JP2000187739A - Method for generating polygon and computer readable recording medium storing program for allowing computer to execute respective processes - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make it possible to approximate a curved surface by a comparatively small number of polygons and to generate polygons to be intuitively easily recognized. SOLUTION: Inner points to be references for generating a polygon are arranged like a grating so that a distance between a curved surface to be approximated and a polygon to be generated is less than a previously determined distance (S201) and a curve expressing the boundary of the curved surface is approximated by a polyline so as to satisfy the previously determined distance (S202). Then the polygon is generated based on the nodes of the polyline approximated to the arranged inner points and the curve (S203).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a polygon generating method, and more particularly, to a method of approximating a curved surface with polygons by considering a distance between the surface to be approximated and the polygon approximating the curved surface. The present invention relates to a polygon generating method capable of reducing the number of polygons required for a computer and a computer-readable recording medium storing a program for causing a computer to execute each step of the method.

[0002]

2. Description of the Related Art For example, when the number of surfaces constituting an object is increased with reference to an object consisting of a hexahedron such as a cube, the appearance of the object becomes a sphere in proportion to the number of increasing surfaces. Approaching.

Conventionally, when defining a curved surface in a three-dimensional space, the distance between the curved surface and the polygon is increased by reducing the size of the polygon with respect to the entire figure and increasing the number of polygons in the same manner as described above. Adjustment was performed to approximate the curved surface.

[0004]

However, in the above-mentioned prior art, it is possible to approximate a curved surface, but it is necessary to reduce the size of polygons with respect to the entire figure and increase the number of polygons. Therefore, there is a problem that the number of necessary polygons increases and the data amount becomes enormous.

The present invention has been made in view of the above, and an object of the present invention is to make it possible to approximate a curved surface with a relatively small number of polygons and to generate a polygon which can be easily recognized intuitively. .

[0006]

According to a first aspect of the present invention, there is provided a method for generating a polygon, comprising the steps of: determining a distance between a curved surface to be approximated and a polygon that approximates the curved surface; A polygon generation method for generating a polygon approximating the curved surface, wherein a reference for generating the polygon is set such that a distance between the curved surface and the generated polygon is equal to or less than a distance determined by the distance information. An inner point arranging step of arranging the inner points in a grid, and an approximating step of approximating a curve representing the boundary of the curved surface with a polyline so as to satisfy the distance determined by the distance information; The polygon is generated based on the interior points arranged in the process and the nodes of the polyline generated when approximating the curve with the polyline in the approximation process. A polygon generation step, is intended to include.

According to a second aspect of the present invention, there is provided a computer-readable recording medium on which a program for causing a computer to execute each step of the polygon generating method according to the first aspect is recorded.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of a polygon generating method according to the present invention and a computer-readable recording medium storing a program for causing a computer to execute each step of the method will be described with reference to the accompanying drawings. This will be described in detail.

FIG. 1 is a block diagram showing an example of a hardware configuration for realizing the polygon generating method according to the present embodiment. FIG. 1 shows an example on the assumption that the polygon generation method according to the present embodiment is realized using a general computer.

A computer 100 shown in FIG. 1 controls a whole, a CPU 101, a ROM 102 storing a boot program and the like, a RAM 103 used as a work area of the CPU 101, and inputs characters, numerical values, various instructions and the like. An input device 104 such as a keyboard and a mouse, and a display device 105 such as a CRT or a liquid crystal display for displaying the result of processing by the CPU 101 (displaying a three-dimensional object formed of polygons). A hard disk 106 for storing an application program or the like (not shown) for implementing the polygon generation method, and a bus 107 for connecting the above-described units
And at least.

The computer 100 shown in FIG.
Is merely an example, and an apparatus having any configuration may be used as long as a polygon generation method according to the present embodiment described later can be realized.

Next, the polygon generating method according to the present embodiment, which is executed by using the application program stored in the hard disk 106, will be specifically described. FIG. 2 is a flowchart illustrating a polygon generation method according to the present embodiment. Here, a polygon generation method will be described with an example of dividing the curved surface shown in FIG. 3 into polygons.

First, it is assumed that a value (distance information) indicating the distance between a curved surface and a polygon that may be generated is specified as a condition for generating the polygon prior to generation of the polygon.

Then, the inner points for polygon generation are arranged in a grid pattern so that the distance between the curved surface and the polygon that may be generated is equal to or less than (or less than) a specified value (S201). The interior points are located at the intersections of the grid. In addition,
What is the distance between the surface and the polygons that can be generated?
It means the distance from an arbitrary point on the polygon that may be generated to the curved surface, and the position and number of points on the polygon for defining the distance can be set arbitrarily.

FIGS. 4 to 6 are explanatory diagrams specifically showing the processing of step S201 in FIG. The curved surface approximated by the polygon is actually a three-dimensional curved surface.
In the case of 01, processing is performed by substituting into two dimensions. That is, the surfaces shown in FIGS. 4 to 6 are actually three-dimensional.

More specifically, in step S201, grids (inner points) are added until the distance between the polygon generated based on each grid of the grid and the curved surface is equal to or less than a specified distance value. (See FIGS. 4 to 6). In other words, the number of squares that become polygons is increased until the distance between the polygon that may be generated and the curved surface becomes equal to or less than the specified distance value. In one square, a polygon of α or β is generated as shown in FIG.

For example, when the distance between the polygon and the curved surface which may be generated corresponding to the hatched area in FIG. 4 is not less than a designated value, as shown in FIG. Add a new grid (inner point) that bisects the eye.

Next, the distance between the polygon and the curved surface, which may be generated corresponding to each of the two hatched squares A and B shown in FIG. 5, is equal to or less than a specified value. It is determined whether there is. Here, if it is determined that the distance between the polygon and the curved surface that may be generated corresponding to the grid A is not smaller than the specified value, the process of adding the grid again as shown in FIG. Be executed.

When the distance between the polygon and the curved surface which may be generated corresponding to each cell is calculated, if all the distances are equal to or less than the specified value, the above-described processing for adding the lattice is performed. To end. This processing is performed in both the u and v directions of the curved surface, and generally a non-equidistant grid is formed.

After performing the processing of step S201, FIG.
As shown in (2), the curve representing the boundary of the curved surface is approximated by a polyline (S202). In this process, polyline nodes as shown by black points in FIG. 8 are generated so as to satisfy a value designated as a distance between a polygon and a curved surface which may be generated.

After approximating the curve with a polyline,
The interior point generated in step S201 and step S202
A polygon is generated based on the nodes of the polyline generated in step (S203). In step S203,
As shown in FIGS. 9A and 9B, a polygon is generated using only points in the grid squares as much as possible. As a result, the distance between the generated polygon and the curved surface is guaranteed.

FIG. 9A is an explanatory diagram showing an example of polygon division of a square with no missing parts, and FIG. 9B is an explanatory diagram showing an example of polygon division of a square with a missing part. FIG. 10 is an explanatory diagram showing polygons generated by executing a process based on the above-described flowchart of FIG. 2 with a distance between a surface and a polygon that may be generated set to 0.2.

As described above, according to the polygon generating method according to the present embodiment, the polygon is generated by dividing the curved surface so that the distance between the curved surface and the generated polygon is equal to or less than a predetermined value. Thus, it is possible to approximate a curved surface with a relatively small number of polygons. In addition, since the curved surface is divided into a grid, a polygon can be generated that can intuitively recognize the result of the division.

The above-described polygon generating method according to the present embodiment is realized by executing a program prepared in advance by, for example, the computer 100 having the configuration shown in FIG. 1 in accordance with the procedure of the flowchart shown in FIG. Is achieved. This program includes a hard disk, floppy (registered trademark) disk, CD-ROM, MO, D
The program is recorded on a computer-readable recording medium such as a VD, and is executed by being read from the recording medium by the computer. Further, this program can be distributed via the recording medium or via a network.

[0025]

As described above, according to the polygon generating method of the present invention (claim 1), the polygons are formed such that the distance between the curved surface and the generated polygon is equal to or less than the distance determined by the distance information. The interior points serving as the reference for generation are arranged in a grid, and the curve representing the boundary of the curved surface is approximated by a polyline so that the distance defined by the distance information is satisfied. Since a polygon is generated based on the nodes of the polyline generated at the time of approximation, it is possible to approximate a curved surface with a relatively small number of polygons. In addition, since the curved surface is divided into a grid, a polygon can be generated that can intuitively recognize the result of the division.

According to the computer-readable recording medium of the present invention (claim 2), a program for causing a computer to execute each step of the polygon generating method according to claim 1 is recorded. A polygon generation method that can approximate a curved surface with a relatively small number of polygons by causing a computer to read and execute the polygons, and easily generate polygons that are easy to intuitively recognize the result of division. It is possible to do.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example of a hardware configuration for realizing a polygon generation method according to an embodiment of the present invention.

FIG. 2 is a flowchart showing a polygon generation method according to the embodiment of the present invention.

FIG. 3 is an explanatory diagram showing a curved surface to be subjected to polygon division by the processing shown in FIG. 2;

FIG. 4 is an explanatory diagram showing a process of generating a grid in step S201 of FIG. 2;

FIG. 5 is an explanatory diagram showing a process of generating a grid in step S201 of FIG. 2;

FIG. 6 is an explanatory diagram showing a process of generating a grid in step S201 of FIG. 2;

FIG. 7 is an explanatory diagram illustrating an example of a polygon generated in the first grid of the grid generated by the process of step S201 in FIG. 2;

FIG. 8 is an explanatory diagram showing polylines and nodes generated in the process of step S202 in FIG. 2;

9A and 9B are explanatory diagrams specifically showing the processing of step S203 in FIG. 2, wherein FIG. 9A shows an example of polygon division of a square with no chip, and FIG. 9B shows polygon division of a square with a chip It is explanatory drawing which shows the example of each.

FIG. 10 is an explanatory diagram showing a polygon generated based on the processing shown in FIG. 2;

[Explanation of symbols]

 Reference Signs List 100 computer 101 CPU 102 ROM 103 RAM 104 input device 105 display device 106 hard disk 107 bus

Claims (2)

[Claims] 1. Based on distance information defining the distance between a curved surface to be approximated and a polygon that approximates the curved surface,
A polygon generation method for generating a polygon approximating the curved surface, wherein a reference for generating the polygon is set so that a distance between the curved surface and the generated polygon is equal to or less than a distance determined by the distance information. An inner point arranging step of arranging inner points in a grid, and an approximating step of approximating a curve representing a boundary of the curved surface with a polyline so as to satisfy a distance determined by the distance information; A polygon generation step of generating the polygon based on the interior points arranged in the step and nodes of the polyline generated when the curve is approximated by the polyline in the approximation step. . 2. A computer-readable recording medium on which a program for causing a computer to execute each step of the polygon generating method according to claim 1 is recorded.