JPH0585933B2 - - Google Patents

Description

[Detailed Description of the Invention] [Technical Field] The present invention relates to CAD (Computer Aided Design),
This invention relates to a device for creating or modifying a desired three-dimensional shape in an NC machine tool or the like.

[Background Art] 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 expresses a desired shape by using a dense point sequence or point group and line elements, and the surface shape description expresses the desired shape by using a dense point sequence or point group and line elements. After that, a desired shape is expressed by performing interpolation processing based on function approximation between those points. In addition, the solid model 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 a three-dimensional shape, and has a problem in that it cannot fully demonstrate its functions. In addition, 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 consistently between the two. be.

For example, even when using the above solid model, by combining simple shapes,
Although it is possible to express a part of a three-dimensional shape, it is difficult to express a free and detailed shape due to its nature, so it is natural that the modeling process must be performed consistently from shape expression to shape creation. This means that it is difficult.

[Object of the Invention] The present invention has been made by focusing on the above-mentioned conventional problems, and an object of the present invention is to provide a single shape creation device that can be freely accessed throughout the entire process from designing to manufacturing a model, etc. This is the purpose.

[Summary of the invention] In order to achieve this object, the present invention first provides the following features:
Set a triangle of the desired shape (first stage triangle),
This first stage triangle is divided into four triangles (second stage triangles), each of these second stage triangles is again decomposed into four parts, these operations are repeated to form a large number of triangles, and these many triangles are divided into four triangles (second stage triangles). A dense polyhedron is formed by a series of triangles.

If this formation creation process is displayed on a display, the shape creation process itself is CAD.
Furthermore, 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, a keyboard 1 and a light pen 2 are provided for inputting positional information regarding the shape to be created, that is, positional information of the shape to be drawn. Further, an arithmetic circuit 3 that performs predetermined arithmetic processing based on input signals from input means such as a keyboard 1 and a light pen 2 is built-in. A display 4 that displays the shape created in this way is provided, a printer 5 that prints the shape, and an external storage device 6 that stores the shape as a predetermined signal such as a magnetic signal or an optical signal.
and is provided.

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. A large number of triangles are formed by decomposing and repeating these division operations, and a dense polyhedron is formed by continuation of these large numbers of triangles. These division processes are shown in Figure 2~
FIG. 13 is shown in sequence.

In FIG. 2, a first stage triangle is shown.

First, as an initial stage of forming a dense polyhedron,
A triangle T10 having a desired shape is set. This triangle T10 will be called a first stage triangle. This first stage triangle T10 has vertices P11, P12,
P13 and sides R11, R12, and R13.
Based on this first stage triangle T10, the triangle is successively divided into four parts.

For convenience of explanation, the first stage triangle T10 is projected onto the projection plane 10 in FIG. 2, and the vertices of the projected triangle are P11a, P12a, and P13a.

Generally, for example, points P12, P13, P13
A dividing point is provided in the space near either the left or right of the plane surrounded by a and P12a, but here, for the sake of simplicity, a point 21 is provided within this plane, and this point P21 is set as the first point. Use as split vertices. Similarly, a point P22 is provided in a plane surrounded by points P13, P11, P11a, and P13a, and this point P22 is set as the second division vertex, and points P11, P12, P12
A point P23 is provided within the plane surrounded by a and P11a, and this point P23 is defined as the third division vertex. In addition,
A method or means for obtaining the first to third divided vertices P21, P22, and P23 from each of the vertices P11, P12, and P13 will be described later.

These first, second and third divided vertices P21, P22,
By connecting P23, a central triangle T20 is set. A peripheral triangle T21 is set by one side of the central triangle T20 and the point P11, a peripheral triangle T22 is set by the other side of the central triangle T20 and the point P12, and the central triangle T20
The surrounding triangle T2 is defined by the remaining sides of and the point P13.
Set 3.

In other words, first, after setting the first stage triangle T10, arbitrarily set three points, connect these three points to each other to create a central triangle, and connect one of the three arbitrary points to the central triangle. Create three peripheral triangles outside the central triangle by using arbitrary sides of the central triangle.

The state in which the first stage triangle T10 is divided into four triangles in this way is shown in FIG.
A plan view thereof is shown in FIG.

In this way, the basis for creating a dense polyhedron is created based on one triangle.

Next, in FIG. 3, the intersections of the vertices P22 and P23 with the projection plane 10 are P22a and P2
3a, points P23, P22, P22
A point P31 is provided in the plane surrounded by a and P23a, and this point 31 is set as a new first division vertex. Similarly, points P22, P11, P11a, P2
A point P32 is provided within the plane surrounded by 2a, and this point P32 is set as a new second division vertex, and the point
1. Set a point P33 in the plane surrounded by P23, P23a, and P11a, and set this point P33 as a new third point.
Use as split vertices.

FIG. 5 shows a state in which the peripheral triangle T21 is divided into four triangles.

1st, 2nd, and 3rd division vertices P31 in FIG.
A new central triangle T30 is set by connecting P32 and P33. This central triangle T30
Another peripheral triangle T31 is set by one side of the central triangle T30 and the point P11, another peripheral triangle T32 is set by the other side of the central triangle T30 and the vertex P23, and the rest of the central triangle T30 is edges and vertices P
33, another peripheral triangle T33 is set. In this way, triangle T21, which is one of the second stage triangles, can be divided into four triangles again.

Figure 5 shows one peripheral triangle T in Figure 4.
Only for 21, the state where the triangle is decomposed into four is shown, but other surrounding triangles T22, T
23 and the central triangle T20 can be similarly divided into four triangles.

FIG. 6 shows a state in which the other peripheral triangles T22, T23 and the central triangle T20 are each divided into four parts.

In addition, when the first stage triangle is divided into four, the central triangle and the peripheral triangle are called the second stage triangle, and when the second stage triangle is divided into four parts, the central triangle and the peripheral triangle are called the third stage triangle. , and the division is repeated in the same manner up to the nth stage triangle. In this way, by sequentially dividing into four triangles based on the first stage triangle T10 and repeating this dividing operation a predetermined number of times, a dense polyhedron can be constructed.

The greater the number of n stages, the higher the accuracy or denseness of the created polyhedron.

FIG. 7 shows the central triangle T20 and peripheral triangles T21, T22, and T23 shown in FIG. 4 separately.

In this Fig. 7, three peripheral triangles T2
1, T22, and T23 in counterclockwise order (numbers 1, 2, and 3 in the example), and then the central triangle T20 is given an identification number (number 4 in the example). ) is attached. Also,
Second stage triangle T20, T21, T22, T23
The same identification number as the above-mentioned identification number is given to each side in clockwise order. By doing this, the second stage triangles T20, T21, T2
2, T23 has the advantage that the topological structure can be determined similarly to the planar graph.

An identification number is also provided for each side of the second stage triangle. That is, focusing on one second-stage triangle, identification numbers are provided for each side so that the sum of the identification number of one vertex and the identification number of the opposite side of that vertex is 4.

FIG. 8 shows an identification number assigned to each third-stage triangle when the triangle is decomposed to the third-stage. That is, as shown in FIG. 7, identification numbers 1 to 4 are used in the second stage triangle, and in the third stage triangle, the identification number starts from 5, and first, the number 4 included in the peripheral triangle T21 (identification number 1) is used. Identification numbers 5 to 8 are assigned to the three triangles in the clockwise direction and in the order of the central triangle, and then similarly, the peripheral triangles T22, T2
3. Four identification codes are attached to each of the central triangles T20 in this order. The same applies to the identification numbers for the fourth and subsequent triangles.

FIG. 9 shows the case where only the third stage triangle T31 is divided into four parts.

In the above example, as the division is performed, the created surface is a concave surface, but if the division apex is taken upward in the figure, the created surface becomes a convex surface. Furthermore, the combination of concave and convex surfaces can be freely selected, such as having a concave surface in some parts and a convex surface in other parts.

FIGS. 10 to 13 show cases in which the projected shape changes when the first stage triangle is divided. In other words, in the case of FIGS. 2 to 9, even if the first stage triangle T10 is divided into several stages, the projected triangle is the same as the first stage triangle T10, but in the case of FIGS. In the case of Figure 13, if the first stage triangle T10 is divided into four, the projected shape is the first stage triangle T10.
Unlike, it expands and contracts in the horizontal direction.

FIG. 10 shows that when the first stage triangle T10 is divided into four, the entire shape expands, and FIG. 11 is a plan view of FIG. 10.

FIG. 12 shows that when the first-stage triangle T10 is divided into four, its entire shape is contracted, and FIG. 13 is a plan view of FIG. 12.

In the case of FIGS. 10 to 13 above, the first to third division vertices are set at positions other than the side surfaces of the triangular prism shown in FIG. 2. That is, the first to third division vertices may be provided at arbitrary positions.

Figures 10 to 13 are examples of dividing a first-stage triangle into second-stage triangles, but the division into n-th stage triangles is also convoluted, and the shape can be contracted arbitrarily. .

FIG. 14 is a block diagram showing one embodiment of the present invention, which is included in the calculation means 3 in FIG.

In the figure, the first stage triangle setting means B0 is a first stage triangle T10 which is a triangle having a desired shape.
This is to establish the following.

The first division apex setting means B1 selects any two vertices of the first stage triangle T10 and the first stage triangle T10.
10 in a plane containing any point other than the plane
A dividing vertex is provided. Further, the second divided vertex setting means B2 selects two vertices of other combinations among the first stage vertices and the first stage triangle T10.
The third dividing vertex setting means B3 sets the two vertices of the remaining combination of the vertices of the first stage triangle T10 and , the third division apex is provided in a plane that includes any point other than the plane of the first stage triangle T10.

Further, the central triangle setting means B4 connects the first divided vertex, the second divided vertex, and the third divided vertex to set the central triangle, and the peripheral triangle setting means B5 connects one side of the central triangle. Three surrounding triangles are set by the vertices of the first stage triangle T10. The storage means B7 stores information on the results of dividing each triangle.

Further, the division repeating means B6 sets the first to third division vertices again for each of the central triangle and the peripheral triangle, newly sets the central triangle and the peripheral triangle based on these first to third division vertices, and The same operation is sequentially repeated for the triangles formed by , and each triangle is divided into four triangles.

Next, an example of means for determining the dividing vertices required in this embodiment will be explained.

15 to 35 are diagrams showing the principle of determining the above-mentioned dividing vertices.
The figure diagrammatically shows the principle of finding dividing vertices two-dimensionally. 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.

That is, the first point 11 provided at an arbitrary position,
3 is a diagram showing a second point 12, a first straight line L1 passing through the first point 11, and a straight line L2 passing through the second point 12. FIG. Note that it is assumed that the first point 11, the second point 12, the first straight line L1, and the second straight line L2 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.
is the point P11 in FIG. 2, and the second point 12
is considered to be point P13 in FIG.

To set these, for example, by setting the light pen 2 at an arbitrary position on the display 4, the first point 11 thereof is set. Next, in the same manner, a second point 12 is set at an arbitrary position other than the first point 11. Furthermore, a first straight line L1 passing through the first point 11 is provided, and the direction of this straight line L1 is set by the keyboard 1. Also, a second straight line L passing through the second point 12
2 is provided, and the direction of the straight line L2 is similarly set. The intersection of straight lines L1 and L2 is defined as intersection 13.

Note that in the above explanation, information regarding the position of a point or the direction of a straight line is transmitted using the keyboard 1 and the light pen 2.
However, the input information is not limited to these, and may be input using other input means such as a digitizer.

FIG. 16 shows a basic triangle and an isosceles triangle created from the state of FIG. 15.

The line segment connecting the first point 11 and the second point 12 is designated as L3, and this line segment L3 is called a string. Here, the line segment L3 is called a chord because it is a part of the desired shape (contour line) between the first point 11 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.

A triangle surrounded by three lines L1, L2, and L3 will be called a basic triangle. Of the three sides of this basic triangle, excluding the side formed by the chord L3, the short side is the side formed by the straight line L1 in the above example, and this short side is the point 1
This is a line segment connecting point 1 and point 13. Create an isosceles triangle with the short sides as equal sides so that it overlaps the basic triangle.

That is, the length is the same as the length from the intersection 13 to the first point 11, and is set on the second straight line L2 from the intersection 13. This point is indicated as 21. Therefore, the other equilateral side of the isosceles triangle is point 2 in Figure 15.
1 and the intersection point 13. First point 11
Let L4 be the line segment connecting the point 21 and the point 21.

FIG. 17 is an explanatory diagram for determining the necessary constant α when determining the third point. Here, the third point corresponds to a dividing vertex such as point P22 in FIG. 2.

Let L5 be a straight line that bisects the interior angle of the first point 11 in the isosceles triangle. Its interior angle is ∠(13)〓
It is. Here, ∠(13)〓(21) means point 13 and point 1
1 and the line segment connecting points 11 and 21, and the same method of expressing angles will be used below.

The constant α is determined as follows.

α={Area of Δ(21)〓(13)} /{Area of Δ〓〓(22)} Note that Δ(21)(13)〓 is point 21, point 11, point 1
A triangle surrounded by 3 is shown, and the same method of representation for triangles is adopted for the following.

FIG. 18 is an explanatory diagram for finding the inner center of the above-mentioned isosceles triangle.

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 at point 21 of the isosceles triangle. These bisectors L5, L
6 intersection point, that is, the incenter of the isosceles triangle, is the point 23
shall be. Also, the midpoint between point 11 and inner center 23 is point 24, and the midpoint between point 21 and inner center 23 is point 2.
5.

FIG. 19 is an explanatory diagram for finding the inner center of the basic triangle.

The bisector of the interior angle at point 11 of the basic triangle is a straight line L7, the bisector of the interior angle at point 12 of the basic triangle is a straight line L8, and these bisectors L
The point 14 is the intersection of 7 and L8, that is, the inner center of the basic triangle.

FIG. 20 is an explanatory diagram when determining the unbalance amount S.

In order to find the third point above, the parameter α
Another parameter β is also required, and in order to obtain this parameter β, it is necessary to determine the unbalance amount S. The unbalance amount S is based on the difference between the attributes of the basic triangle and the attributes of the isosceles triangle.

In order to obtain the unbalance amount S, first, FIG. 18 and FIG. 19 are overlapped. Then, bisectors L7 and L8 are extended, a perpendicular line L9 is provided to point 24, and point 2
A perpendicular line L10 is provided at 5. Perpendicular line L9 and bisector L
8 and the first straight line L1 is S1, and the triangle surrounded by the perpendicular L10, the bisector L7, and the second straight line L2 is S2.
The unbalance amount S is determined as follows.

S={area of S1}−{area of S2} However, the unbalance amount S may be determined by a method other than the above.

FIG. 21 is an explanatory diagram when calculating the distance d from the inner center 14 of the basic triangle to the third point that is currently being calculated.

Let L11 be a straight line connecting the inner center 14 of the basic triangle and the intersection point 13. This straight line L11 is a bisector of the interior angle at the intersection point 13 of the basic triangle. It is assumed that the third point to be determined now is indicated as a point 33, and that this third point 33 exists on the straight line L11. Conversely, there is a point where the bisector L11 and the shape to be created intersect, and this intersecting point is called the third point 33;
I'm trying to find 3. And the third point 33
Let the distance between the inner center 14 of the basic triangle be d.

This distance d 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 the length from the first point 11 to the second point 12.

22 and 23 show the third point at the third point 33.
FIG. 3 is an explanatory diagram when finding a straight line L13.

Here, the third straight line L13 is a tangent to the shape outline at the third point 33. That is, when a contour line of a desired shape is created between the first point 11 and the second point 22, the tangent to the contour line at the third point 33 is the third straight line L13. Conversely, the third straight line 13 connects its third point 33 with the first point 33.
This is the straight line necessary to create a new third point between point 11 of . To create this third straight line L13, do as follows.

The straight line passing through the first point 11 and point 33 is L9, and the straight line passing through the second point 12 and point 33 is L10.
and the bisector of the angle of intersection between straight lines L10 and L9 is L
12. This bisector L12 is shown in FIG. In the plane of the basic triangle, bisector L12
Let L13 be a straight line that intersects with θ at an angle of θ and also passes through the third point 33. The angle θ can be determined as follows.

θ=δ·(α·S)/A This parameter δ is called a tangent control parameter, and A is the area of the basic triangle.

The straight line L13 created in this way is the third straight line L13. Using this third straight line L13,
By executing the operations explained in FIGS. 15 to 21, the position of a new third point (the point corresponding to point P32 in FIG. 3) can be determined.

FIG. 24 is an explanatory diagram when a new third point is determined as described above.

In other words, the third point 33 is the second point shown in FIG.
The third straight line L13 is considered as a substitute for point 12, and the third straight line L13 is
Considered as a substitute for the second straight line 12 shown in Figure 8, the first line
The operations explained in FIGS. 5 to 21 are repeatedly performed. Point 21a is point 2 shown in FIG.
1, and point 13a corresponds to point 13 shown in FIG. Therefore,
Δ〓(33)(13a) is a new basic triangle,
Δ〓(21a)(13a) is a new isosceles triangle.

Then, by performing operations similar to those shown in FIGS. 22 and 23, a new third straight line can be obtained. Here, the third point explained up to FIG. 23 is the division vertex P2 in FIG.
2, the new third point becomes the dividing vertex P32 in FIG.

Furthermore, a similar operation is performed between the second point 12 and the third point 33 to create another new third point.
, another new third straight line is determined.

In this way, the first point 11 and the second point 12
A dense polyhedron can be formed by setting a large number of dividing vertices between , forming triangles using the set dividing vertices, and continuing these triangles.

In addition, in order to make changes to the dense polyhedron once created according to the above principle, it is sufficient to change each parameter, and these parameters include the first point 11, the second point 12 (i.e., P11,P
12, P13), the direction of the first straight line L1, the direction of the second straight line L2, and constants β and δ.

Examples of changing parameters in this way are shown in FIGS. 25 to 27.

FIG. 25 shows how the locus of the divided vertices can be changed when only the direction of the first straight line L1 and the direction of the second straight line L2 among the above parameters are changed. It is something.

In the figure, locus C is the locus of the dividing vertices when the first straight line is L1 and the second straight line is L2, and is considered to be one cross section of a dense polyhedron, as already explained. It is set according to the method. Here, the first point 11
, the second point 12, the position control parameter β,
If the first straight line is set to L1b and the second straight line is set to L2b without changing the tangent control parameter δ,
The trajectory C changes to a trajectory indicated by a two-dot chain line Cb.
A feature of the case where the directions of the first and second straight lines L1 and L2 are changed is that the convex portion of the trajectory changes upward or downward with respect to the bisector L11.

That is, the first straight line L1 is rotated clockwise (in this case, the second straight line L2 is rotated counterclockwise).
In this case, as can be seen by comparing the two-dot chain line trajectory Cb with the shape C, the convex portion of the trajectory Cb moves below the bisector L11. Reverse the first straight line L1, rotate counterclockwise (in this case, rotate the second straight line L1
2 is rotated clockwise), the convex portion of the changed trajectory moves above the bisector L11.

In this case, it is necessary to avoid a situation in which both straight lines L1 and L2 become parallel to each other as a result of rotation of the first and second straight lines L1 and L2, respectively. This is to prevent the trajectory from having an inflection point at the first point 11 or the second point 12. Therefore, if the locus may have an inflection point at the first point 11 or the second point 12, the rotation between the first straight line L1 and the second straight line L2 There is no need to place any special restrictions on the state.

FIG. 26 shows how the shape can be changed when only the position control parameter β among the above parameters is changed.

When the position control parameter β is changed, the degree of expansion of the entire shape, that is, the curvature of the trajectory changes. Second
FIG. 6 shows a change in the trajectory when the position control parameter β is changed to a negative value after the trajectory C is once determined by setting the position control parameter β to a positive value. In this way, when the parameter β is changed to a negative value, the trajectory Cc becomes smaller when compared with the trajectory, and the string L3 becomes smaller.
approach.

That is, when the position control parameter β is set to 0, the shape passes through the inner center 14 of the basic triangle. When the parameter β is set to a positive value, the trajectory expands so that it approaches the intersection 13 side rather than the inner center 14, and the β
The larger the size of the curve, the closer it gets to the intersection point 13. Conversely, when the parameter β is set to a negative value, the locus is contracted so as to approach the string L3 side rather than the inner center 14, and as the absolute value of the parameter β becomes larger, the trajectory is contracted closer to the string L3. In other words, the trajectory C approaches a straight line. In the name of the position control parameter β, the “position” refers to the position of the generated trajectory that intersects the bisector L11, and when the position control parameter β is changed, the position of the intersection changes. This is what I did. Therefore, for other parts of the created trajectory, only the curvature of the trajectory 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 created trajectory will not protrude from the basic triangle. There is no.

FIG. 27 shows how the trajectory can be changed when only the tangent control parameter δ among the above parameters is changed.

When the tangent control parameter δ is changed, the bulge of the shape can be reduced between the two points (corresponding to the first point and the second point at that time) used when creating the shape (or modifying the shape). It can be changed.

That is, assume that a locus C between the first point 11 and the second point 12 is once determined. in this case,
The third straight line L13 is the same as the tangent to the trajectory C at the third point 33. Then, at the next point in time after the third point 33 and the third straight line L13 are determined, the first point 11 and the third straight line L13 are determined according to the direction of this tangent line L13 and the direction of the first straight line L1. A new third point is determined between the point 33 and the trajectory is gradually determined.

By the way, changing the tangent control parameter δ means changing the direction of the tangent (third straight line L13). Therefore, changing the tangent control parameter δ is the same as changing the direction of the second straight line L2 when first creating the shape, and can be considered in the same way as explained in FIG. 25. I can do it. However, in this case, since the first straight line L1 does not change, there is a discontinuity in the middle of the shape (third point 33).

Specifically, when the third straight line L13 is changed in the direction of the straight line L13d by changing the tangent control parameter δ at the third point 33, the third point 33 and the first point 11 The trajectory changes to the one shown by the two-dot chain line Cd. That is, when the third straight line L13 is rotated clockwise by changing the tangent control parameter δ,
At the bottom of the bisector L11, the generated shape expands to the right in the figure. This tangent control parameter δ is
This is significant because it increases the degree of freedom in shape creation operations.

Further, the position control parameter β and the tangent control parameter δ are used to generate a shape between the third point 33 and the first point 11 or between the first point 33 and the second point 12. The values of the parameters β and δ can be changed between all points on the trajectory C and other points, as well as when performing curve or shape correction. Therefore, not only can the shape of the entire trajectory C be modified, but also the shape of a desired portion of the trajectory C can be freely modified easily.

FIG. 28 is an explanatory diagram showing the principle of simply obtaining the third straight line.

Point 34 is the intersection of the extension of the straight line L9 and the second straight line L2, and the intersection of the extension of the straight line L9 and the first straight line L
1 is the point 35, and these points 34 and 35
Draw a straight line L14 connecting them, and draw a straight line L14 by moving this straight line L14 in parallel above the third point 33.
5. This straight line L15 is used instead of the third straight line L13. When θ is uncertain in accuracy,
It is convenient to use the straight line L15 obtained as described above as the third straight line.

The above description usually involves creating or modifying a planar shape. However, by applying this shape creation, it is possible to create or modify three-dimensional shapes. That is, by first creating a planar shape as described above and stacking the shapes thus created, it is possible to create a shape as a so-called flexible wire frame or network frame.

Further, although the above description is for creating a shape, it can also be applied to describing an existing shape. That is, it is sufficient to first roughly create a shape that is 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 second point 12,
The direction of the first straight line L1 and the direction of the second straight line L2 may be changed.

Next, the principle of three-dimensionally determining the trajectory of the divided vertices will be explained.

In this case, instead of suddenly creating a three-dimensional trajectory, the idea is to create a three-dimensional contour of the trajectory and then create a desired shape by continuing the contours.

FIG. 29 is a diagram showing a state in which the first point 51, the second point 52, the first straight line L51, and the second straight line L52 are set. Note that the first straight line L51 passes through the point 51, and the second straight line L52 passes through the point 52. Then, a string 50 is provided by connecting the first point 51 and the second point 52. The reason why the straight line connecting the first point and the second point is expressed as a string is because the first
The reason is the same as that described in Figure 6.

Here, it is assumed that the extension of the first straight line L51 and the extension of the second straight line L52 do not intersect. In other words, the trajectory of the divided vertices that will be created from now on is three-dimensional, and therefore the first point 51 and the second point 51
The outline to be drawn between the point 52 and the point 52 often does not exist on one plane. Further, the first straight line L51 should be a tangent to the contour line at the first point 51, and the second straight line L5
2 should be the tangent to the contour at the second point 52. For this purpose, the first straight line L5
1 and the second line L52 do not intersect in many cases.

FIG. 30 is a diagram showing a state in which the first straight line L51 is orthogonally projected onto a surface constituted by the chord 50 and the second straight line L52. A straight line obtained by orthogonally projecting this first straight line L51 is designated as L53. That is, string 50
When light is applied perpendicularly to the surface composed of the lines L52 and L52, the shadow of the first straight line L51 becomes
shall be.

FIG. 31 is a diagram showing a state in which the second straight line L52 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 L52 is designated as L54. That is, string 50
When light is applied perpendicularly to the surface composed of and straight line L51, the shadow of second straight line L52 becomes straight line L54.
shall be.

Figure 32 is a diagram for creating a basic triangular pyramid.

Point 53 and point 54 are connected, and this straight line is defined as L55. In this way, lines L50, L51, L5
There are four faces surrounded by 2, L53, L54, and L55, and the triangular pyramid surrounded by these faces is called a basic triangular pyramid.

FIG. 33 is a diagram for creating a temporary triangle Σ.

A point 55 on the line segment L55 is determined by the torsion control parameter ε. This torsion control parameter ε
is obtained from the following formula.

ε=D1/D2 Here, D1 is the distance from point 54 to point 55, and D2 is the distance from point 54 to point 53. In that case, the distances D1 and D2 are determined depending on the case, and when the torsion control parameter ε, which is the ratio of the distances D1 and D2, is changed, the created shape changes.

Further, the torsion control parameter ε may be obtained as a ratio of angles. A line segment connecting this point 55 and the first point 51 is designated as L56, and a line segment connecting the point 55 and the second point 52 is designated as L57. The triangle surrounded by these lines L50, L56, and L57 is called a provisional triangle Σ.

FIG. 34 is a diagram for creating a basic triangle within the temporary triangle Σ.

The orthogonal projection of the first straight line L51 onto the provisional triangle Σ is defined as a straight line L58, the orthogonal projection of the second straight line L52 onto the provisional triangle Σ is defined as a straight line L59, and these straight lines L
Let the intersection of 58 and straight line L59 be point 56.

Straight line L58 and straight line L59 created in this way
The triangle surrounded by and the line segment 50 is a three-dimensional basic triangle necessary to create a three-dimensional locus of divided vertices, and this three-dimensional basic triangle is used to create a two-dimensional shape. This corresponds to the basic triangle created in FIG. 16 when

FIG. 35 is an explanatory diagram for creating an isosceles triangle from a three-dimensional basic triangle.

That is, the three-dimensional basic triangle can be treated in the same way as the basic triangle in FIG. 16, and thereby, when creating a shape at that point, it can be considered in the same way as the two-dimensional one described above. That is, the basic triangle for three dimensions Δ(52)(51)
(56) and the isosceles triangle Δ(59)(51)(56), if the same operations as shown in FIGS. 15 to 23 are performed, the third point 71 and the third point in three dimensions A straight line L73 is obtained.

However, when creating a three-dimensional locus of divided vertices, it is necessary to use the torsion control auxiliary parameter φ. That is, the tangent to the point 71 on the outline of the shape to be determined has an angle with the third straight line L73 within the plane of the three-dimensional basic triangle. This certain angle is the torsion control auxiliary parameter φ, and it is necessary to take this angle into consideration.
A straight line (tangent) that takes into account the torsion parameter φ in this manner is L72.

In FIG. 35, the symbols shown in brackets [ ] correspond to the points or straight lines shown in FIGS. 15 to 24.

In this way, by performing the operations shown in FIGS. 29 to 35 using the straight line considering the torsion control auxiliary parameter φ and the first straight line L51 or the second straight line L52, a new A new third point and a new third straight line can be obtained. By repeating these operations, a three-dimensional locus outline of the divided vertices can be obtained. By dividing the triangle one after another according to the division vertices created in this way, it becomes easy to create a dense polyhedron.

Also, for example, the coordinates of the first point 51 are (2.0,
0.0, 0.0), the direction cosine of the first straight line L51 is (0.0, 0.7232, 0.6906), the coordinates of the second point 52 are (0.0, 2.0, π), and the direction cosine of the second straight line is ( −0.7232, 0.0, 0.6906), position control parameter β is 0, and tangent control parameter δ is 0.
When the torsion parameter ε is 0.5 and the torsion control auxiliary parameter φ is −0.0467, the locus of the divided vertices created by them forms a constant slope linear shape (spiral).

FIG. 36 is a block diagram showing an embodiment of a device for determining dividing vertices used in the present invention.

a first point setting means 81 for setting the first point 11 at an arbitrary position, the principle of which is shown in FIG. 28;
A second point setting means 82 is provided for setting a second point 12 at an arbitrary position other than the first point 11. Also, a first straight line setting means 83 for setting a first straight line L1 passing through the first point 11 in an arbitrary direction, and a second straight line L2 passing through the second point 12.
A second straight line setting means 84 is provided for setting the line in an arbitrary direction. These setting means 81 to 84 include input means such as a keyboard 1 and a light pen 2. In addition, as shown in FIGS. 15 to 23, the position of the first point 11 and its first
The position of the third point 33 and the third straight line L13 including this third point 33 are determined according to the direction of the straight line L1, the position of the second point 12, and the direction of the second straight line L2. A third point/straight line determining means 85 for determining the direction is provided. Using arithmetic circuit 3,
It functions as the third point/straight line determining means 85.

The principle for determining the locus of the divided vertices two-dimensionally is the same as that explained in FIGS. 15 to 23, and in order to determine the locus of the divided vertices three-dimensionally, It is necessary to use the principle explained in the figure. The arithmetic circuit 3 has a circuit configuration that realizes all of these principles. Also,
A computer may be used instead of the arithmetic circuit 3.

Further, the third point/straight line determining means 85 includes an input means 86 for inputting parameters β, δ, ε, φ, etc.
is provided. As this input means 86,
Keyboard 1 etc. can be considered. A storage device 87 is provided for storing information on each point determined by the third point/straight line determining means 85.

The embodiment shown in FIG.
point 11, the first straight line L1, the second point 12, and the second
The third point is found from the straight line.

FIG. 37 shows how each means 81 to 84 is determined based on a point that has already been set or determined and the direction of a straight line at that point, and a point newly determined by determining means 85 and the direction of a straight line at that point. A control means 88 is provided for repeatedly controlling and arranging a large number of points between the first point 11 and the second point 12. The operation of this control means 88 is the same as the principle explained in connection with FIG.

In particular, FIG. 38 is a block diagram of an apparatus for two-dimensionally determining the trajectory of divided vertices. In this block diagram, there is a first point setting means 81 for setting the first point 11 at an arbitrary position, the principle of which is shown in FIG. second point setting means 82 for setting the second point 12;
and is provided. Further, a first straight line L1 passing through the first point 11 is set in an arbitrary direction.
a straight line setting means 83; A second straight line setting means 91 for dimension is provided.

In addition, as shown in FIGS. 15 to 17, the string L connecting the first point 11 and the second point 12
3, the first straight line L1, and the second straight line L2, of the three sides of the basic triangle, create an isosceles triangle whose two short sides, excluding the side formed by the chord L3, are equilateral. An isosceles triangle creating means 92 is provided.

Then, as the principle is shown in FIGS. 18 to 24 and 28, the position of the third point and the third point are determined based on the difference between the attributes of the basic triangle and the attributes of the isosceles triangle. A third point calculating means 93 is provided for calculating the direction of the included straight line.

The third point calculation means 93 is comprised of the following constituent elements. That is, an incenter position calculation means 93a (applying the principle of FIGS. 18 and 19) that calculates the inboard center position of the basic triangle and the inboard center position of the isosceles triangle, and a A straight line connecting one vertex of a basic triangle and the incenter of that basic triangle, excluding the apex,
A first vertex surrounded by a perpendicular bisector of a line segment connecting a vertex opposite to the one vertex in an isosceles triangle and the inner center of the isosceles triangle, and a side opposite to the one vertex. a first triangle area calculation means 93b (applying the principle of FIG. 20) for calculating the area of a triangle; a straight line connecting the other vertex of the basic triangle and the incenter of the basic triangle, excluding the apex of the specific angle; A second vertex surrounded by a perpendicular bisector of a line segment connecting the opposite vertex in the isosceles triangle to the inner center of the isosceles triangle with respect to the other vertex, and the side opposite to the other vertex. A second triangle area calculation means 93c (applying the principle of FIG. 20) calculates the area of the triangle of , and calculates the difference between the area of the first triangle and the area of the second triangle from the position of the inner center of the basic triangle; Calculating means 93d (a third point) calculates a position on the bisector of the specific angle, which is a position separated by a distance corresponding to the distance between the first point and the second point, as the position of the third point. Application of principles in Figures 21 to 23)
It is composed of:

Furthermore, the third point calculating means 92 has a constant β,
Means 94 for inputting δ, ε, φ is provided, a third
A storage device 87 is provided for storing information on each point determined by the point calculation means 92. The arithmetic circuit 3 can perform the functions of the basic triangle/isosceles triangle creating means 92 and the third point calculating means 93.

[Effects of the Invention] According to the present invention, a shape can be easily created or the created shape can be easily modified by a series of many small triangles. Therefore, it can be applied to shape processing machines such as NC machine tools, shape recognition devices, image processors, automatic drafting machines, and image creators. In this case, in the above device or machine,
Three-dimensional manipulation or mechanical drive can be performed.

As mentioned above, the present invention has the advantage of being a single shape creation device that is freely accessible throughout the entire process from design 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 is a diagram showing a first stage triangle, Fig. 3 is a diagram divided into second stage triangles, and Fig. 4 is a diagram of the system shown in Fig. 3. The plan view, Figure 5, is a diagram in which only some of the triangles are divided into third stage triangles, and Figure 6 is a diagram in which all second stage triangles are divided into third stage triangles.
Figure 7 is an exploded view of Figure 4, Figure 8 is a plan view of Figure 6, Figure 9 is a diagram partially divided into 4th stage triangles, Figure 10 is an exploded view of Figure 4. FIG. 11 is a plan view of FIG. 10, FIG. 12 is a view of the second stage completely deflated, FIG. 13 is a plan view of FIG. 12, and FIG. 14 is a plan view of the present invention. A block diagram showing one embodiment, Fig. 15 is a diagram showing the settings of the first stage necessary to determine the dividing vertices, and Fig. 16 shows the basic triangle and isosceles triangle created from the state of Fig. 15. FIG. 17 is an explanatory diagram for determining the necessary constant α when determining the third point (divided vertex), and FIG. 18 is an explanatory diagram for determining the inner center of an isosceles triangle. Figure 19 is an explanatory diagram for finding the inner center of a basic triangle, Figure 20
The figure is an explanatory diagram for determining the unbalance amount S, the 21st
The figure is an explanatory diagram when calculating the distance d from the inner center of the basic triangle to the third point that is currently being calculated.
Figures 22 and 23 are explanatory diagrams for finding the third straight line at the third point, and Figure 24 is an explanatory diagram for finding the third straight line at the third point.
An explanatory diagram when finding the point (new dividing vertex),
Figure 25 is a diagram showing how the locus of the dividing vertex can be changed when only the direction of the first straight line and the direction of the second straight line are changed among the parameters. The figure shows the parameters
Figure 27 is a diagram showing how the trajectory of the divided vertices can be changed when only the position control parameter β is changed.
A diagram showing how the locus of the divided vertices can be changed when only the tangent control parameter δ is changed, FIG. 28 is an explanatory diagram showing the principle of simply finding the third straight line, FIG. 29 shows the first point,
Figure 30 shows the state in which the second point, the first straight line, and the second straight line are set. The figure shown in FIG. 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,
Figure 32 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 within the provisional triangle Σ, and Figure 35 is a three-dimensional locus of divided vertices. FIG. 36 is a block diagram showing one embodiment of the device for setting the dividing vertices, FIG. 37 is a block diagram showing another embodiment of the dividing vertex setting device,
FIG. 38 is a block diagram showing another embodiment of the dividing vertex setting device. 1...Keyboard, 2...Light pen, 3...
Arithmetic circuit, 4... Display, 5... Printer, 6... External storage device, 11, 51... First point, 12, 52... Second point, L1, L51...
First straight line, L2, L52...Second straight line, 3
3, 71...Third point, L13, L72...Third point
straight line, 81...first point setting means, 82...second
Point setting means, 83... First straight line setting means, 84...
...Second straight line setting means, 85...Third point/straight line determining means, 91...Two-dimensional second straight line setting means, 92
...Isosceles triangle creation means, 93...Third point calculation means, 93a...Incenter position calculation means, 93b...
First triangle area calculation means, 93c...Second triangle area calculation means, 93d...Calculation means, P21, P
31...first division vertex, P22, P32...second
Divided vertices, P23, P33...Third divided vertices, T
10...First stage triangle, T20, P30... Central triangle, T21, T22, T23, T31, T
32, T33... Surrounding triangle, B0... First stage triangle setting means, B1... First division apex setting means, B2... Second division vertex setting means, B3... Third division vertex setting means, B4... ...Peripheral triangle setting means, B5... Central triangle setting means, B6... Division repeating means.

Claims (1)

[Claims] 1. A first stage triangle setting means for setting a first stage triangle which is a triangle having a desired shape; A first division according to two vertices of any side of the first stage triangle; a first dividing vertex setting means for setting vertices; a second dividing vertex setting means for setting second divided vertices according to two vertices related to other sides among the vertices of the first stage triangle;
a dividing vertex setting means; a third dividing vertex setting means for setting a third dividing vertex according to two vertices of the remaining sides among the vertices of the first stage triangle; a central triangle setting means for setting a central triangle by connecting the divided vertices and the third divided vertex; and a periphery for setting three peripheral triangles by one side of the central triangle and the vertex of the first stage triangle. A shape generating device comprising: a triangle setting means; and; 2. In claim 1, the means for providing each dividing vertex according to the two vertices of the first stage triangle is arranged such that a first straight line passing through one of the vertices of the first stage triangle is arbitrarily set. means for setting in the direction of; a second
means for setting the straight line in an arbitrary direction; according to the position of the one vertex and the direction of the first straight line, the position of the other vertex and the direction of the second straight line; A shape generating device comprising: means for setting one of three points; and a shape generating device. 3. A first-stage triangle setting means for setting a first-stage triangle that is a triangle having a desired shape; and a first division that provides a first division apex according to two vertices on arbitrary sides of the first-stage triangle. Vertex setting means; Second division vertex setting means for setting second division vertices according to two vertices on 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 related to the sides; and setting a central triangle by connecting the first division vertex, the second division vertex, and the third division vertex; Central triangle setting means; Surrounding triangle setting means for setting three peripheral triangles by one side of the central triangle and the vertex of the first stage triangle; For each of the central triangle and the peripheral triangle, A dividing repeating means that sets the first to third dividing vertices, sets the central triangle and the peripheral triangle, and sequentially repeats the same operation for the triangle formed by these, dividing each triangle into four triangles; ; A shape generating device characterized in that it forms a dense polyhedron by continuation of a large number of triangles formed based on the first stage triangle.