JPH01292474A - Arithmetic unit for solid interference - Google Patents

Abstract

PURPOSE:To attain solid interference computing processing based upon a solid modeler by moving two solids in the separating or superposing direction of the two solids when they are contacted with each other. CONSTITUTION:An intersection deciding part 22 decides respective intersections between faces, between a face and a ridgeline, etc., from plural solid information inputted from an input part 21. Since contact between solids disables calculation, a moving direction calculating part 23 calculates the separating direction of plural contacting solids or the deeply superposed direction when the deciding part 22 decides contact, and a distance increasing/decreasing part 24 moves one solid by a minimum value to be processed by a computer to remove their contact and an arithmetic processing part forms three-dimensional data.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to computers, and particularly to a steric interference calculation device suitable for constructing a three-dimensional solid model on a computer.

[Conventional technology]

In order to improve the efficiency of various design tasks, we are using CAD/CAM (Computer Aided Design/Manufacturing).
/Computer Aided Manufacturer
uring) is attracting attention. In recent years, the processing speed and storage capacity of computers have improved dramatically, making it possible to construct three-dimensional models on computers. Among 3-dimensional CAD models, a modeler called a solid modeler has the advantage of being able to hold data on the inside and outside of a solid, so it can be used to construct data for volumetric calculations, applications, and thermal application calculations.

As a method of creating a three-dimensional solid using a solid modeler, it is possible to use a set operation that combines simple basic solids and constructs them horizontally (for example, as disclosed in Yokogawa Hewlett Packard Card Co., Ltd. Catalog, rME Series 30). )
.

The lid modeler is configured as a computer system as shown in FIG. This system includes a computer main body 3 to which a CRT1 as a display device, a keyboard 2 and a mouse 4 as input devices are connected. Three-dimensional coordinate data is input from the keyboard 2, and the position of the three-dimensional object is specified using the mouse 4.

FIG. 6 is a block diagram showing the detailed configuration of the computer main body 3. As shown in FIG.

The bus 5 includes a numerical calculation device 6 for performing numerical calculations, a data storage device 7 for storing numerical data, a mathematical formula storage device 8 for storing formula data for the solid modeler, and a data control device 9 for controlling the flow of data. is connected. Furthermore, the bus 5 includes a keyboard interface 10 . for inputting/outputting the keyboard 2 , the CRTI, and the disk device 13 . A CRT interface 11 and a disk interface 12 are each connected.

In such a system, each of the numerical calculation device 6, the data storage device 7, and the formula storage device 8 is controlled by the data control device 9 based on the contents entered on the keyboard 1 and the contents stored on the disk of the disk device 13. , and combine simple basic solids to construct new solids while moving data.

As shown in FIGS. 7(a) and 7(b), the solid modeler represents the surface of a three-dimensional solid as a polyhedral patch, and has information on nine vertices and edges as data. Figure 7 (
The data in a) is the data for the cube shown in Figure 7(b), and includes the coefficients of the equations of the six faces, the edges that make up one face, the two vertices that make up one edge, and each vertex. X, Y
, shows the relationship between Z coordinates as data.

Next, the operation of combining two basic solids will be explained with reference to FIG.

When creating a new solid by combining basic solids, first check the interference between the surfaces of the basic solids and generate interference lines (Figures 8(a) and (b)). This interference line should form a loop, and the original basic solid can be divided into two or more parts by the interference line. Next, as shown in FIG. 8(C), interference &11
A solid contained in one of the basic solids 11 and 12 (basic solid 12 in this example) divided by 0 (basic solid 12)
a and one of 12b) is removed. Next, Fig. 8(d)
.

When the interference lines are connected to each other as shown in (e), a solid that is the sum of the original basic solids is generated.

Next, a processing method for examining interference between three-dimensional surfaces will be described.

When finding the interference line of a solid, we focus on the surfaces of the solid and investigate the interference between the surfaces of the solid. Then, after finding the interference line and finding the interference between all the surfaces, use that interference line as the interference line between solids.

FIG. 9(a) shows a state in which two surfaces, surface A and surface B, interfere with each other. First, find the intersection of the edges of planes A and B. Surface B is ridgeline A,,12. l.

14, it is only necessary to calculate the intersections between the plane B and the edges 11 to 14.

Here, the equation of surface B is AI-! -By+C,+D=0, and the coordinates of the starting point v1 and ending point v2 of the ridge line l are V+
=(X++ 3'++ 2+)Vz=(Xz・ )
'z+Zz), then the fulcrum P+ = (X31 yi+ 21
can be expressed as the following equation.

Axs+ BF3+ C, 3+ D -QXt -X
z 'Jr-'! tZ+
-Zz satisfies this equation (1) (x3 + '12
*22), the intersection point P can be found. If we find all the intersection points of the edges in this way, we get
The intersection point P1 and the intersection point P are found. A line segment whose starting and ending points are these two intersection points becomes an interference line. Similarly, the interference line between the surface C and the surface shown in FIG. 9(b) can be obtained using the above method. In this way, interference lines can be calculated for all surfaces of the solid.

Interference line j? When +, lt, is, and lla are interconnected, a loop is formed as shown in FIG. 10, and the processing shown in FIG. 8(c) is performed based on this interference line loop. The basic solid 12 shown in FIG. 8(c) is the basic solid 1
It is cut by 2a and 12b.

Of these, the basic solid 12a is removed because it is included in the basic solid 11, leaving only the basic solid 12b. Whether or not the basic solid 12a is included in the basic solid 12 is determined by determining whether one of the vertices of the basic solid is inside or outside the basic solid 12. This point position determination is
If a half-line is extended from the vertex toward infinity and this half-line does not intersect any surface of the basic solid 12, it can be determined that the point is outside the basic solid. When the remaining solids are combined based on interference lines after removing the solid inside the partner, a new solid is generated.

The above-described processing for finding interference lines or determining point positions is performed by a numerical calculation device 6 shown in FIG.

[Problem to be solved by the invention]

However, in conventional 3D interference calculation devices, calculation of interference lines, point position determination processing, etc. are all performed by numerical calculation devices, so there is a limit to the numerical values that can be handled.
Since the number of significant figures is 6 digits for 32-bit calculations and about 12 digits for double precision (64-bit calculations), calculation errors often become a problem.

In particular, with solid modeler equipment, there are problems such as interference lines not forming loops, so the surface between solids.

Problems arise when edges and vertices touch each other.

Figures 11 (a) to (g) show various contact states, and Figure (
In a), solids A and B are in contact with each other at their vertices, in figure (b), their vertices are in contact with each other, in figure (e), their vertices are in contact with each other, and in figures (e), their vertices are in contact with each other, and in figures (d) and (e), their edges are in contact with each other. Figure (f) shows the case of contact between an edge and a surface, and Figure (g) shows a case of contact between surfaces. In these cases, it is impossible to generate interference lines, and calculation errors are likely to occur. Therefore, in the worst case, the system of the solid modeler device may go down and malfunction.

The present invention solves such conventional problems, and aims to provide a 3D interference calculation device that prevents the system from going down even when 3D objects are in contact with each other at their faces, edges, or vertices. shall be.

(Means for solving vs,!!) In order to achieve the above object, the present invention provides a three-dimensional solid interference calculation device that constructs a solid using set operations. Intersection determining means for checking mutual contact, and coordinate moving means for moving the coordinates of surfaces, ridges, and vertices in a direction in which the solid body expands or contracts when contact is determined by the means. This is what I did.

[For production]

When contact is determined between surfaces, edges, and vertices, the coordinates of the surfaces, edges, and vertices in contact are increased or decreased by a predetermined distance to prevent contact between the surfaces, edges, and vertices;
Allow set operations to be performed.

〔Example〕

Hereinafter, one embodiment of the present invention will be described based on the drawings.

FIG. 1 is a block diagram showing a three-dimensional interference calculation device according to the present invention.

In FIG. 1, the input unit 21 receives data for set calculations from the keyboard 2, the disk device 13, etc., and the intersection determination unit 22 inputs data for face-to-face, face-to-edge, edge-to-edge, and vertex as shown in FIG. Determine each intersection of and with vertices, faces, and edges.

A moving direction calculating section 23 connected to the intersection determining section 22 calculates each moving direction of a surface, an edge line, and a vertex. A distance increase/decrease unit 24 is connected to the movement direction calculation unit 23, and when interference of three-dimensional data is determined, the distance increase/decrease unit 24 is configured to move the two solids apart or bring them closer together.

The coordinates of the vertices are calculated to increase or decrease by a distance ε (6 will be described later), and this is input to the intersection determination section 22.

Further, a set calculation processing unit 25 is connected to the intersection determination unit 22, and performs set calculation based on set calculation data in which no intersection occurs among faces, edges, or vertices, and calculates a new solid. A display section 26 is provided to display this result on the CRTI.

These are housed in the computer main body 3 shown in FIG. 5, and are connected to each device shown in FIG. 6 via a bus 5. Therefore, in this embodiment as well, as shown in FIG. 7, the equations of all the surfaces of the solid, surface numbers, neighborhood lines, edge configurations, vertices, apex coordinates, etc. are held as data. Based on these data, before performing a set operation, check the overlap between surfaces, the overlap between surfaces and edges, the overlap between edges and so on.

A three-dimensional solid model is expressed as numerical data on a computer. A surface is represented by a collection of edges that make up the surface or a collection of vertices that make up the surface, and the arrangement of the edges and vertices is determined to be clockwise or counterclockwise, and the direction of rotation is related to the normal vector of the surface. to determine the back and front sides. The back side of the surface is the inside of the solid, and the front side of the surface is the outside of the solid. The edge line is specified by the vertices at both ends, and the vertices are specified by three-dimensional coordinates.

The condition for two surfaces to be in contact is that both surfaces are on the same plane (
The ratios of the surface equations, All +B, +C, +D=0, are the same), and all the vertices of the other surface exist within one surface (polygon).

Furthermore, the condition that the vertex and the surface are in contact is that the coordinates of the vertex (x, y
, z) is the surface equation AI+]3. -t-C, +D-0
and the vertex is within the plane.

Also, the condition that two ridges touch is that both endpoints of one ridgeline are above the other ridgeline (the coordinate values of both endpoints are the equation of a straight line).
=AX+B).

When the above conditions are met, set operation is performed 2
It can be determined that surfaces between two solids, vertices and faces, and vertices and edges are in contact (intersect). When performing set operations between solids, first check the above conditions,
Investigate contacts between faces, edges, and vertices. If there is contact with either, set operations will no longer be possible. Therefore, in the present invention, the touching vertices are moved so that the surfaces, edges, and vertices are completely separated or deeply overlapped, and then a three-dimensional set operation is performed.

Next, the processing principle of the present invention will be explained with reference to FIG.

Here, we will take up a case where a set operation is performed on solid A and solid B, which is a rectangular parallelepiped.

FIG. 2(a) shows the state before the set operation is performed, in which solid A is moved and the two solids are superimposed to perform the set operation. In the state shown in FIG. 2(b), since none of the surfaces, edges, and vertices overlap, solids A and B can be combined into one solid by a set operation.

However, in the state shown in FIG. 2(c), solids A and B are connected at only one place, making it a solid that does not exist in reality. In the present invention, when an attempt is made to perform a set operation on the three-dimensional objects in this state, the set operation is performed by moving the overlapping vertices of the three-dimensional objects A and B on the CRTI screen.

Next, the present invention will be explained in detail using the flowchart shown in FIG. 3 (this process starts after the positions of solids A and B are specified).

First, in step 31, solid A,! : Intersection of the planes of H is determined. The data shown in FIG. 7 is used for this intersection determination, and calculations are made taking into account the numerical calculation error t (6 significant digits in single precision 32-bit calculation, about 12 digits in double precision 64-bit calculation).

Here, A, B, C, and D are surface parameters and X.

When FE2 is the coordinate of the vertex, the formula for determining whether the vertex is on a surface is expressed by the following formula.

IA□+By++CzI+D l≦6 ・・・・・・
...(2) C is the error of the computer, and its value is 1
Approximately 0-6 is adopted.

It is determined that the surfaces are in contact when all the vertices constituting the surface are on other surfaces and all the vertices are located within the edge of the surface.

In the contact determination between a surface and an edge, if both end points of the edge are on the surface and within the edge of the surface, it is determined that they are in contact.

After performing intersection determination using such a method in steps 31 to 35, if there is an overlap, that part is
It is displayed in red on the RTI screen to warn the user (step 36), and the intersecting surfaces, edges, and vertices are moved by the minimum value ε that can be expressed within the computer (step 3).
7) Move the intersecting faces, edges, and vertices a little apart and perform set operations.

The data for set calculations in which intersections are eliminated in this way, or data for which there are no intersections from the beginning, are sent to the set calculation processing section 25, where they are subjected to set calculation processing (step 38). The new solid obtained by the set operation is displayed on the CRTI via the display unit 26.

Next, with reference to FIG. 4, intersecting surfaces and ridge lines.

The direction in which the vertex is moved will be explained.

(2) There are two directions in which the edges and vertices can be moved: the direction in which the volume of the three-dimensional object expands and the direction in which it contracts. The direction of expansion is the normal vector direction, and the direction of contraction is the opposite direction of the normal vector. In the case of a surface, as shown in FIG. 4(a), the coordinates of the vertices constituting the surface are moved in the direction of the normal vector of all the surfaces or in the opposite direction of the normal vector. Furthermore, in the case of an edge line, a vector is used that is the average of the normal vectors of the surfaces on both sides of the edge line.

Specifically, as shown in FIG. 4(b), the coordinates of the two vertices of the edge are moved in the direction of the addition vector of the normal vectors of the two surfaces of the edge or in the opposite direction of the addition vector. Furthermore, in the case of a vertex, the average of the normal vectors of all the faces constituting the vertex is used. That is, as shown in FIG. 4(c), the vertex coordinates are moved in the direction of the addition vector of the normal vectors of all surfaces having vertices or in the opposite direction of the addition vector. In both cases, the distance to be moved is ε.

Note that in the above, the direction of movement when surfaces, edges, and vertices come into contact is arbitrary; however, when an operator of the solid modeler selects a command for a set operation, it is possible to specify a set operation in which a solid expands when there is contact. It is conceivable to have a system that selects two set operations, a contracting set operation and a contracting set operation.

〔Effect of the invention〕

As explained above, according to the present invention, two solid surfaces,
Intersection determining means for checking mutual contact between edges and vertices, and when contact is determined by this means, intersecting
Since a coordinate moving means is provided to move the coordinates of the vertices in the direction in which the solid body expands or contracts, it is possible to prevent set operations from being impossible due to contact between surfaces, edges, and vertices, and improve operability. This can prevent system downtime.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 3 is a flowchart showing a processing example of the present invention, and FIG. 4(a),
(b) and (c) are explanatory diagrams of the moving directions of surfaces, edges, and vertices in the present invention, FIG. 5 is a schematic perspective view showing an example of the configuration of the solid modeler, and FIG. 6 is the computer main body 3 shown in FIG. 5. Block diagram showing details of FIG. 7(a),(b)
is an explanatory diagram of the configuration of each data of the solid modeler's vertices and one edge line, Figures 8 (a) to (e) are explanatory diagrams of the operation process of creating a new solid from a conventional basic solid, Figure 9 (a), (
b) is an explanatory diagram for determining interference between surfaces of a solid, FIG. 10 is an explanatory diagram showing loop formation of interference lines, and FIGS. 11(a) to (
g) is an explanatory diagram showing various states of contact between two solids. 1... CRT, 2... Keyboard, 3... Calculator body, 4...
...Mouse, 5...Bath, 6.
・・・・・・・・・Numerical calculation device, 7・・・・・・・・・
Data storage device, 8... Mathematical formula storage device,
9... Data control device, 21...
...Input section, 22...Cross determination section,
23...Movement direction calculation unit, 24...
... Distance increase/decrease section, 25... Set operation processing section. Figure 2 Figure 4 Figure 5 Figure 6 Figure 7 (a) Figure 8 (CI) (e) Figure 9 Figure 10 Parent section! 2

Claims (1)

[Claims] In a three-dimensional solid interference calculation device that constructs a solid using set operations, an intersection determining means for checking mutual contact between surfaces, edges, and vertices of two solids, and when contact is determined by the means. A three-dimensional interference calculation device comprising: coordinate moving means for moving coordinates of surfaces, edges, and vertices in a direction in which the three-dimensional object expands or contracts.