JPS60221872A - Intersection point position detecting device for shape generation - Google Patents

Abstract

PURPOSE:To obtain a shape generating device which can execute an access freely by detecting an intersection point containing face which has an intersection point to a prescribed straight line from plural divided faces, dividing this intersection containing face into a prescribed number and detecting an intersection point containing face, and repeating it. CONSTITUTION:A face dividing device B12 divides a prescribed face into a prescribed number of faces, and a detected face setting device B11 has a desired shape and sets a face to be detected t10 for detecting an intersection point position. Also, the device B12 divides the face to be detected t10 into a prescribed number, and from thse plural divided faces, an intersection point containing face is detected. Also, this intersection point containing face is divided into a prescribed number again, and from these plural divided faces, its intersection point containing face is detected, and an intersection point of a straight line DL and the face to be detected t10 is derived by repeating these operations.

Description

[Detailed Description of the Invention] [Technical Field] The present invention relates to (:, A[) (Computer Ai
The present invention relates to a device for creating a desired three-dimensional shape or modifying the 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 the desired shape by using a dense point sequence or a school of fish and line elements, and the surface shape description expresses the desired shape by using a dense point sequence or a school of fish and line elements. between those points,
A desired shape is expressed by performing interpolation processing based on function approximation. In addition, 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 conventional technology lacks flexibility in expression when expressing a three-dimensional shape, and has a problem in that it cannot fully demonstrate its functions. In addition, the expression of shapes is one aspect of modeling processing, and the creation of shapes is also one aspect of modeling processing, but there is a problem that they cannot perform modeling processing together. be.

For example, even when using the above solid model, it is possible to express a part of a three-dimensional shape by combining simple shapes, but due to its nature, it is difficult to express a free and detailed shape. Naturally, this means that it is difficult for one person to perform the modeling process from shape expression to shape creation.

[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 in the entire process from designing to manufacturing a model, etc. This is the purpose.

Specifically, there are devices that can easily detect the intersection of a given straight line and a given surface, and devices that can easily create a cut surface by cutting a given surface in a straight line or curve. The purpose of the present invention is to provide a device that can easily create a line of intersection, which is a series of points where a predetermined surface intersects with another surface, and a control device, a processing device, etc. based on each of these devices. do.

[Summary of the Invention] In order to achieve this object, the present invention first divides a predetermined surface into a predetermined number, and from among the plurality of divided surfaces, divides a plurality of divided surfaces into intersections having intersections with a predetermined straight line. Detect the surface, divide this intersection-containing surface into a predetermined number of surfaces again, detect the intersection-containing surface from among the divided surfaces, and repeat these operations to create a predetermined straight line and the first surface. This is to detect the intersection with

Further, in order to cut a surface linearly or curved, the above operation is repeated while moving a predetermined straight line in a predetermined direction.

Furthermore, in order to obtain a mutual line, the other surface other than the reference surface is divided into a predetermined number of surfaces, and from among the divided surfaces, the divided surface has both sides with respect to the reference surface. The intersecting plane is detected, this intersecting plane is again divided into a predetermined number of planes, the intersecting plane is again detected from among the plurality of divided planes, and these operations are repeated.

If this intersection position detection process is displayed on a display, the process itself is CAD, and the data regarding the shape created in this way can be used as is to operate NG machine tools, etc. It is.

Embodiment of the Invention] FIG. 1 is an overall diagram of a system showing an embodiment of the invention.

First, a keyboard 1 is used to input positional information regarding the shape to be created, that is, the positional information of the shape to be drawn. A light pen 2 is provided.

And keyboard 1. A calculation circuit 3 that performs predetermined calculation processing based on input signals from input means such as a light pen 2 is built-in. A display 4 for displaying the shape created in this manner is provided, a printer 5 for printing the shape, and an external storage device 6 for storing the shape as a predetermined signal such as a magnetic signal or an optical signal. It is being held.

Next, the principle of the main utterance will be explained.

The present invention first divides a predetermined surface into a predetermined number, and from the back of the plurality of divided surfaces, the intersection with a predetermined straight line is located on the right.
Detect a curved intersection-containing surface, divide this intersection-containing surface again into a predetermined number of surfaces, detect the intersection-containing surface from among the divided 1=multiple surfaces, and repeat these operations to divide the intersection-containing surface into a predetermined number. It detects the intersection between a straight line and the first plane. An example of these processes is shown in FIGS. 2-5.

FIG. 2 is a graph showing a detected surface t10 whose intersection point is detected and a straight line DL intersecting this detected surface t10.

Here, it is assumed that the straight line DL and the detected surface t10 intersect at an intersection point CP. However, it is assumed that the actual position of the intersection point CP on the coordinates is not yet known. We are now trying to determine the coordinates of this intersection point CP. It is assumed that the only known values at present are the coordinates of each vertex of the detection surface t10, the coordinates of the passing point of the straight line D1-, and the direction thereof.

In FIG. 3, the detected surface tlO is divided into four triangles t20. t2
1. t2'2. This shows the state of division at t23.

The above four triangles are a central triangle t20, peripheral triangles t21 . t22 and t23 (the operation of dividing the triangle into four will be explained in Figures 18 onwards).

In the process of this division, the coordinates of each vertex of the central triangle t20 are determined. Here, the intersection CP is the central triangle t20
Suppose that it exists within. A surface including the intersection point CP, such as the above-mentioned central triangle t20, is called an intersection-containing surface.

Next, the triangle is divided into four again, but the above triangle t2
Instead of dividing all of 0-t23, only triangle t20, which is the intersection-containing surface, is divided.

In FIG. 4, the central triangle t20, which is a surface containing an intersection point, is divided into four triangles t31. t32. t33. This figure shows the state of division at t34.

In this case, the coordinates of each vertex of the central triangle t30 are determined. Here, it is assumed that the intersection point CP exists within the peripheral triangle t33. In the above case, the peripheral triangle 33 becomes the intersection-containing surface.

Next, among the triangles t30 to t33, only triangle t33, which is the intersection-containing surface, is divided.

FIG. 5 shows the surrounding triangle t33, which is an intersection-containing surface, and four triangles t40. t41. t42. This figure shows a state where the image is divided at t43.

In this case, the coordinates of each vertex of the central triangle t40 are determined. Here, it is assumed that the intersection point CP exists within the central triangle t40. In the above case, the central triangle t40 becomes the intersection-containing surface.

By repeating these operations, the coordinates of the intersection CP between the straight line DL and the detected blood t10 can be detected. Furthermore, the greater the number of repetitions, the higher the accuracy of the coordinates of the intersection point CP.

In the above example, the detected surface t10 is a flat surface, but it may be a curved surface.

FIG. 10 is a block diagram showing an embodiment of the present invention based on the above principle.

In the figure, the straight line setting means B10 is for setting a straight line D L passing through a desired point and having a desired direction, and the detection surface setting means B11 is for setting a straight line D L that has a desired shape and detects the intersection position. The detected surface t10 is set as follows.

Further, the surface dividing means B12 is for dividing a predetermined surface into a predetermined number of surfaces, and the intersection containing surface detection means 813 is for dividing a predetermined surface into a predetermined number of surfaces.
An intersection-containing surface, which is a surface including the intersection of the straight line DL and the detected blood t10, is detected from among the plurality of surfaces divided by the surface dividing means B12. Note that the reference numeral B14 stores information such as the coordinates of the requested intersection.

That is, the surface dividing means B12 divides the detected surface t10 into a predetermined number of surfaces, and from among the plurality of divided surfaces,
Detect an intersection-containing surface, divide this intersection-containing surface into a predetermined number of surfaces again, detect the intersection-containing surface from among the divided surfaces, and repeat these operations to determine the straight line DL and the detected object. Blood tl.

This is to find the intersection with .

In other words, among the divided surfaces, only the intersection-containing surfaces are divided and judged, so there is an advantage that the overall calculation processing speed is high.

The calculating means 3 shown in FIG. 1 has the functions of a straight line setting means B10, a detected surface setting means B11, a surface dividing means B12, and an intersection containing surface detecting means B13.

FIGS. 6 and 7 are dimensional diagrams illustrating the principle of another embodiment of the present invention.

Figure 6 is basically the same as Figures 2 to 5, but
It shows the locus of intersection points when the straight line DL is moved linearly.

In other words, the intersection of the detection surface t10 and the straight line DLI is CPl
Then, the straight line is linearly and sequentially translated in parallel to the position of DLn, and the intersection point at this time is set as CPn. In each intersection detection from intersection CP1 to CPn, the operations explained in FIGS. 2 to 5 are repeatedly executed.

Figure 7 is basically the same as Figures 2 to 5, but
This figure shows the locus of the intersection points that occur when the straight line DL is sequentially moved in parallel in a curved manner.

In FIG. 6.7, the detected blood t10 may be a curved surface. Examples of these are shown in FIGS.

FIG. 8 shows a locus CL of intersections that occurs when an elliptical surface is used as the detection surface and a straight line is translated in parallel on the 2X plane. This locus OL is considered to be a cutting line of the ellipsoid.

In Figure 9, a hyperbolic paraboloid is used as the detection surface, and xy
It shows a locus CL of intersections that occurs when a straight line DL is translated in parallel on a plane.

This locus CL can be considered as a cudding line of a hyperbolic parabolic body.

FIG. 11 is a block diagram showing an embodiment based on the principle shown in FIG. 6.7. Note that the same members as those shown in FIG. 10 are designated by the same reference numerals, and the explanation thereof will be omitted.

In the figure, the linear moving means 820 moves the straight line D by a predetermined distance 1", and moves the straight line DL in parallel or in a non-parallel manner. .

-4, the surface to be detected tlO is detected by the surface dividing means B12.
is divided into a predetermined number (a number other than four is also acceptable), and this divided l [detects an intersection-containing surface from among the plurality of faces, divides this intersection-containing surface again into a predetermined number, and calculates the The intersection point-containing surface is detected from among the plurality of surfaces, and these operations are repeated to detect the intersection point between the straight line and the detected surface t10, and the straight line O is detected by the linear movement means B20.
Once L is moved, the same operation as above is repeated for each of the straight lines DL.

The calculating means 3 shown in FIG. 1 has the functions of a straight line setting means B10, a detected surface setting means B11, a surface dividing means B12, an intersection containing surface detecting means B13, and a linear moving means B20.

12 to 15 illustrate the principle of another example of the present invention.

This invention obtains an intersection line (intersection line) between an interoperator having a reference surface and an interoperator having a surface different from the reference surface (opposite surface). Then, the present invention divides the other surface into a predetermined number of parts, detects from the back of the plurality of divided faces a face (crossing face) in which the divided face has both sides with respect to the reference plane, and The intersecting plane is again divided into a predetermined number of planes, the intersecting plane is again detected from among the plurality of divided planes, and these operations are repeated.

The operation of dividing the opponent surface into a predetermined number of parts is performed in the 18th step as described above.
The manner in which the above-mentioned intersecting planes are arranged will be explained in the following figures.

In FIG. 12, the mating surface U10 is located above the reference surface U1, and both surfaces u1. This shows a case where uio do not intersect with each other. In this case, when looking at the opposing surface U10 from the upper left to the lower right in FIG. 12, the vertex LIP11 of the opposing surface UIO. UPl2 and UPl3 are projection points UP11a, UPI2a, and LJP13a of the reference plane U1, respectively.
All directions with respect to are positive (the direction from the lower left to the lower right is positive).

On the other hand, in FIG. 13, the mating surface U10 is located below the reference surface U1, and both surfaces U1. This shows a case where U10 does not intersect with each other. In this case, when looking at the opponent surface LJ10 from the upper left to the lower right in FIG.
10 vertices UP11. UP12. UP13 is the reference plane U
1, each projection point LJP11a, UPI2a, UP
All directions to the right of 13a are negative.

FIG. 14 shows a case where the other surface U10 intersects the reference surface U1.

In this case, the other side I
When looking at J10, the direction in which the vertex UP11 of the opposite surface U10 is to the right with respect to the projection point UP11 a of the reference surface U1 is positive, but the vertex LJPI 2°UPl 3 is The direction with respect to the projection points UPI2a and UP13a is negative.

In other words, when viewed from a predetermined direction, one 10 of the opponent surface U10
When the direction in which a point is to the right with respect to the reference plane U1 is different from the direction that the other vertices of the opponent surface 10 have with respect to the reference plane U1 when viewed from the predetermined direction, the opponent surface U10 is crossed. It is determined that the surface is a surface (a surface having portions on different sides with respect to the reference surface). And the first
In Figure 4, phase [13L is indicated by a chain double-dashed line.

FIG. 15 shows a case where the opposing surface U10 is divided into four triangles in the case of FIG. 14.

These four triangles are a central triangle U20, a peripheral triangle U21 . U22. It is with U23. For each of these four triangles, the above judgment is made as to whether or not they are intersecting planes, and as a result, the intersecting planes are triangles U20. L122
．． U23. ! :Become. The triangle is then divided into four parts again, but only the intersecting planes are subject to this division. Therefore, triangle U21 is not divided. In this way, in the process of the operation, some items are not subject to division, which has the advantage of increasing the calculation speed accordingly.

Roughly, cross plane U20. u22. Each of U23 has 4
The intersection plane is detected for each divided triangle, and these operations are repeated to obtain a large number of minute intersection planes, and the continuation of these becomes the intersecting line SL. . Note that the ullζ surface or the other surface may be a curved surface.

FIG. 16 shows a mutual line SL created by a curved surface of a catenary curve and an ellipsoidal curve. In the figure, the broken lines indicate hidden parts of each curved surface.

FIG. 17 is a block diagram showing an embodiment of the present invention based on the above principle.

In the figure, the reference surface setting means B30 sets a reference surface U1 having a desired shape, and the other surface setting means B31
is to set a mating surface U10 that has a desired shape and is different from the reference surface U1.

Further, the surface dividing means B32 divides a predetermined surface into a predetermined number of surfaces, and the intersecting surface detecting means B33 detects that each vertex of the surface into which the other surface U10 is divided by the surface dividing means B32 is a reference. This is to detect intersecting planes that are planes that exist on different sides with respect to the plane U1. Incidentally, the reference numeral B14 is for storing position information such as the requested intersecting line.

That is, the opposing surface U10 is divided into a predetermined number by the surface dividing means B32, the intersecting surface is detected from among the plurality of divided surfaces, and this intersecting surface is again divided into a predetermined number,
The intersecting planes are detected from the backs of the divided/q plurality of planes, and these operations are repeated to detect intersecting lines between the other plane U10 and the reference plane U1. Here, the reference surface U1 and the other surface U10 are relative, and the relationship may be understood in reverse.

The calculation means 3 shown in FIG. 1 includes a reference plane setting means B30,
It performs the functions of the mating surface setting means B31, the surface dividing means B32, and the intersecting surface detecting means B33.

Next, the operation of dividing the detection surface t10, the reference surface U1, the other surface Ulo, etc. will be explained.

First, set a triangle of the desired shape (first stage triangle),
This first stage triangle is divided into four triangles (second stage triangle)
Consider the case where each of the second-stage triangles is again decomposed into four parts, these division 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. The first stage triangle corresponds to each of the detection surface t10, the reference surface U1, and the opposing surface UIO. These division processes are sequentially illustrated in FIGS. 18 to 29.

FIG. 18 shows the first stage triangle.

First, as an initial stage of forming a dense polyhedron, a triangle T10 having a desired shape is set. This triangle TIO is the first
Let's call it a stepped triangle. This first stage triangle TI
O is the vertex P11. P12゜PI3 and sides R11, R12
, R13.

Based on this first stage triangle TIO, the triangle is successively divided into four parts.

For convenience of explanation, in FIG. 1, the first stage triangle T10 is projected onto the projection plane 10, and the vertices of the projected triangle are designated Plla, P12a, and P13a.

Generally, for example, point Pi2. 'P13. Pl　3a.

A dividing point is provided in the space near either the left or right of the plane surrounded by Pl 2a, but here, for the sake of simplicity, a point 21 is provided within this plane, and this point P21 is Use as split vertices. Similarly, point P13. P11. P1
A point P22 is provided in the plane surrounded by 1a and P13a, and this point P22 is set as the second division vertex, and the point P11. P12. P
A point P2'3 is provided within the plane surrounded by Pi1a and Pi1a, and this point P23 is set as the third division vertex. In addition, each vertex P
11, Pl2. 1st to 3rd division loss point P21゜P from Pl3
22. The operation to close P23 will be explained from FIG. 31 onwards.

1.2.3 Division loss point 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, and the other side of the central triangle T20 and the point P12 are set.
The surrounding triangle T22 is set by the remaining sides of the central triangle T20 and the point P13.
Set 23.

In other words, first, after setting the first stage triangle T10,
By arbitrarily setting three points and connecting these three points to each other, a central triangle is created, and one of those three points is
Create three peripheral triangles outside the central triangle using a point and any side of the central triangle.

A state in which the first stage triangle T10 is divided into four triangles in this manner is shown in FIG. 19, and a plan view thereof is shown in FIG. 20.

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

Next, in FIG. 19, vertex P22. When the intersections of each of P23 and the projection plane 10 are P22a and P23a, the point P23. P22. A point P31 is provided within the plane surrounded by P22a and P23a, and this point 31 is set as a new first divided vertex. Similarly, point P22. P11. P1
A point P32 is provided within the plane surrounded by 1a and P22a, and this point P32 is set as a new second division vertex, and the points pii,
Point P3 in the plane surrounded by p23, P23a, Plla
3, and this point P33 is set as a new third division vertex.

FIG. 21 shows the peripheral triangle T21 divided into four triangles.

1.2.3 division vertex P31゜P3 in Figure 19 ()
2. By connecting P33, a new IC central triangle T
Set 30. 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 Another peripheral triangle T33 is set by the side and the vertex P33.

In this way, one of the second stage triangles, triangle T2
1 can be divided into four triangles again.

FIG. 21 shows one peripheral triangle T 2 in FIG. 20.
Although only the triangle shown in FIG. 1 is divided into four, the other peripheral triangles T22°-r 23 and the medium triangle T20 can each be divided into four triangles in the same way.

FIG. 22 shows another peripheral triangle T22. T23, J, and medium flame triangle T20 are also shown divided into four parts.

In addition, when the first stage triangle is divided into four, the middle 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. This is called a 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. 23 shows the central triangle T20, the peripheral triangle T21. T22. T23 is shown separated.

In this FIG. 23, three peripheral triangles T21 and T2
2. , T23 in counterclockwise order (numbers 1, 2.3 in the example), and then the central triangle T20 with an identification number (number 4 in the example).
It is attached. Also, the second stage triangle T20. T21.
T22. The same identification number as the above-mentioned identification number is given to each side of T23 in clockwise order. By doing this, the second stage triangle T20. T21. The advantage of T22° and D23 is that the topological structure can be determined in the same way as a planar graph.

An identification number is also provided for each side of the second stage triangle. That is, if we focus on one second-stage triangle,
An identification number is 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.

Figure 24 shows the division up to the third stage triangle.
An identification number is attached to each of the third stage triangles. That is, as shown in FIG. 23, the identification numbers 1 to 4 are used in the second stage triangle, and the identification number starts from 5 in the third stage triangle.
First, identification numbers (5 to 8) are assigned to the four triangles included in the peripheral triangle T21 (identification number 1) in the clockwise direction and in the order of the central triangle, and then similarly, the peripheral triangle T2
2°T23. Four identification codes are attached to each of the central triangles T20 in this order. The same applies to the identification numbers assigned to the fourth and subsequent triangles.

FIG. 25 is a diagram showing 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 moves 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. 26 to 29 show cases in which the projected shape changes when the first stage triangle is divided. In other words, in the case of FIGS. 18 to 25, even if the ff11 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 the figure, when the first stage triangle T10 is divided into four, its projected shape is expanded and contracted in the horizontal direction, unlike the first stage triangle T10.

FIG. 26 shows the overall shape of the first stage triangle T10 divided into four parts, and FIG. 27 is a plan view of FIG. 26.

FIG. 28 shows that when the first stage triangle T10 is divided into four parts, its entire shape is contracted, and FIG. 29 is a plan view of FIG. 28.

In the case of FIGS. 26 to 29 above, the first to third classification points are set at positions other than the side surfaces of the triangular prism shown in FIG. 18. That is, the first to third division I exit points may be provided at arbitrary positions.

Figures 26 to 29 are examples of dividing a first-stage triangle into second-stage triangles, but the shape can be arbitrarily contracted in the same way when dividing into n-th stage triangles. .

FIG. 30 is a block diagram when performing the above division, and these functions are possessed by the calculation means 3 in FIG. 1.

In the figure, the first-stage triangle setting means BO sets a first-stage triangle T10, which is a triangle on the right side of the desired shape.

The first division loss point setting means B1 sets a first division loss point in a plane including two arbitrary vertices of the first stage triangle T10 and an arbitrary point other than the plane of the first stage triangle T10. It is something that Further, the second division loss point setting means B2 sets a second division loss point in a plane that includes two vertices of the first stage vertices according to another combination μ and an arbitrary point other than the plane of the first stage triangle T10. The third division loss point setting means B3 sets two vertices in the remaining combinations among the vertices of the first stage triangle T10 and any arbitrary point other than the plane of the first stage triangle T10. A third division loss point is provided in a plane containing the points.

Moreover, the central triangle setting means B4 sets the first divided vertex and the second divided vertex.
A medium-fired triangle is set by connecting the dividing loss point and the third dividing loss point, and the surrounding triangle setting means B5 connects one side of the medium-fired triangle and the vertex of the first stage triangle T10 to set a medium-fired triangle.
This sets two surrounding triangles. The storage means 87 stores information on the results of dividing each triangle.

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

Next, an example of an operation for determining dividing vertices will be described.

Figures 31 to 51 are diagrams showing the principle of determining the dividing vertices, and Figures 31 to 40 are diagrams showing the principle of determining the dividing vertices two-dimensionally. be.

In addition, up to FIG. 51, the thick line portion indicates the newly generated portion in that figure.

FIG. 31 shows the first stage settings necessary for determining the dividing vertices.

That is, it is a diagram showing the 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 1-1 and the second straight line L2 exist on the same plane. In other words, the first point 11 and the second point 12
We are trying to create a dividing vertex at a desired position between It is something.

To set these, for example, by setting the light ben 2 at any position on the display 4,
The first point 11 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 L passing through the first point 11
1 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.

In the above description, information regarding the position of a point or the direction of a straight line is input to the keyboard 1. Although input is performed using the light pen 2, the information is of course not limited to this, and may be input using other input means such as a digitizer.

FIG. 32 shows a basic triangle and an isosceles triangle created from the state of FIG. 31.

Connect the first point 11 and the second point 12, and make this line segment 13
This line segment L3 is called a string. Here, the line segment L3 is called a chord because it creates a part of the desired shape (contour FA) between the first point 11 and the second point 12, and the contour line is a circular arc. This is because line segment L3 corresponds to a string. This line segment L3 corresponds to side R12 in FIG.

Three lines Ll, L2. The triangle surrounded by L3 is
Let's call it the 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 This is a line segment connecting point 11 and point 13. Create an isosceles triangle whose short sides are equal to each other so that it overlaps the basic triangle.

In other words, 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 sides of the isosceles triangle are the line segments connecting point 21 and intersection 13 in FIG. The line segment connecting the first point 11 and point 21 is 1-4
shall be.

FIG. 33 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. 18.

(11) (21). Here, / (13) (11
)(21) is a line segment connecting points 13 and 11, and a line segment connecting points 11
The angle defined by the line segment connecting the point 21 and the point 21 is shown in FIG.

The constant α is determined as follows.

α-(Area of Δ(21)(11)(1'3))/(Δ(
12H11) (area of (22)) Note that Δ(21) (11) (13) indicates a triangle surrounded by points 211, 112, and 13, and the same method of expression for triangles is adopted for the following.

FIG. 34 is an explanatory diagram when 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 6 be the bisector of the interior angle at point 21 of the isosceles triangle. Let point 23 be the intersection of these bisectors and 5.16, that is, the center of the isosceles triangle. Also, from point 11 to inner center 23
The midpoint from point 21 to inner center 23 is set as point 24, and the midpoint between point 21 and inner center 23 is set as point 25.

FIG. 35 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 the straight line L7
The bisector of the interior angle at point 12 of the basic triangle is defined as a straight line tilL8, and the intersection of these bisectors [7°L8, ie, the interior center of the basic triangle, is defined as point 14.

FIG. 36 is an explanatory diagram when determining the unbalance amount S.

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

To find the unbalance ωS, first, overlap FIGS. 34 and 35. Then, the bisector [,7 and L8 are extended, and a perpendicular line L9 is provided at the point 24, and a perpendicular line L10 is provided at the point 25. Let 81 be the triangle surrounded by the perpendicular L9, the bisector L8, and the first straight line L1, and let 82 be the triangle surrounded by the perpendicular L10, the bisector L7, and the second straight line L2.
shall be.

The unbalance amount S is determined by the following J:.

5=(area of 31)-(area of S2) However, the unbalance ms may be determined by a method other than the above.

FIG. 37 is an explanatory diagram for calculating the distance 111d from the inner center 14 of the basic triangle to the third point that is currently being determined.

A straight line connecting the inner center 14 of the basic triangle and the intersection 13 is Lll
shall be. This straight line L11 is a bisector of the interior angle at the intersection point 13 of the basic triangle. The third thing I'm trying to find now is
This point is indicated as point 33, and this third point 33 is the straight line 111.
It is assumed that it exists on top of . Conversely, thirds 1
There is a point where i1L11 and the shape to be created intersect, and this intersecting point is called a third point 33, and the third point 33 is about to be found. Then, the distance between the third point 33 and the inner center 14 of the basic triangle is defined as 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.

Figure 36.39 shows the third straight line [
FIG.

Here, the third straight line L13 is a tangent to the shape outline at the third point 33. In other words, if a contour line of a desired shape is created between the first point 11 and the second point 22, the third point
The tangent to the contour line at point 33 is the third straight line 1-
It is 13. Conversely, the third straight line ta13 is a straight line necessary to create a new third point between the third point 33 and the first point 11. To create this third straight line L13, do as follows.

The straight line passing through the first point 11 and point 33 is L9, the straight line passing through the second point 12 and point 33 is LIO, and the straight line L10
112 covers the bisector of the intersection angle between and L9. This bisector 112 is shown in FIG. Let L13 be a straight line that intersects the bisector [12 at an angle of θ within the plane of the basic triangle 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 the tangent control parameter, and 8 is the area of the basic triangle.

The straight line 113 created in this way is the third straight line L13. By using this third straight line L13 and performing the operations explained in FIGS. 31 to 37, the position of a new third point (the point corresponding to point P32 in FIG. 19) is determined. be able to.

FIG. 40 is an explanatory diagram when a new third point is determined as described above.

In other words, the third point 33 is shown in FIG.
2, the third straight line L13 is considered as a substitute for the second straight line 12 shown in FIG. 28, and the operations explained in FIGS. 31 to 37 are repeatedly executed. Point 21a corresponds to point 21 shown in FIG. 32, and point 13
Point a corresponds to point 13 shown in FIG. 31. Therefore, Δ(1′1)(33)(13a) is a new basic triangle, and Δ(11)(21a)(13a) is a new isosceles triangle.

Then, by performing operations similar to those shown in FIGS. 38 and 39, a new third straight line can be drawn. Here, if the third point explained up to FIG. 39 is the dividing vertex P22 in FIG.
The point 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, triangles are formed by the set dividing vertices, and when these triangles are connected, a dense polyhedron is formed. be able to.

Furthermore, in order to make changes to the dense polyhedron that has been created according to the above principle, it is sufficient to change each parameter.
This parameter is 1. First point 11. Second point 1
2 (i.e., points P11, P12, PI3)
direction of straight line L1, direction of second straight line 1i1L2, constant β
, δ.

Examples of changing the parameters in this way are shown in FIGS. 41 to 43.

FIG. 41 shows that among the above parameters, when only the direction of the first straight line L1 and the direction of the second straight line L2 are changed,
This shows how the trajectory of the divided vertices can be changed.

In the figure, the trajectory C is the trajectory of the divided vertices when the first straight line is set to 11 and the second straight line is set to L2,
This is considered to be one cross section of a dense polyhedron, and is set using the method described above. Here, if we set the first straight line to Llb and the second straight line to L2b without changing the first point 11, the second point 12, the position control parameter β, and the tangent control parameter δ, , the trajectory C changes to a trajectory indicated by a two-dot chain line cb. to 1st ゜2
The straight line L1. A feature when the direction of L2 is changed is that the convex portion of the trajectory changes upward or downward with respect to the bisector 1-11.

J, when the first straight line L1 is rotated clockwise (in this case, the second straight line L2 is rotated counterclockwise),
The locus cb of the two-dot chain line can be seen by comparing it with the shape C: J: In other words, the convex portion of the locus cb moves below the bisector line 1-11. In this case, when the first straight line L1 is rotated counterclockwise (in this case, the second straight line L2 is rotated clockwise), the convex part of the changed trajectory is the bisector L1. It moves upwards.

In this case, the 1.2nd straight line L1. As a result of rotating L2, both straight lines 11. A situation in which L2 are parallel to each other must be avoided. This is the first point 11 or the second point
This is to prevent the trajectory from having an inflection point at point 12. Therefore, if the locus may have an inflection point at the first point 11 or the second point 12, then the first straight line L1 and the second straight line $! There is no need to set a special t111 limit on the rotational state between JL2 and JL2.

FIG. 42 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. FIG. 42 shows a change in the trajectory when the position control parameter β is changed to a negative value after the position control parameter β is set to a positive value and the trajectory C is once determined. In this way, when the parameter β is changed to a negative value, the trajectory Cc becomes smaller when compared with the trajectory C, and the string L
Approaching 3.

That is, when the position control parameter β is set to O, the shape passes through the inner center 14 of the basic triangle. Its parameter β
When is set to a positive value, the trajectory approaches the intersection 13 side rather than the inner center 14, and the larger the size of β, the closer the intersection 1
Dress even closer to 3. Conversely, if the parameter β is set to a negative value, the locus will shrink so that it approaches the chord L3 side rather than the inner center 14, and the larger the absolute value of the parameter β, the closer the trajectory will be to the chord L3. It shrinks to . 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 111, and when the position control parameter β is changed, the position of the intersection changes. This is what I did. Therefore, only the curvature of the created trajectory changes in the rounded part of the trajectory. 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 go outside the basic triangle. do not have.

Figure 43 shows how the trajectory changes when only the tangent control parameter δ is changed among the above parameters.
It shows what you can do and what you can do.

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

That is, there is a trajectory C between the first point 11 and the second point 12.
Suppose that has been decided once. In this case, the third direct aL1
3 is the same as the tangent to the trajectory C at the third point 33. Then, the third point 33 and the third straight line L13
At the next point in time when is determined, the direction of this tangent L13 and the first
A new third point is determined between the first point 11 and the third point 33 according to the direction of the straight line L1, and a trajectory is gradually determined.

By the way, changing the tangent control parameter δ means changing the direction of the tangent (third straight line L 13 ). Therefore, changing the tangent control parameter δ is a
This is the same as changing the direction of L2, and can be considered in the same way as explained in FIG. 42. 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 113 is changed in the direction of the straight line L13d by changing the tangent control parameter δ at the third point 33, the connection between the third point 33 and the first point 11 is changed. In the meantime, the trajectory changes to the two-point class IfACd. That is, when the third straight FI 1113 is rotated clockwise by changing the tangent control parameter δ, the generated shape expands to the right in the figure at the bottom of the bisector 111. 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 set between the third point 33 and the first point 11, or between the first point 33 and the first point 11.
This is a case where shape creation or shape modification is performed between the point 33 and the second point 12.
It is possible to change the values of the parameters β and δ at points J3 between all points on the trajectory C and other points. 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. 44 is an explanatory diagram showing the principle of simply finding the third straight line.

The intersection of the extension of the straight line L9 and the second straight line L2 is defined as a point 34, the intersection of the extension of the straight line 110 and the first straight line L1 is defined as a point 35, and the straight line 114 connecting these points 34 and 35 is defined as A straight line drawn by moving this straight line 1i1L14 in parallel onto the third point 33 is defined as L15. This straight line L15 is used in place of the third straight line Ll,3. When the accuracy of θ is uncertain, it is convenient to use the straight line 115 determined 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 direction of the first straight line L1 and the direction of the second straight line L2 may be changed by 12 degrees at the second point.

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

In this case, instead of creating a three-dimensional locus all at once, the idea is to create a three-dimensional outline of the locus and then create a desired shape by connecting the outlines.

FIG. 45 shows the first point 51. Second point 52. First straight line L51. It is a figure which shows the state where the 2nd straight line L52 is 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 chord is the same as the reason described in FIG. 16.

Here, the extension line of the first straight line L51 and the second straight line L52
shall not intersect with the extension line of In other words, the trajectory of the divided vertices that will be created from now on is three-dimensional, so the contour line that will be drawn between the first point 51 and the second point 52 will not be able to be drawn on one plane. Often non-existent. 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 of the contour at J3 to the second point 52. For this reason, the first straight line [51 and the second straight line L52 often do not intersect.

FIG. 46 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 15
3]°. That is, when light is applied perpendicularly to the surface composed of the string 50 and the straight line L52, the first straight line L51
Let the shadow of the line L53 be the straight line L53.

FIG. 47 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 154
shall be. That is, when light is applied perpendicularly to the surface formed by the string 50 and the straight line L51, the shadow of the second straight line L52 is cast into the straight line L54.

FIG. 48 is a diagram for creating a basic pentagonal pyramid.

Point 53 and point 54 are connected, and this straight line is designated as 155. In this way, line L50. L51. L52, L53. L
54. There are four faces surrounded by L55, and the pentagonal pyramid surrounded by these faces is called the basic pentagonal pyramid.

FIG. 49 is a diagram for creating a temporary triangle Σ.

One point 55 of the line segment L 551 is determined by the torsion control parameter ε. This torsion control parameter ε is calculated from the following equation.

ε-D 1 /D 2 Here, Dl is the distance from point 54 to point 55, and D
2 is the distance from point 54 to point 53.

Distance 11tD1. In that case, D2 is determined depending on the case, and if the torsion control parameter ε, which is the ratio to this distance l1101.02, is changed, the shape formed by g1 changes.

Further, the torsion control parameter ε may be expressed 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 157. These lines L50, L56. L57
The triangle surrounded by is called a provisional triangle Σ.

FIG. 50 is a diagram for creating a basic triangle within the provisional triangle Σ.

The orthogonal projection of the first orthogonal FAL51 onto the provisional triangle Σ is the straight line 1
58, and the orthogonal projection of the second straight line L52 onto the temporary triangle Σ is a straight line L59, and these straight lines L58 and the straight line I! J1
Let the intersection with 59 be a point 56.

Straight line 158, straight line L59, and line segment 5 created in this way
The triangle surrounded by 0 and 0 is the three-dimensional basic triangle required when creating a locus of three-dimensional divided vertices, and this three-dimensional basic triangle is the 16th triangle when creating a two-dimensional shape. This corresponds to the basic triangle made in the figure.

FIG. 51 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 shown in FIG. 32, and thereby, when creating a shape at that point, it can be considered in the same way as the two-dimensional one described above. In other words, the three-dimensional basic triangle Δ(52) (51056) and the isosceles triangle polishing Δ
Based on (59), (51), and (56), Figures 31-
If you perform the same operation as in Figure 39, the third
A point 71 and a third straight line L73 are obtained.

However, when creating a three-dimensional trajectory of the divided vertices, it is necessary to use the torsion control auxiliary parameter φ. The tangent to the point 71 on the outline of the shape to be claimed 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.

The straight line (tangent line) that takes into account the torsion parameter φ is 172.

In FIG. 51, the symbols shown in brackets [ ] are
This corresponds to the points or straight lines shown in FIGS. 1 to 40.

In this way, by the straight line considering the torsion control auxiliary parameter φ and the first straight line 151 or the second straight line L52,
By performing the operations shown in FIGS. 45 to 51, 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, O,
O, O, O), and the direction cosine of the first straight line L51 is (0
,O,0,7232,0,6906) and the second point 5
The coordinates of 2 are (0, 0, 2° 0, π), and the direction cosine of the second straight line is (-0.

7232, O, O, 0,6906), position control parameter β is O, tangent control parameter δ is 0, torsion parameter ε is 0.5, and torsion control auxiliary parameter φ is -0,0467. Then, the locus of the divided vertices created by them forms a constant slope linear shape (spiral).

FIG. 52 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.
A second point setting means 82 is provided for setting the second point 12 at an arbitrary position other than point 1. Also, the first point 11
The first straight line L1 passing through is set in an arbitrary direction.
The straight line setting means 83 and the second straight line setting means 84 for setting the second straight line @L2 passing through the second point 12 in an arbitrary direction are KQ G-J. These setting means 81 to 84 include the keyboard 1. There is an input means such as a light pen 2. Moreover, as the principle is shown in FIGS. 31 to 39, the position of the first point 11 and the direction of the first straight line L1, the position of the second point 12 and the direction of the second straight line L2, A third point that determines the position of the third point 33 and the direction of the third straight line L13 including this third point 33 according to the direction.
A straight line determining means 85 is provided. The arithmetic circuit 3 is used to perform the function of the third point/straight line determining means 85.

The principle of finding the locus of the divided vertices two-dimensionally is as follows in the 31st
This is the same as that explained in FIGS. 46 to 39, and in order to determine the locus of the divided vertices three-dimensionally, it is necessary to use the Iζ principle explained in FIGS. 46 to 51. The arithmetic circuit 3 has a circuit configuration that realizes all of these principles. Furthermore, a computer may be used instead of the arithmetic circuit 3.

Furthermore, the third point/straight line determining means 85 includes a parameter β
, δ, ε, φ, etc., is provided. As this input means 86, the 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.

In the embodiment shown in FIG. 52, the first point 11 is
From the first straight line L1, the second point 12, and the second straight line,
This brings up the third point.

FIG. 53 shows how each means 81 to 84 is determined based on the point that has already been set or determined and the direction of the straight line at that point, and the point newly determined by the determining means 85 and the direction of the straight line at that point. Repeatedly control the first point 11
control means 8 for arranging a number of points between and the second point 12;
8. The operation of this control means 88 is as follows:
The principle is the same as that described with respect to FIG.

In particular, FIG. 54 is a block diagram of a device that two-dimensionally determines the trajectory of divided vertices. In this block diagram,
A first point setting means 81 for setting the first point 11 at an arbitrary position, the principle of which is shown in FIG.
A second point setting means 82 is provided for setting the second point 12 at an arbitrary position other than point 1. Also, the first point 11
A first straight line L1 that passes through and covers is set in an arbitrary direction.
For two-dimensional use, the second straight line 1i1L2 is set in an arbitrary direction within a plane that passes through the straight line setting means 83 and the second point 12, and also includes the first point 11 and the first straight line L1. A second straight line setting means 91 is also provided.

In addition, as shown in FIGS. 31 to 33, the chord L3 connecting the first point 11 and the second point 12, the first straight line L1, and the second straight line L2 Isosceles triangle creation means 92 that creates an isosceles triangle whose two short sides, excluding the side formed by the chord L3, are equilateral among the three sides of the basic triangle to be formed.
This is the setting.

Then, as shown in FIGS. 34 to 40 and FIG. 44, the position of the third point and the third
A third point calculation means 93 is provided for calculating the direction of a straight line including the point.

The third point calculating means 93 will be explained in detail and consists of the following constituent elements. That is, an incenter position calculating means 93a (applying the principle of FIG. 18.19) that calculates the position of the center of the basic triangle and the position of the center of the isosceles triangle, and a means for calculating the specific angle shared by the basic triangle and the isosceles triangle. Perpendicular to a straight line that connects one vertex of a basic triangle and the center of the basic triangle, excluding the vertex, and a line that connects the opposite vertex of the isosceles triangle to the one vertex and the center of the isosceles triangle. a first triangular surface v4 calculation means 93b (applying the principle of FIG. 20) for calculating the area of a first triangle surrounded by a bisector and a side opposite the one vertex; and a vertex of the specific angle. perpendicular to the straight line connecting the other vertex of the basic triangle and the incenter of the basic triangle, and the line segment connecting the opposite apex of the isosceles triangle to the other apex and the incenter of the isosceles triangle, except for a second triangle area calculating means 93G (applying the principle of FIG. 20) for calculating the area of a second triangle surrounded by the bisector and the side opposite the other vertex; and a position of the center of the basic triangle. , the position is located at a distance corresponding to the difference between the area of the first triangle and the area of the second triangle, and the distance between the first point and the second point, and is located at the knee of the specific angle. The calculation means 93d (an application of the principles shown in FIGS. 37 to 39) calculates the position on the equal dividing line as the position of the third point.

Further, the third point calculation means 92 contains constants β and δ.

A means 94 for inputting ε and φ is provided, and a storage device 87 for storing information on each point determined by the third point calculation means 92 is provided. The derivation circuit 3 is capable of performing the functions of the basic triangle/isosceles triangle creation means 92 and the third point calculation means 93.

[Effects of the Invention] The present invention makes it possible to easily detect the intersection point between a predetermined straight line and a predetermined surface, and to easily create a cut surface by cutting the predetermined surface linearly or curved. Alternatively, a mutual line, which is a series of points where a predetermined surface intersects with another surface, can be easily obtained. Therefore, shape processing machines such as NG machine tools,
It can be applied to shape recognition devices, image processors, automatic drafting machines, and image creators. In this case, three-dimensional manipulations or mechanical drives can be carried out in the above-mentioned devices or machines.

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 drawings]

Fig. 1 is an overall diagram of a system showing an embodiment of the present invention, Fig. 2 is a diagram showing a detected surface whose intersection point is detected and a straight line that intersects this detected surface, and Fig. 3 is a diagram showing the detected surface. Figure 4 is a diagram showing a surface divided into four triangles. Figure 4 is a diagram showing a central triangle t20, which is an intersection-containing surface, is divided into four triangles. Figure 5 is a diagram showing a peripheral triangle t33, which is an intersection-containing surface. A diagram showing the state divided into four triangles, 11~-' Figure 6 is basically the same as Figures 2 to 5, but it shows the locus of the intersection when the straight line DL is moved linearly. The figure shown, Figure 7, is the second
Although it is basically the same as Figure 5, it shows the locus of the intersection when the straight line DL is sequentially translated in a curved manner.
Figures 3 and 8 are diagrams showing the locus CL of the intersection when an ellipsoid is used as the detection surface, and Figure 9 is the locus O of the intersection when a hyperbolic paraboloid is used as the detection surface.
10 is a block diagram showing an embodiment based on the principle shown in Figs. 2 to 5, and Fig. 11 is a block diagram showing an embodiment based on the principle shown in Fig. 6.7. Figure, 1st
Figure 2 shows the case where the reference surface and the other surface do not intersect with each other, FIG. 13 shows the case where the reference surface and the other surface do not intersect with each other, and FIG. 14 shows the case where the other surface intersects with the reference surface. FIG. 15 is a diagram showing the case of FIG. 14,
Diagram showing the case where the opponent surface is divided into four triangles, 1st
Fig. 6 is a diagram showing a mutual line SL created by a curved surface by a catenary curve and an ellipsoidal surface, Fig. 17 is a block diagram showing an embodiment of the present invention based on the principle of Figs. 12 to 15, and Fig. 18. is a diagram showing the first stage triangle, Figure 19 is a diagram divided into second stage triangles, Figure 20 is a plan view of Figure 19, Figure 21 is a diagram partially divided into third stage triangles, Figure 22 is a diagram in which all second-stage triangles are divided into third-stage triangles, Figure 23 is an exploded view of Figure 20, Figure 24 is a plan view of Figure 22, and Figure 25 shows only a portion of the 4th stage triangles. Figure 26 is a diagram divided into stage triangles, Figure 26 is a diagram showing the entire second stage expanded, and Figure 27 is a diagram showing the second stage.
6 is a plan view, FIG. 28 is a view of the second stage in its entirety contracted, FIG. 29 is a plan view of FIG. 28, FIG. 30 is a block diagram showing an embodiment of the present invention, and FIG. Figure 32 shows the settings of the first stage necessary to determine the dividing vertices, Figure 32 shows the basic triangle and isosceles triangle created from the state in Figure 31, and Figure 33 shows the settings for the third stage. Explanatory diagram for determining the necessary constant α when setting points (divided vertices), No. 34
The figure is an explanatory diagram when finding the inner center of an isosceles triangle, Fig. 35 is an explanatory diagram when finding the inner center of a basic triangle, Fig. 36 is an explanatory diagram when determining the unbalanced ms, and Fig. 37 is an explanatory diagram when finding the inner center of a basic triangle. An explanatory diagram when calculating the distance d from the inner center of the basic triangle to the third point that is currently being sought. Figures 38 and 39 are explanatory diagrams when calculating the third straight line at the third point. Figure 40 is an explanatory diagram when setting a new third point (new dividing vertex), and Figure 41 is an explanatory diagram when setting a new third point (new dividing vertex). A diagram showing how the trajectory of the divided vertices can change if the
Figure 4.2 is a diagram showing how the locus of the divided vertex can be changed when only the position 1jJtil parameter β is changed among the parameters, and Figure 43 is a diagram showing how the trajectory of the divided vertex can be changed among the parameters Fig. 44 is a diagram showing how the locus of the divided vertices can be changed when only the parameter δ is changed; Figure 45 shows the first point, second point, and first straight line when determining the three-dimensional locus of the dividing vertices. Figure 47 shows the orthogonal projection of the first straight line onto the surface composed of the chord and the first straight line. Figure 48 is a diagram for creating a basic pentagonal pyramid, Figure 49 is a diagram for creating a provisional triangle, Figure 50 is a diagram for creating a basic triangle within a provisional triangle Σ, and Figure 51 is a diagram for creating a basic triangle in the provisional triangle Σ. FIG. 52 is a block diagram showing an embodiment of a device for determining the dividing vertex i, and FIG. FIG. 54 is a block diagram showing another embodiment of the division apex setting device.1...Keyboard, 2...Light Ben, 3...Arithmetic circuit, 4 ...Display, 5...Printer, 6
...External storage device, tlO...Detected surface, CP...
・Intersection, D...straight line, CL...; cutting line, Ul...reference surface, Ul, 0... mating surface, B10
... Straight line setting means, B11... Detected surface setting means,
B12... Surface dividing means, B13... Intersection containing surface detection means, B14... Storage means, 820... A-line moving means, B30... Reference plane setting means, 831... Opposite surface setting Means, B32... Surface dividing means, B33... Cross plane detection means, 11.51... First point, 12.52.
...Second point, Ll, L51...First straight line, L2.
L52...second straight line, 33.71...third point,
Ll3.172... Third 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...
3rd point/straight line determining means, 91... 2nd straight line am for two dimensions
fixed means, 92...isosceles triangle creation means, 93...
Third point calculation means, 93a... Inner center position calculation means, 93
b...First triangle area calculation means, 93G...Second triangle area calculation means, 93d...Calculation means, P21P3
1...First division loss point, P22.1) 32...Second division loss point, P23. P33...Third classification point, T10.
...First stage triangle, T20. P2O...Medium fire triangle T21. T22. T23. T31, 1”32.T33・
...Peripheral triangle, BO...First stage triangle setting means B
1...First division point setting means, B2...Second division loss point setting means, B3...Third division loss point setting means, B4.
. . . Peripheral triangle setting means, B5 . . . Central triangle setting means, B6 . . . Division repeating means. Patent Applicant Ryozo Setoguchi Figure 2 Figure 3 t20 Figure 6 Figure 7 Figure 8 Figure 9 Added Figure

Claims (1)

[Claims] (1) Straight line setting means for setting a straight line passing through a desired point and having a desired direction; detection surface setting means; surface dividing means for dividing a predetermined surface into a predetermined number of surfaces; and a surface dividing means for dividing a predetermined surface into a predetermined number of surfaces; including an intersection point between the straight line and the detected surface from among the plurality of surfaces divided by the surface dividing means. an intersection-containing surface detection means for detecting an intersection-containing surface that is a surface; Detect the surface, divide this intersection-containing surface into a predetermined number of surfaces again, detect the intersection-containing surface from among the divided surfaces, and repeat these operations to separate the straight line and the detected surface. 1. An intersection point position detection device in shape creation, characterized by detecting an intersection point with. (2. In claim 1, the surface dividing means is a device for dividing the predetermined surface into four triangles. (3) Desired point A straight line setting means for setting a straight line passing through and having a desired direction; A detection surface setting means for setting a detected surface having a desired shape and whose intersection position is to be detected; a surface dividing means for dividing into a predetermined number of surfaces; an intersection-containing surface for detecting an intersection-containing surface that is a surface including an intersection between the straight line and the detected surface from among the plurality of surfaces divided by the surface dividing means; a surface detection means; a linear movement means for moving the straight line by a predetermined distance; the surface to be detected is divided into a predetermined number by the surface division means, and from among the plurality of divided surfaces, The intersection-containing surface is detected, the intersection-containing surface is again divided into a predetermined number of surfaces, the intersection-containing surface is detected from among the plurality of divided surfaces, and these operations are repeated to separate the straight line and the An intersection point position detecting device for shape creation, characterized in that the intersection point with the detected surface is detected, and the same operation as described above is repeated for the straight line moved by the linear moving means. (4) Claims In claim 3, the surface dividing means divides the predetermined surface into four triangles.(5) In claim 3, An intersection position detecting device for shape creation, characterized in that the linear moving means continuously moves the straight line in parallel. (6) Claim 3 provides that the linear moving means , the intersection point position detecting device for shape creation is characterized in that the straight line is moved in parallel on the - straight line. (7) In claim 3, the linear moving means moves the straight line on a curved line. An intersection position detecting device for shape generation, characterized in that the intersection point position detection device in shape creation is characterized in that the intersection point position detection device in shape creation is characterized in that the intersection point position detection device in shape generation is A mating surface setting means for setting different mating surfaces; and a surface dividing means for dividing a predetermined surface into a predetermined number of surfaces. and an intersecting surface detection means for detecting intersecting surfaces that are surfaces that exist on different sides from each other; Detect the intersecting plane from among them, divide this intersecting plane again into a predetermined number of planes, detect the intersecting plane from among the plurality of divided planes, and repeat these operations to form the intersecting plane with the other plane. An intersection position detection device in shape creation, characterized by detecting a line of intersection with the reference plane. (9) The intersection point position detecting device for shape creation according to claim 8, wherein the surface dividing means divides the predetermined surface into four triangles. (10) In claim 8, the intersecting plane detection means includes a direction in which one vertex of the predetermined plane has with respect to the reference plane when viewed from a predetermined direction, and a direction in which one vertex of the predetermined plane has with respect to the reference plane when viewed from the predetermined direction. An intersection point position detecting device in shape creation, characterized in that the predetermined surface is determined to be the intersecting surface when the directions of other vertices of the predetermined surface with respect to the reference plane are different from each other.