JP2001052205A - Method for generating polygon approximating degenerative curved surface and storage medium stored with same generating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To actualize a generating method for a polygon which can decide whether or not a sample point is in the curved surface encircled with border curves with high precision. SOLUTION: This is a method for generating a polygon approximating such a degenerative curved surface that some of border curves representing the curved surface are made to degenerate. In this case, one end point (degeneration point) of one degenerative curved surface is represented in a parameter space (S1) and the position of a node of a polyline in the parameter space is found (S2). Another end point of the degenerative curve is represented in the parameter space at a different position from the mentioned end point (S3) and the polygon approximating the degenerative curved surface is generated in the parameter space with multiple lines (polyline) including the line connecting both the mentioned end points (S4). Then it is decided whether the sample point is inside or outside the polygon (S6) to decide whether or not the sample point is inside or outside the object curved surface.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

In the present invention, a part of a plurality of boundary curves representing a curved surface of a three-dimensional solid, which is implemented in a dedicated three-dimensional solid processing device or an information processing device such as a personal computer, is degenerated. The present invention relates to a method for generating a polygon that approximates a degenerated surface, and more particularly to a method for generating a polygon that can determine with high accuracy whether a sample point is inside or outside a curved surface surrounded by a boundary curve.

[0002]

2. Description of the Related Art Conventionally, in a CAD / CAM system using a graphics display device and a computer,
A process of generating a three-dimensional solid and performing various determinations on the generated three-dimensional solid is performed. In addition, 3
A dimensional solid refers to a shape generated as solid model data in a boundary representation format, and a solid model in the boundary representation format defines an area closed in a three-dimensional space by elements such as ridges, vertices, and faces. It is a representation of a solid body. On such a three-dimensional solid,
For example, processing such as determining whether a sample point is inside or outside a curved surface surrounded by a boundary curve, determining whether a surface surrounded by a boundary curve is a plane, and the like are performed. . FIGS. 11A and 11B show an example of a curved surface surrounded by four boundary curves L according to the present invention. As described above, a curved surface usually has four boundary curves and four corners. For example, as shown in FIG. 11C, a curved surface where point B and point C overlap and the boundary curve between BC is degenerated There is also. In other words, there is a curved surface having a plurality of adjacent points coincident (such a point is called a degenerate point) and having a boundary curve of length 0 (such a curved surface is called a degenerate curved surface). Conventionally, including such a degenerated surface, each of a plurality of boundary curves surrounding the curved surface is approximated by one or more straight lines, and the curved surface is approximated by a polygon. However, in the related art, when generating a polygon approximating the above-described degenerated curved surface, the degenerated boundary curve is not considered.

For this reason, in a degenerate surface as shown in FIG. 2, although sample points (indicated by black circles in the surface of FIG. 2) are inside the boundary curve, as shown in FIG. When the boundary curve is approximated by a polyline (a plurality of straight lines shown by bold lines in FIG. 10) in the parameter space, some sample points are erroneously determined to be outside the boundary curve. In the above description, the parameter space is a space that represents a curved surface, and associates coordinate values in a three-dimensional space with coordinate values (called parameters) in a two-dimensional space. FIG.
For example, as shown in FIG. 2, when a curved surface is divided into four equal parts in the vertical direction (v-axis direction) based on left and right boundary curves, and four equally in the horizontal direction (u-axis direction) based on upper and lower boundary curves. , The coordinate values in the parameter space are as shown in the figure. That is, the coordinate values (parameters) in the parameter space of the lower left and upper right corner points of the curved surface are (0, 0) and (1, 1), respectively.
And the four boundary curves become four sides of a square in the parameter space. Therefore, if the left boundary curve is shorter than the right and upper and lower boundary curves as shown in the figure, the left boundary curve has a relatively elongated shape in the parameter space.

[0004]

As described above, in the prior art, when generating a polygon approximating a degenerated surface, a degenerated boundary curve is not taken into account. When judging whether or not it is, there is a problem that an erroneous judgment is made. An object of the present invention is to solve such a problem of the prior art, and to provide a polygon generation method and a polygon generation method capable of determining with high accuracy whether a sample point is on a curved surface surrounded by a boundary curve. An object of the present invention is to provide a storage medium storing a program for realizing the program.

[0005]

According to the first aspect of the present invention, there is provided a method of generating a polygon which approximates a degenerated surface in which a part of a plurality of boundary curves representing a surface is degenerated. In the above, the two end points of one degeneration curve are represented at different positions in the parameter space, and a polygon approximating the degeneration surface by a plurality of lines including a line connecting the two end points is generated in the parameter space.
According to a second aspect of the present invention, in the method of generating a polygon according to the first aspect, when the three points are reduced to one reduction point, the three points are represented at different positions in the parameter space. One degenerate curve is made to appear, and a polygon approximating the degenerate surface by a plurality of lines including two lines connecting the three points in order is generated in the parameter space. According to a third aspect of the present invention, in the polygon generating method according to the first or second aspect, it is determined whether the sample point transferred to the parameter space is inside or outside the generated polygon. Is determined to be inside or outside a curved surface surrounded by a boundary curve. According to a fourth aspect of the present invention, there is provided a storage medium readable by a machine, wherein a program for generating a polygon according to the method for generating a polygon according to any one of the first to third aspects is recorded. It is characterized by having been done.

[0006]

According to the first aspect of the present invention, the two end points of one degenerate curve are represented at different positions in the parameter space, and a plurality of lines including lines connecting the end points are provided. A polygon approximating the degenerate curved surface is generated in the parameter space by the above line. According to the second aspect of the present invention, in the first aspect of the present invention, when the three points are degenerated to one degenerate point, the three points are represented at different positions in the parameter space, A polygon approximating the degenerated surface is generated in the parameter space by a plurality of lines including two lines connected in order. According to a third aspect of the present invention, in the first or the second aspect of the present invention, it is determined whether the sample point transferred to the parameter space is inside or outside the generated polygon, whereby the sample point is set to the boundary curve. It is determined whether it is inside or outside the curved surface surrounded by. In the invention according to claim 4, claim 1 is
4. A program for generating a polygon according to the method for generating a polygon according to claim 1.
It is stored in a storage medium such as a D-ROM, a floppy disk (FD), and a hard disk (HD).

[0007]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a three-dimensional stereoscopic processing apparatus according to an embodiment of the present invention.
As shown in the figure, a three-dimensional solid processing device according to this embodiment includes a data processing unit 1 for processing solid model data in a boundary expression format relating to a three-dimensional solid, such as a polygon generation process according to the present invention, a keyboard and a text display. Operation display unit 2 including devices, 3 from solid model data
A three-dimensional shape generator 3 for generating three-dimensional shape (three-dimensional solid) data, a graphic display device 4 for displaying a three-dimensional solid according to the three-dimensional shape data generated by the three-dimensional shape generator 3, a three-dimensional solid on paper Plotter 5, output to
A communication control unit 6 for obtaining solid model data from the outside via a network is provided. In addition,
Solid model data (hereinafter abbreviated as data) can be input via a removable storage medium or can be generated internally. Further, the data processing unit 1 has a memory storing a program and a CPU operating according to the program.

FIG. 2 shows a degenerate curved surface according to the present invention.
In FIG. 2, there are three boundary curves, a curve connecting V0, V1, and V2, a curve connecting V2, V3, and V4, and a curve connecting V4, V5, and V0, and point V0 is a degenerate point. is there. Hereinafter, the operation of this embodiment will be described according to the operation flow shown in FIG. First, the data processing unit 1
Extracts the data of the target curved surface from the obtained data, and obtains the coordinate values of each vertex (for example, four corners) from the extracted data. Further, a coordinate value of the degenerate point is searched from the coordinate values (S1). The four coordinate values are sequentially compared, and if there is one having the same coordinate value, it is used as the coordinate value of the degenerate point (see FIG. 2). Then, the degenerate point (V0 in the example of FIG. 2)
Are associated with, for example, the coordinates (1, 0) in the parameter space (see FIG. 4). As a result, as shown in FIG. 4, the degeneracy curve starting from the degeneracy point and extending in the v-axis direction is set in the parameter space. Next, the data processing unit 1 extracts nodes on the boundary curve (V1, V3, V3 in the example of FIG. 2) from the extracted data of the curved surface.
The coordinate value of 5) is obtained, and the vertex previously obtained (FIG. 2)
In the example, the coordinate values of V0, V2, and V4) are combined with the coordinate values of V0, V2, and V4, and are set as nodes of a polyline (a plurality of straight lines) forming a polygon (polygon) that approximates a curved surface. Then, in the example of FIG. 2, each of the vertices V2 and V4 is associated with the coordinates (0, 1) and (0, 0) in the parameter space (FIG. 5).
Are shown as v2 and v4. v0 is a degenerate point) (S2).
Further, for example, a v coordinate value in the parameter space of V3 is obtained from the relative positional relationship of point V3 with respect to V2 and V4 (u
The coordinate value is 0) (shown as V3 in FIG. 5), V0, V of point V5
The u coordinate value in the parameter space of V5 is obtained from the relative positional relationship with respect to 4 (v coordinate value is 0) (shown as v5 in FIG. 5) (S2). Subsequently, an end point of the degeneration curve that has not been positioned is added to the coordinates (1, 1) in the parameter space (shown as v0 'in FIG. 5) (S3). That is,
As described in “Prior Art”, both the short boundary curve and the long boundary curve have the same length in the parameter space. However, in the present invention, the boundary curve having a length of 0 is also a long boundary curve as an extreme case of the short boundary curve. Make it the same length as the boundary curve. Further, the data processing unit 1 obtains a u coordinate value in the parameter space of V1 from the relative positional relationship of the point V1 with respect to V0 ′ and V2 (v coordinate value is 1) (shown as v1 in FIG. 5),
A polygon expanded by adding v0 'is generated in the parameter space by a polyline connecting v0, v0', v1, v2, v3, v4, and v5 with a straight line (S4). Next, the coordinate values in the parameter space of each sample point shown in FIG. 2 are obtained from the relative positional relationship from each boundary curve (S5).
Is determined to belong to the quadrangle (that is, the generated polygon) shown in FIG. The sample points belonging to the quadrilateral are within the target curved surface, otherwise, it is determined that they are outside the curved surface (S6). Thus, according to this embodiment, in the prior art shown in FIG. 10, a sample point (i1 or the like) erroneously determined to be outside the polygon to which v0 ′ is not added is also correctly determined to be within the curved surface.

FIG. 6 shows another example of a degenerate curved surface, and FIG. 7 shows its parameter space. In this example, two boundary surfaces are degenerated, and V0 is a degenerate point where three points coincide. Such a degenerate point is represented, for example, by the coordinates (1, 1) in the parameter space.
(Shown as v0 in FIG. 7), and a boundary curve connecting V0, V1, and V2 is associated with a straight line parallel to the v-axis, starting from v0. Therefore, the coordinates of v2 are (1, 0).
In such an example, the node V3 on the boundary curve connecting V2, V3, and V0 shown in FIG. 6 is associated with, for example, the position shown as v3 in FIG. 7 in the parameter space. It is generated as shown by the thick line in FIG. Therefore, although all the sample points are within the target curved surface as shown in FIG. 6, most of the sample points are determined to be outside the curved surface as shown in FIG. On the other hand, according to the present invention, V V in FIG.
V0 ′ and V0 ″ that match 0 are added to the coordinates (0,1) and (0,0) in the parameter space as v0 ′ and v0 ″, respectively. Therefore, as illustrated, it is correctly determined that all the sample points shown in FIG. 6 are within the target curved surface.

FIG. 8 shows another example of a degenerate surface.
FIG. 9 shows the parameter space. Also in this example, two boundary surfaces are degenerated, but the degeneration points are V0 and V1. That is, V0 and V0 'and V1 and V1' are each reduced to one point. Such degenerate points V0 and V1 are respectively defined as coordinates (0, 1) and (1,
0) (shown as v0 and v1 in FIG. 9), V0 and V
2. The u coordinate value in the parameter space of V2 is determined from the relative positional relationship of point V2 on the boundary curve connecting V1 to V0 and V1 (v coordinate value is 1) (shown as v2 in FIG. 9).
Also, the V of point V3 on the boundary curve connecting V0, V3, and V1
The u coordinate value in the parameter space of V3 is obtained from the relative positional relationship with respect to 0 and V1 (v coordinate value is 0) (v3 in FIG. 9).
As shown). Therefore, the polygon according to the prior art is generated as shown by the thick line in FIG. Therefore, although all the sample points are within the target curved surface as shown in FIG. 8, some sample points are determined to be outside the curved surface as shown in FIG. On the other hand,
In the present invention, V0 ′ and V1 that match V0 in FIG. 8 so that two degenerate curves appear in the parameter space.
Are added to the coordinates (0,0) and (1,1) in the parameter space as v0 'and v1', respectively. Therefore, as illustrated, it is correctly determined that all the sample points illustrated in FIG. 8 are within the target curved surface. As described above, according to the present invention, even if a plurality of boundary curves are degenerated, a plurality of end points of the degeneration curve are added to the parameter space to generate a polygon, so that a correct inside / outside determination of a sample point is performed. be able to. Even when three points are degenerated to one degenerate point, two end points can be added to determine the correct inside / outside of the sample point. Although the above description has been given of the case of the three-dimensional three-dimensional processing device, the present invention can be similarly applied to a general-purpose information processing device such as a personal computer, and a program programmed according to the polygon generating method of the present invention can be attached and detached. By storing the data in a possible storage medium and loading the storage medium into an information processing apparatus that has not been able to perform the polygon generation method according to the present invention, polygon generation according to the present invention is realized in the information processing apparatus. You can also.

[0011]

As described above, according to the present invention, the following effects can be obtained. In the invention according to claim 1,
Since both end points of one degeneration curve are represented at different positions in the parameter space, and a polygon approximating the degeneration surface by a plurality of lines including a line connecting the both end points is generated in the parameter space, It is possible to determine whether or not a sample point is within a curved surface surrounded by a boundary curve by using a polygon having high similarity. According to the second aspect of the present invention, in the first aspect of the present invention, when three points are degenerated to one degenerate point, the three points are represented at different positions in the parameter space, and Since a polygon approximating the degenerate surface is generated in the parameter space by a plurality of lines including two lines connecting the points in order, even if three points are reduced to one degenerate point, the similarity is improved. It is possible to determine whether or not a sample point is within a curved surface surrounded by a boundary curve by using a polygon having a high value. According to a third aspect of the present invention, in the first or second aspect of the present invention, it is determined whether the sample point transferred to the parameter space is inside or outside the generated polygon. Since it is determined whether the sample point is inside or outside the curved surface surrounded by the boundary curve, it is possible to determine with high accuracy whether the sample point is inside the curved surface surrounded by the boundary curve. According to the fourth aspect of the present invention, a program programmed according to the polygon generating method according to the first to third aspects is stored in a removable storage medium or the like. The information processing apparatus according to any one of claims 1 to 3, wherein the information processing apparatus is loaded in an information processing apparatus in which the polygon generation method according to the invention described in claim 3 is not possible.
The effects of the described invention can be realized.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a three-dimensional stereoscopic processing apparatus according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram of a polygon generation method showing an example of an embodiment of the present invention.

FIG. 3 is an operation flowchart of a polygon generation method showing an example of an embodiment of the present invention.

FIG. 4 is another explanatory diagram of the polygon generation method showing one example of the embodiment of the present invention;

FIG. 5 is another explanatory diagram of the polygon generating method showing one example of the embodiment of the present invention;

FIG. 6 is an explanatory diagram of a polygon generation method showing another embodiment of the present invention.

FIG. 7 is another explanatory diagram of a polygon generating method showing another embodiment of the present invention.

FIG. 8 is an explanatory diagram of a polygon generating method showing still another embodiment of the present invention.

FIG. 9 is another explanatory diagram of a polygon generating method showing still another embodiment of the present invention.

FIG. 10 is an explanatory diagram of a polygon generation method showing an example of a conventional technique.

FIG. 11 is an explanatory diagram of a polygon generation method according to the present invention and the related art.

FIG. 12 is another explanatory diagram of the polygon generation method according to the present invention and the prior art.

[Explanation of symbols]

 1: data processing unit 2: operation display unit 3: three-dimensional shape generation unit 4: graphics display device 6: communication control unit

Claims (4)

[Claims] 1. A method for generating a polygon that approximates a degenerated surface in which a part of a plurality of boundary curves representing a curved surface is degenerated, wherein both end points of one degeneration curve are represented at different positions in a parameter space, A polygon generating method, wherein a polygon approximating a degenerated surface by a plurality of lines including a line connecting both end points is generated in the parameter space. 2. The polygon generating method according to claim 1, wherein when the three points are reduced to one reduction point, the three points are represented at different positions in a parameter space to generate two reduction curves. And generating a polygon in the parameter space that approximates the degenerated surface by a plurality of lines including two lines sequentially connecting the three points. 3. A polygon generating method according to claim 1, wherein the sample point is surrounded by a boundary curve by determining whether the sample point shifted to the parameter space is inside or outside the generated polygon. A polygon generating method for determining whether the curved surface is inside or outside. 4. A machine-readable storage medium storing a program for generating a polygon according to the method of generating a polygon according to claim 1. Description: