JPH10255078A - Shape inside and outside deciding method and deciding device for optional point in numeric value shape data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a device which shortens the time that decides whether an optional point in numeric value shape data exists in a free curved surface that is represented by a complicated formula or not. SOLUTION: This device comprises a 1st storage device in which numeric value shape data is stored, a 2nd storage device which stores evaluation point data that is undergone inside and outside decision, a 3rd storage device which stores a program, a 4th storage device that stores inside and outside decision results and a central processing unit 5 which controls a series of the operations and executes calculation, and the unit 5 reads shape data that is represented in a complicated formula and evaluation point data that performs inside and outside decision from the 1st and 2nd storage devices, based on a program of the 3rd storage device, approximates the outer surface of the shape data in the set of triangles, extends a half line from the evaluation point, counts the number of intersections of the approximated outer surface and the half line, decides that an evaluation point exists inside the outer surface when the number of intersections is odd and decides that the evaluation point exists outside the outer surface when it is not odd.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a CAD system,
Converts numerical shape data into a set of basic shapes such as tetrahedron, pentahedron, and hexahedron for structural analysis using the finite element method, and points with arbitrary coordinate values are converted into three-dimensional solid shapes specified by mathematical expressions. And a method for determining whether or not it is inside the device. The “inside / outside shape determination device” refers to a device that determines whether or not a point having an arbitrary coordinate value is inside a three-dimensional solid shape specified by a mathematical expression.

[0002]

2. Description of the Related Art In the prior art, a free-form surface represented by a complex mathematical expression is extended from a point of evaluation to a half-line, and the number of points of intersection with the surface is counted. It is determined whether or not there is.

Generally, a free-form surface is defined by recursively defining a higher-order expression, and a set of the free-form surfaces defines an outer surface of a three-dimensional solid shape.
In the conventional method, a half-line is extended from an evaluation point, and the half-line is a free-form surface 1 constituting an outer surface of a three-dimensional solid shape.
For each one, it is asked whether or not it has an intersection.
The number of intersections with the set of all free-form surfaces that make up the outer surface of the three-dimensional solid shape determines whether it is inside the three-dimensional solid shape (inside if the total number of intersections is odd, and if it is even) Is determined to be outside). In calculating the intersection, a free-form surface is recursively defined. Therefore, it is necessary to repeatedly calculate whether or not an intersection exists.

[0004]

However, the prior art has the following problems. (1) Since the free-form surface constituting the outer surface of the three-dimensional solid shape is defined by recursively defining a higher-order equation, it is necessary to repeatedly calculate the intersection between the free-form surface and the half-line. I needed to do the calculations. (2) In order to find an intersection between a free-form surface represented by a complicated mathematical expression and a half-line, it is generally necessary to repeatedly calculate, and a lot of calculation time is spent.

The present invention provides a method and an apparatus capable of solving these problems, that is, approximating a free-form surface constituting an outer surface with a set of triangles that can be expressed by a linear expression,
It is an object of the present invention to provide a method and an apparatus for reducing the time required for determination by determining an intersection between the triangle and the half-line and performing an inside / outside determination.

[0006] By approximating with a triangle, the number of surfaces constituting the outer surface of the solid shape increases, but since the intersection is determined analytically, the total calculation time required for the inside / outside judgment can be reduced.

[0007]

[Means for Solving the Problems]

(Explanation of terms) The "evaluation point" refers to a candidate point for generating a node, which is an intersection of finite elements, when division by the finite element method is automatically performed by a computer.

A node is generated for the candidate point based on the result of the inside / outside determination. The evaluation points are specified by three-dimensional coordinates on a storage device of the computer. The “evaluation point” in the present invention is the same as the “evaluation point” in the conventional technology, and the “semi-straight line” in the present invention is the same as the “semi-straight line” in the conventional technology. (First Means) The method for determining the inside / outside of a shape of an arbitrary point in numerical shape data according to the present invention comprises: (A) storing shape data represented by a mathematical expression in a first storage device 1; 2 stores the evaluation point data for performing the inside / outside judgment, (C) stores the program in the third storage device 3, and (D) stores the shape data represented by the mathematical expression of the first storage device in the central processing unit 5. Evaluation point data for performing the inside / outside determination of the second storage device;
The program in the third storage device is read, (E) the central processing unit 5 approximates the outer surface of the shape data with a set of triangles, and (F) the central processing unit 5 extends a half line from the evaluation point. Then, the number of intersections between the approximated outer surface and the half line is counted. (G) When the number of the intersections is odd, the central processing unit 5 determines that the evaluation point is inside the outer surface. If it is determined that it is not an odd number, it is determined that the evaluation point is outside the outer surface, and (H) the result of the inside / outside determination is stored in the fourth storage device 4. (Second Means) The device for determining the inside / outside shape of an arbitrary point in numerical shape data according to the present invention includes (A) a first storage device 1 for storing numerical shape data, and (B) evaluation point data to be determined inside / outside. A second storage device 2 for storing, (C) a third storage device 3 for storing a program, (D) a fourth storage device 4 for storing a result of inside / outside determination, and (E) control and calculation of the series of operations. (F) The central processing unit 5 executes, based on the program in the third storage device, shape data represented by a complex mathematical expression in the first storage device, Reading the evaluation point data for performing the inside / outside judgment of the storage device, approximating the outer surface of the shape data with a set of triangles, extending a half line from the evaluation point, counting the number of intersections between the approximated outer surface and the half line, If the number of the intersections is odd, the evaluation score is Determines that the inside of the surface, if not odd, evaluation points, characterized in that determined to be outside of the outer surface.

That is, according to the present invention, in numerical shape data, an outer surface generally represented by a free-form surface is approximated by a set of triangles whose geometrical calculations are simple, and an arbitrary arbitrary value is assigned to the approximated outer surface. It is a device that determines whether or not to include an evaluation point inside. By arranging a plurality of points on a free-form surface represented by a complex mathematical expression and connecting the points, the free-form surface is formed by a set of triangles. Approximate.

The intersection of the triangle and the half line is calculated analytically, the number of intersections between the approximated outer surface and the half line is counted, and if the number of intersections is odd, the evaluation is made. It is characterized in that it is determined that the point is inside the outer surface, and when it is not odd, it is determined that the evaluation point is outside the outer surface.
(Relationship between triangle and half line) As a method for determining whether or not the evaluation point is inside the solid shape, a half line is extended from the evaluation point, and the number of intersections between the half line and the outer surface of the target solid shape Is inside if the number is odd,
If it is an even number, it can be determined that it is outside.

The present invention improves the efficiency of the inside / outside judgment by approximating the outer surface of a three-dimensional solid shape with a set of triangles and finding the intersection of the approximated curved surface and the extended straight line from the evaluation point. It is.

Therefore, the number of intersections between the extended straight line from the evaluation point and the set of triangles approximating the outer surface is determined. Therefore, it operates as follows.

Generally, a free-form surface is defined by recursively defining a higher-order equation. Therefore, in order to calculate an intersection between a free-form surface and a half-line, it is necessary to perform repeated calculations such as Newton's method. Yes, so many calculations need to be done.

On the other hand, since the calculation of the intersection between the triangle and the half line can be obtained analytically, the calculation of the intersection between the free-form surface and the half line requires a very small amount of calculation. The intersection can be determined analytically. Therefore, by using this property for the inside / outside determination, the time required for finding the intersection can be reduced. In a structural analysis or the like by the finite element method, a given shape is represented by a set of basic shapes, so that even an approximate calculation is practical.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION

(First Embodiment) FIG. 1 shows a first embodiment of the present invention.
3 to FIG. FIG. 1 is a configuration diagram of an apparatus according to a first embodiment of the present invention.

FIG. 2 is a flow chart of the apparatus according to the first embodiment of the present invention. FIG. 3 is a diagram illustrating an example in which numerical shape data is approximated by a set of triangles. As shown in FIG. 1, the inside / outside determination device of the present invention includes a first storage device 1 storing numerical shape data, a second storage device 2 storing evaluation point data to be determined inside / outside, and a program storage device. And a fourth storage device 4 for storing the inside / outside determination results, and a central processing unit (CPU) 5 for controlling a series of operations and executing calculations.

Next, the operation of the central processing unit (CPU) 5 based on a program will be described with reference to FIG. First, shape data represented by a complicated mathematical expression and evaluation point data for performing inside / outside determination are read (Step 20), and the outer surface of the shape data is approximated by a set of triangles (S20).
step21).

Next, a half line is extended from the evaluation point (Step
p22), the number of intersections between the approximated outer surface and the half line is counted (Step 23). If the number of intersections is odd, it is determined that the evaluation point is inside the outer surface, and if it is not odd, it is determined that the evaluation point is outside the outer surface (Step 24). FIG. 3 shows an example in which numerical shape data is approximated by a set of triangles.

[0019]

Since the present invention is configured as described above, it has the following effects. (1) A free-form surface that requires repeated calculations to calculate the intersection
It is approximated by a set of triangles obtained analytically. (2) Therefore, the amount of calculation required for calculating the intersection can be reduced.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an apparatus according to a first embodiment of the present invention.

FIG. 2 is a flowchart of the apparatus according to the first embodiment of the present invention.

FIG. 3 is a diagram showing an example in which numerical shape data is approximated by a set of triangles.

[Description of Signs] 1... 1st storage device 2... 2nd storage device 3... 3rd storage device 4.

Claims (2)

[Claims] (A) A first storage device (1) stores shape data expressed by a mathematical expression, (B) a second storage device (2) stores evaluation point data for performing inside / outside determination, C) Store the program in the third storage device (3), and (D) make the central processing unit (5) determine the shape data expressed by the mathematical expression of the first storage device and determine whether the second storage device is inside or outside. The evaluation point data and the program in the third storage device are read, and (E) the central processing unit (5) divides the outer surface of the shape data into three.
(F) extend a half line from the evaluation point by the central processing unit (5) and count the number of intersections between the approximated outer surface and the half line; (G) the central processing unit According to (5), if the number of the intersections is odd,
The evaluation point is determined to be inside the outer surface, and if not an odd number, the evaluation point is determined to be outside the outer surface. (H) The inside / outside determination result is stored in the fourth storage device (4). A method for determining the inside / outside of a shape of an arbitrary point in numerical shape data. (A) a first storage device (1) for storing numerical shape data; (B) a second storage device (2) for storing evaluation point data to be determined inside / outside; A third storage device (3) for storing, (D) a fourth storage device (4) for storing the inside / outside determination result, and (E) a central processing unit (5) for controlling the series of operations and executing calculations. Consisting of
(F) The central processing unit (5) is based on the program of the third storage device, and the shape data represented by the complicated mathematical expression of the first storage device and the evaluation points for performing the inside / outside determination of the second storage device. Data is read, the outer surface of the shape data is approximated by a set of triangles, a half line is extended from the evaluation point, the number of intersections between the approximated outer surface and the half line is counted, and the number of intersections is
If the number is odd, the evaluation point is determined to be inside the outer surface; if not, the evaluation point is determined to be outside the outer surface. Shape inside / outside judgment device