangent control parameter δ are between the third point 33 and the first point 11, or between the first point 33 and the second point 33 and the second point 12, Shape 01
This is a case where the shape is modified or J is performed. 1. It is easy to change the value, it is easy to modify the shape of the entire locus C (if only it is possible), and it is easy to freely modify the shape of a desired part of the locus C ( Figure 28 shows the original Jql that simply puts the third 11'1 line.
There is an explanatory diagram showing this. The intersection of the extension of the straight line L9 and the second straight line FJ L-2 is one point; 34, the extension of the straight line 11.0 and the first straight line L1
Which intersection point is taken as point 35, draw a straight line L14 connecting these points 34 and 35, move this straight line L14 parallel to the soil of the third point 33, and trace the drawn straight line 115 times. This direction
L15 is used instead of the third straight line L-13. ,0
If the above is uncertain, I.
It is convenient to use i1 line 1-15 as the third straight line.
be. ``Explanation of ``There is a creation or modification of Hei 1fii-like shapes. However, if this shape creation is applied, it is possible to create or modify a three-dimensional shape. In other words, by first creating a planar shape as described above and stacking the shape created in this way, it is possible to fill the shape as a so-called flexible soy Al frame or network frame. Although the above explanation is for creating a shape, it can also be applied to describing an existing shape. In other words, it is sufficient to first roughly create a shape close to the existing shape, and then control the shape by changing the position control parameter β or the tangent control parameter δ with respect to the created shape. In some cases, the first point 11. The direction of the first straight line L1 and the direction of the second straight line L1 may be changed by 12 degrees at the second point. Next, determine the locus of the divided vertices three-dimensionally.
The iI principle will be explained. In this case, instead of suddenly creating a three-dimensional locus, the idea is to create a three-dimensional contour line of the locus and then create a desired shape by continuing the contour lines. FIG. 29 shows point 'l' 51. Second point 52. Set the first straight line -551, the second straight line Fll I-52, and set the IC
FIG. 1 shows the state. Note that the first straight line [51 is the point 51
, and the negative 12 straight line L52 passes through Sada 52. Then-C1 A string ;)0 is established by connecting the first fish 51 and the second point 52. i connecting the first point and the second fish
The reason for expressing the t'j line as a string is the same as that described in FIG. 16. Here, it is assumed that the extension line of the first line 1-51 and the extension line of the second straight line 1-52 do not intersect. Suna 4
However, the trajectory of the split loss Jj1 that will be created from this is a three-dimensional curve e, but (the '1st point 51 and the second point 51)
Between 2 and 1111, the contour line from now on is r? 6-L, often absent. Also, the first 11 lines! i 'I is u + 'l's Buddha t5゛1) that circle ζ・1; the tangent of the line is the (20th) vj line 152 is the second line! The contour of tJ on j2; there is b (1) l'' which should be tangent to l. In many cases, it does not intersect with. Figure 30 LJ, chord 50 second straight line L52 do'cJia
It is an lc diagram showing a state in which the first straight line L51 is oriented q4 on the surface formed by the first straight line L51. A straight line 153 is an orthogonal projection of this first straight line L51. That is, when light is applied perpendicularly to the surface composed of the string 50 and the straight line L52, the shadow of the first straight line 51 is straightened to 53. FIG. 31 is a diagram showing a state in which the second direct mL52 is orthogonally projected onto a surface constituted by the chord 50 and the first straight line L51. A straight line obtained by orthogonally projecting this second straight line Lb2 is 154
shall be. 1, that is, when light is applied perpendicularly to the surface formed by the string 50 and the straight line 51, the shadow of the second straight line 1-52 is 11 lines L 5 /1. FIG. 32 is a diagram of the basic triangular forceps. Connect s'X 53 and point 5/I and take this straight line [55. In this way, lines 150,1-51. L52,
There are four faces surrounded by C53, L5/I, and C55, and the triangular forceps surrounded by these faces are called the basic pentagonal pyramid. FIG. 33 is a diagram for creating a defining triangle Σ. One point ξ)5 on the line segment L5J can be requested by the torsion control parameter ε. This torsion control parameter εt can be determined from the L-order equation. ε-1) i / D 2 Here, ri 1 is the distance from member 54 to IAi 55, and the distance from D 21J 5/1 to point 53 (distance a 'c
be. Distance nth) 1.1) 24; The shape of the object changes. See you again! Q+lI Illll parameter, it's embarrassing to compare Kakuma. child(
1) J:;j 15 mi) and the first r: (i !□5
The line segment connecting ゛1 is l−ji 6, and 吃j E) j
Take a line segment L57 connecting this point and the second point 52. 1 A pentagon with 1 river between these bars 1150, 6 and 157 is called a triangle with definite angles. 334th stomach, there is a diagram of 1 regular triangle inside the 2, which makes 4 triangles. The first 11 pages! 1. −51 free i constant I − i to the square Σ
The river bank is defined as a straight line 158, the orthogonal projection of the second line [52 onto the provisional triangle Σ is defined as a straight line 59, and the intersection of these straight lines 58 and the straight line 19L59 is defined as a point 56. This sea urchin - (3-dimensional required when the resulting straight line L5 (3), the rectangle surrounded by the straight line 1-59, and the line segment 50 create and cover the locus of the three-dimensional dividing vertices; 11; II
This three-dimensional basic triangle corresponds to the U-triangle created in FIG. 16 when creating a two-dimensional shape. FIG. 35 is an explanatory diagram for creating an isosceles triangle from a three-dimensional basic triangle. The three-dimensional basic triangle mentioned above can be treated in the same way as the basic triangle in the 16th term 1, so that when creating a shape at point A, it can be treated in the same way as the two-dimensional one described above. You can think about it. That is, based on the three-dimensional basic triangle Δ(52)(51)(56) and the isosceles triangle IΔ(59)(51)(5(i)
If you perform the same operations as shown in Figures 5 to 23, the point 71 of J month II3 and the third direct Fll 1-73 will become IT in three dimensions.
, 1 will be given. However, when creating a three-dimensional trajectory of divided vertices, JI
It is necessary to use the M rate system υ11 auxiliary buff meter φ. Rinawachi claim J: On the contour line of the undulating shape (13I)
s: j 7 'I's connection; 1 is the third 1゛I coin 11
-733 for three-dimensional use 4. A certain corner 1a in the plane of the U triangle is ij. This certain corner KL is a screw skewer system υ1
1 auxiliary parameter φCi & S, one to this angle 11; IW
There is a mustsen that can be placed in I. 1 In this way, there are 172 (tangent lines) 1clI'i lines (tangent lines) by taking into account the torsion kipuff meter ψ.
The points shown in Figures 5 to 24 are 1. : corresponds to a straight line. In this way, considering the torsion control auxiliary parameter φ, the straight line bf, t and the first straight line I! ll l-51 or 1= is the second ii
l + Ell + - 52 and J: Therefore, by performing the lc operation shown in Figure 35 from the negative 129 (j), c1 a new third point J3 and a new third 11''i line. 1! It is possible to do C.By repeating these operations, it is possible to create a ring tS line of the three-dimensional a locus of the divided vertices. By dividing triangles one after another according to o, o>, the direction cosine of the first straight line L51 is (0, O, 0, 7232, 0, 6906), and the position (vote) of the second point 52 is (0, 0, 2° 0, π ), the direction cosine of the second straight line is (, -, 0. 7232.0.0, 0.6906), and the system 611
If the parameter β is O, the tangent control parameter δ is 0, the torsion parameter ε is 0.5, and the torsion control auxiliary parameter φ is -0,0467, the locus of the divided vertex created by these is as follows. Constant slope linear shape (spiral)
to accomplish. FIG. 36 is a block diagram illustrating an embodiment of the apparatus for determining the dividing jlfj points used in the present invention. The principle is shown in FIG. 28. A first point setting means 81 sets the first point 11 at an arbitrary position 1 as shown in FIG. Set 12 second
A point setting means 82 is provided. Also, the first point 1
a first straight line setting means 83 for setting a first straight line L1 passing through the second line 12 in an arbitrary direction; and a second straight line setting means 83 for setting a second straight line L2 passing through the second line 12 in an arbitrary direction. Means 84
and is the set number. These setting means 81 to 84 include the keyboard 1. There are input means such as lie 1 to pen 2. In addition, as the principle is shown in Figs. 15 to 23,
゛The first straight line at the position of the first point 11 [1 direction and the position 63 of the second point 12 J: and the second straight line L
A third point/i-line determining means 85 is provided for determining the position of the third point 33 and the direction of the third straight FllL i 3 including the third point 33 according to the direction of the third point 33 ( There is. Performance n
By using the circuit 3, the third point/straight line determining means 85 is operated. The principle for finding the locus of the 10 divided points in a two-dimensional manner is the same as that explained in Figures 15 to 23'C. For this purpose, it is necessary to use 15 [immediate], which was explained in J3 in Figs. 30 to 33E5. The performance circuit 3 has a circuit configuration that realizes all of these principles.Also, instead of the performance circuit 3, a =J computer is used. Furthermore, the third point/straight line determining means 85 has a parameter β.
, δ, ε, φ, etc., is provided. As this input means 86, a keyboard 1 etc. can be considered. Each point determined by the third straight line determining means 85 is provided. A storage device 87 is provided for storing information on the first point 11.
The third point can be found from the first straight line 1, the second point 12, and the second straight line. FIG. 37 shows the following points based on the already set or determined point J3 and the direction of the straight line J3 to that point, and the point newly determined by the determining means 85 and the direction of the straight line to that point. A control means 88 is provided which repeatedly controls each means 81 to 84 and arranges a large number of points between the first point 11 and the second fish 12. The operation of this control means 88 is the same as the principle explained in connection with FIG. FIG. 38 is a block diagram of a device for two-dimensionally determining the locus of division concerns. In this block diagram,
The principle is shown in FIG. A second value setting means 82 for setting the point 12 is provided. Also, a first alignment means 83 for setting the first ii'I line L1 passing through the first point 11 in an arbitrary direction, and a second point '12
, but t) the first point ゛11 etc. the first i white line [1
The second straight line J3 is in the plane formed by τ414 [
2nd jli t' for two dimensions where 2 is set in any direction
There is a setting number for the AW setting means 91, etc. In addition, the j and 4" llj are shown in FIGS. 15 to 23.
-3 and the first straight line 1. The back of the three sides of the basic triangle formed by -1 and the second straight line [2, 12 sides except for the side with the chord L3, 11-! 71 Creating an isosceles triangle with q sides of one side , Nii, based on the attributes of the basic diagonal and the l1ii 1!l phase 3t of the isosceles triangle, the third
A third point display means 93 is provided for directing the direction of the straight line including the position j;j and the third point. In detail, this third performance means 93 consists of the following constituent publications. In other words, the incenter position disease n that affects the incenter position of the basic triangle and the incenter position of the isosceles triangle
Except for the means 93a (application of the principle of Fig. 18.19) and the vertices of specific angles shared by the basic triangle and the isosceles triangle,
A straight line connecting one vertex of a basic triangle and the inner center of the basic triangle, and a perpendicular bisector of a line connecting the opposite vertex of the isosceles triangle to the one vertex and the inner center of the isosceles triangle. , a first triangle area calculation means 93b (an application of the original LIll in FIG. 20) for calculating the area of a first triangle surrounded by the one vertex and the opposite side; Excluding C1 Perpendicular to the straight line connecting the other vertex of the basic triangle and the center of the basic triangle and the line connecting the center of the isosceles triangle, the ICC point opposite in the isosceles triangle to the 10 points of the corner. Bisector and +
'+i+The second triangular face surrounded by the vertex and the opposite side f? The second triangle area operation 01 stage 93c (ltl ]!l! application of Fig. 20) which operates 1,
From the characteristics of the inner center of the basic triangle, we can calculate the difference in area between the first triangular face (tube and the second triangle) and the distance n1 between the first J:, i and the second 1j, (. #1] Away from the location e city C1 bisector 1 of the specific angle ``l as the position of the third summer ja) Exit means g 3
d (application of the principle of FIGS. 2114 to 23). Further, the third point) ψth) means 92 includes constants β and δ. A means 94 for manually calculating ε and φ is installed, and a storage device 87 for storing information on each point determined by the third point calculation means 92 is installed. The circuit 3 includes the basic triangle/isosceles triangle creation means 92 and the third point sieve means 9.
It is possible to perform the functions of 3 and 3. "Effects of the Invention" The present invention is capable of easily creating a shape or modifying the created shape by a series of many small triangles. Shape processing such as shape recognition equipment, image O setza, etc.
This can be applied to automatic drafting and image creators. In this case, the above device or machine can be used for three-dimensional operation or machine driving. . As shown in item L, the present invention has the advantage of being a single shape forming device that can be freely accessed throughout the entire process from installation to manufacturing.

[Brief explanation of the drawing]

Fig. 1 is an overall diagram of a system showing an embodiment of the present invention, Fig. 2 shows a first stage triangle, Fig. 3 is a diagram divided into second stage triangles, and Fig. 4 is a diagram showing a third stage. Figure 5 is a diagram in which only some of the triangles are divided into third stage triangles, Figure 6 is a diagram in which all the second stage triangles are divided into third stage triangles, and Figure 7 is an exploded view of Figure 4. Fig. 8 is a plan view of Fig. 6, Fig. 9 is a diagram partially divided into 4th stage triangles, Fig. 10 is a diagram of the entire 2nd stage expanded, and Fig. 10 is a plan view, FIG. 12 is a view of the second stage in its entirety contracted, FIG. 13 is a plan view of FIG. 12, FIG. 14 is a block diagram showing an embodiment of the present invention, and FIG. 15 Figure 16 shows the basic triangle and isosceles pentagon created from the situation in Figure 15. Figure 17 shows the settings for the first stage necessary to determine one point per division. When finding the third point (split vertex),
An explanatory diagram for determining the necessary constant α, No. 18- is an explanatory diagram for finding the inner center of an isosceles triangle, Fig. 19 is an explanatory diagram for finding the inner center of a basic triangle, and Fig. 20 is an explanatory diagram for finding the inner center of an isosceles triangle. Unbalance amount S
Figure 21 is an explanatory diagram when determining
1, 22, and 23 are explanatory diagrams for inserting the third straight line extending from the third line to the third line, and the second
Figure 4 is an explanatory diagram when setting a new third point (1'i division vertex). Figure 25 shows only the direction of the first straight line and the direction of the second straight line among the parameters. If you change
Fig. 26 is an IC diagram showing how much the locus of the 111 divided points can change.
+I +c is a diagram showing how the locus of I can be changed (!u). Figure 27 shows the parameters,
A diagram showing how the locus of the divided vertices can be changed when only the tangent control parameter δ is changed, and Figure 28 shows the principle of setting the third straight line by one quotient. The explanatory diagram, Fig. 29, shows the three-dimensional locus of the divided vertices.
The first point. Figure 30 shows the state in which the second point, first straight line, and second straight line are set.
Figure 31 is a diagram showing the state in which the first straight line is orthogonally projected, and Figure 31 is a diagram showing the state in which the second straight line is orthogonally projected onto the surface composed of the chord and the first straight line. The figure is a diagram for creating a basic triangular pyramid, Figure 33 is a diagram for creating a provisional triangle, Figure 34 is a diagram for creating a basic triangle in a color-constant triangle Σ, and Figure 35 is a three-dimensional locus of the dividing In point. FIG. 36 is a block diagram of an embodiment of a device for setting divided vertices, and FIG. 37 is a block diagram showing another embodiment of the device for setting divided vertices. , Figure 38 shows minute 2.11.
FIG. 3 is a block diagram showing another embodiment of the beat point setting device. 1...keyboard, 2...ra-(1~pen, 3...
・Enta) circuit, 4...display, 5...printer, 6...external storage device r(, i i + 51...
・First point, 12.52...Second throat, (, L'l
, L51...first straight line, 12,1-52...second straight line
ifi F, A, 33.71...Third 5 Ki, L1
3, [72...33rd +1JFA z, 81...
- Id 1 point setting means, 82...Second point setting means, 83
...1st shift 1: 3A setting 1 stage, (3/I...2nd I
'1 line step f step, 85... 3rd point/straight line determining means, 9
1...For two dimensions>Ti 2 ii'+i line setting means Setting means...Two excellent sides: [square 41 formation 1" step, 93...
23rd Joen Oer Dan, '93 a =... IGLi in my heart
t performance 0 means, 93 L)--1st E-gon area) νi
n means, 93G...second triangle fr+act(>means,
93d...0 output means, I) 21.1-'31...'1st division loss +: a, P22, P32'''B2
′j,) i! , 1Hfj point, P23. P333...
・Third division Ici point, 110...First stage triangle, 1
20.1130...Central triangle, 121. "1" 22
゜”+23.+33 'l, I'32.+33・
...Peripheral square, +30...1st (71t7+ with 12 steps of diagonal setting, 13'I''・Tts'l division 10 points setting D1, 1]2...2nd division l (eye! a setting means, B3... 23rd divided IC port 11 setting 1 stage, B
4... Peripheral triangle setting means, B5... Central triangle setting means, B6... Division repeating means. Special applicant Ryozo Setoguchi Figure 1 13 Figure 9

Claims (1)

[Claims] (1) It is a triangle that has a desired shape! Step 31 Setting a triangle; Setting any three points; Creating a central triangle by connecting these three points; One point among the three vertices of the first step triangle. and the side of the central triangle corresponding to this one point -C1 Creating three peripheral triangles outside the central triangle: By the central triangle and the three peripheral triangles, a sum 14. A shape creation method characterized by comprising: a second step of configuring triangles; (2) Setting a first stage triangle, which is a triangle having a desired shape; Setting arbitrary three points; Creating a central triangle by connecting these three points; By 11j of the three 11 points of the first stage triangle and the side of the central triangle corresponding to this one point,
creating three peripheral triangles outside the central triangle; constructing a total of 814 second-stage triangles by the central triangle and the three peripheral triangles; moving the three peripheral triangles in the counterclockwise direction; assigning identification numbers to the central triangle in the order of 1, and then attaching an identification number to the central triangle; attaching the identification numbers to the sides of each second-stage triangle in clockwise order; A shape creation method characterized by determining a topological structure for the second-stage triangle, similar to a planar graph. (3) In claim 2, an identification number 1 is attached to each side of each of the second stage triangles in the order of the clockwise direction.
1.2.3, and each second stage triangle has an identification number of 1°2,3 in counterclockwise order with respect to its vertex (
=J, and the sum of the identification number of one vertex of each of the second stage triangles and the identification number of the opposite side of that vertex is 4. (4) Setting a first stage triangle, which is a triangle that extends to the right of the desired shape; Setting arbitrary three points; Creating a central triangle by connecting these three points; First step: connecting one point on the back of the three vertices of the triangle and the side of the central triangle corresponding to this one point to create three peripheral triangles outside the central triangle: The fire triangle is a union i consisting of the three surrounding triangles.
t By repeating the above steps for each of the four second stage triangles (-1 U for each of said second stage triangles, the sum of 14 triangles consisting of one central triangle and three peripheral triangles) Setting a 3-step triangle 19
By repeating the above steps a predetermined number of times, a large number of small triangles are formed based on the triangles of the previous two first steps, and a dense polyhedron is formed by the continuation of these large numbers of small triangles. A shape creation method characterized by: (5) a first stage triangle setting means for setting a first stage triangle which is a triangle having a desired shape; a first divided vertex is set according to two vertices on any side of the first stage triangle; a first division apex setting means for providing; a second division apex setting means for providing a second division vertex according to two vertices related to other sides among the vertices of the first stage triangle; a third division vertex setting means for setting a third division vertex according to two vertices on the remaining sides behind the vertex; the first division vertex, the second division vertex, and the third division I;
A central triangle setting means for setting a central triangle by connecting the point I; and a peripheral triangle setting means for setting three peripheral triangles by one side of the central triangle and the apex of the N81 stage triangle. Shape creation device 0 (6) Claim 5, wherein the means for setting each divided vertex according to the two vertices of the first stage triangle comprises: means for setting a first straight line passing through one of the vertices in an arbitrary direction; and a means for setting a second white line passing through another Ifi point of the first stage triangle in an arbitrary direction. Means of: Of+note one 10th position J3Jζ
and IyI, depending on the direction of the first straight line, the position -3 of the 1rj point of the sen, and the direction of the second straight line. means and a shape generating device characterized by comprising: (7) a first stage triangle setting means for identifying a first stage triangle i, which is a triangle on the right side of the desired shape; a first division υj vertex setting means (setting a first division lfj ratio) corresponding to two vertices related to arbitrary sides of the 'i diagonal; a second division vertex setting means for setting 10 second division points according to the two vertices;
3rd division ln where 10 points are set according to the vertices of the third division
point step determining means; central triangle setting means for connecting the first divided vertex, the second divided vertex, and the third divided vertex to set a central triangle; one side of the central triangle and the third divided vertex; a peripheral triangle setting means for setting three peripheral triangles according to the vertices of the first-stage triangle; and for each of the central triangle and the peripheral triangle,
Set the first and third division vertices, set the central triangle and the peripheral triangles, and repeat the same operation on the triangles formed by these, dividing each into four triangles. A shape generating device comprising: a dividing repeating means; and forming a dense polyhedron by continuation of a large number of triangles formed based on the first stage triangle.