JP2001022962A - Device and method for processing area division - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform division processing of a processing object area into a plurality of polygonal areas, so that a curved patch can be interpolated smoothly in a three-dimensional shape. SOLUTION: A mesh generating part 30 first simply performs division processing of a processing object area and generates initial mesh data obtained by burying the processing object area with a plurality of square faces. Next, the part 30 adds a square face to a part coming into contact with the frame of the processing objet area, for instance, so that an arbitrary point of the frame of the processing object area can be included only in one or two square faces. When the optional point of the frame of the processing object area is prevented from being shared by three or more square faces, a curved patch can be interpolated in the processing object area, without deforming the shape of the frame.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to, for example, CAD (Compu
The present invention relates to an area division processing apparatus and method for performing division processing into polygonal areas so as to smooth a three-dimensional shape created by a ter Aided Design) system.

[0002]

2. Description of the Related Art For example, in order to design a three-dimensional shape using a CAD device and display it to a CAD user,
On the surface of the designed shape, processing to divide a target area (processing target area) for display processing into a plurality of rectangular areas (area division processing), and further insert curved surface patches for smooth connection to each other (Surface patch interpolation processing). For example, 'J. Hahn, Filling Po
lygonal Holes with Rectangular Patches, inbook "Th
e Theory and Practice of Geometric Modeling "edit.
W. Strasser, HP Seidel, pp. 81-91, 1989 (Reference 1) 'discloses a method of dividing a processing target region into polygons and interpolating a surface patch.

[0003] For example, in M. Eck, H. Hoppe, Autom
atic Reconstruction of B-SplineSurfaces of Arbitra
ry Topological Type, Computer Graphics (SIGGRAPH),
pp. 325-334, 1996 (Reference 2) 'discloses a method of associating a three-dimensional shape represented by a triangular mesh with a surface patch.

[0004] For example, in 'M. Hosaka, Modeling of
Curves and Surfaces in CAD / CAM, Springer-Verlag Ber
Lin Heidelberg, 1992 (Reference 3) 'discloses a method of inserting a fillet by applying a fillet generation process, for example, a kind of operation of a CAD apparatus for rounding a corner where three edges of a hexahedron gather. .

However, the method disclosed in Document 1 is based on the premise that the polygonal region to be subjected to the surface patch interpolation processing is geometrically convex. It may not be possible to adapt to the patch interpolation process. Reference 2 refers to the surface patch interpolation processing when the three-dimensional shape is geometrically open. However, according to the method disclosed in Reference 2, the boundary of the open shape changes. Problem. Reference 3 discloses only a process of inserting a fillet into a processing target region having a specific shape such as a corner portion of a hexahedron.

[0006]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems of the prior art, and determines whether or not a polygon area to be processed is convex. Regardless of the geometrical conditions of the n-dimensional (three-dimensional) shape and the polygonal region, such as whether or not the shape to be processed is closed, a plurality of processing target regions are used so that the surface patch can be smoothly interpolated. It is an object of the present invention to provide an area division processing apparatus and method that can perform division processing into polygonal areas. In addition, the present invention does not limit an n-dimensional (three-dimensional) shape to be processed to a specific shape such as a hexahedron, and can smoothly interpolate a curved surface patch so as to interpolate a curved surface patch. It is an object of the present invention to provide an area division processing device and a method thereof that can divide an image into a plurality of polygonal areas. It is another object of the present invention to provide an area division processing apparatus and method capable of interpolating a smooth curved surface patch without changing a boundary of a shape to be processed.

[0007]

Means for Achieving the Object [Area Division Processing Apparatus] In order to achieve the above-mentioned object, an area division processing apparatus according to the present invention defines an area (target area) to be processed in a two-dimensional or more shape. , An area division processing apparatus for performing division processing into a plurality of predetermined polygonal areas (polygonal areas), which is included in a boundary line (frame line) between the target area and an area having a shape other than the target area. Any point, according to the prescribed rules,
Frame line region dividing means for dividing a portion (frame line region) of the target region, which is in contact with the frame line, into a plurality of the polygon regions so as to be included in one or more of the polygon regions;
An undivided area dividing unit that divides a portion (undivided area) of the target area that is not divided into the plurality of polygonal areas into one or more polygonal areas.

Preferably, the frame region dividing means divides the frame region so that an arbitrary point of the frame is included in one or two polygon regions.

Preferably, the frame line area dividing means includes an arbitrary point other than a break point of the frame line included in one or two polygonal regions, and a break point of the frame line is The frame region is divided so as to be included in the two polygon regions.

The frame region dividing means divides the frame region into a plurality of polygonal regions corresponding to the angles formed at the break points of the frame line so that the break points of the frame line are shared. I do.

Preferably, the two-dimensional or more shape is a three-dimensional shape, and each of the plurality of polygon regions shares a vertex with another polygon region.

Preferably, the plurality of polygonal areas are quadrangular areas each sharing a vertex with another polygonal area.

[Effects of Region Division Processing Apparatus] The region division processing apparatus according to the present invention includes an n-dimensional (n>1; hereinafter, n = 3 is a specific example) dimensional shape generated by a CAD apparatus or the like. A processing target area to be processed (hereinafter, a processing target area to be displayed in the surface of the three-dimensional shape is a specific example) is defined as an area other than the processing target area and the processing target area (excluding the processing target area). In order to avoid the loss of smoothness at the boundary line (frame line) of the (area), the processing target area is defined by m curves or straight ridges and m folding points (corners). (M>2; hereinafter, m = 4 is a specific example). The non-processing area is
It does not matter whether it is a region outside the processing target region (external non-target region) or a region inside the processing target region (internal non-target region). Also, it is determined whether the internal region has an area. It doesn't matter.

That is, the region dividing processing device according to the present invention divides a processing target region in a three-dimensional shape into a plurality of rectangular regions (rectangular surfaces) sharing vertices and edges between adjacent rectangular surfaces. . At this time, the division processing device according to the present invention is arranged so that any point of the frame line of the external non-target region and the internal non-target region is included in one or two quadrangular faces. If there is a broken point in the line (break point), be sure that this point is shared by two (or the number corresponding to the angle of the frame line at the break point) square, The target area is divided into a plurality of rectangular planes.

In other words, according to the division processing apparatus of the present invention, from any point on the frame line, at most one ridge line of the rectangular surface extends toward the inside of the processing target area, and at least two ridge lines of the rectangular surface The processing target area is divided into a plurality of quadrilateral surfaces so that does not extend from one point on the frame line, and the ridge line of the quadrilateral surface always extends from the folding point on the frame line.

[First Area Division Processing Apparatus] In the first area division processing apparatus according to the present invention, the frame area division means may convert the frame area of the target area into a plurality of polygons. Dividing into undivided areas, the undivided area dividing means includes:
An undivided region other than the frame region divided into the plurality of polygon regions is divided into the plurality of polygon regions.

[Operation of the first frame area dividing means] In the first area dividing processing apparatus, the frame area dividing means breaks into, for example, a frame when the processing target area is not divided at all. If there are points (break points), the external non-target area and the internal non-target area are set so that the ridge line of the quadrangular surface extends from each of the break points and each of the points obtained by dividing the break points at equal intervals. A portion (frame line area) in contact with the frame is divided into a plurality of quadrangular faces.

As described above, by dividing the frame region by the frame region dividing means, any one point of the frame line can be set to one or two.
Are included in each of the quadrilateral faces, and
The condition of being shared by the quadrilateral surfaces is maintained.

[Operation of the first undivided area dividing means]
In the region division processing device of
When the dividing process of the frame region is completed, the frame region dividing means divides the region other than the frame region (undivided region) into a quadrangular surface.

[Second region division processing device] In the second region division processing device according to the present invention, the undivided region division means divides the target region into a plurality of the polygon regions, The frame line area dividing means may select one or two of the arbitrary points included in the frame line other than the folded line.
The frame region is divided into a plurality of polygon regions so as to be included in the polygon regions.

The frame region dividing means connects one point included in each of the two ridge lines of the polygon region adjacent to each other including one point included in the frame line, and Add a rectangular area.

[Operation of Second Undivided Area Dividing Means]
In the region division processing device of
At the stage where the processing target area is not divided at all, all of the processing target area is regarded as an undivided area, and for example, only the condition that the ridge line of the square surface extends from the break point of the frame line is considered, and other conditions are considered. Instead, the processing target area is simply divided into a plurality of rectangular planes. By this division processing, the condition that the break point of the frame line is shared by the two rectangular surfaces is maintained.

[Operation of Second Frame Line Area Dividing Means] In the second frame line area dividing means, the frame line area dividing means includes a plurality of rectangular surfaces obtained as a result of division by the undivided area dividing means. Among the ridge lines, a ridge line connecting two points on two adjacent ridge lines extending from the frame line is created, and a quadrilateral surface is added to an area in contact with the frame line.

As described above, the frame line area dividing means adds a new quadrangular surface to the frame line region, so that an arbitrary point of the frame line is included in only one or two quadrangular surfaces. The condition that line breaks are always shared by two square faces is maintained. In other words, it is clear that, in the portion of the frame line that is included only in one or two square faces, the above condition is maintained even after the addition of a new square face. In addition, a portion where two or more ridge lines extend from one point of the frame line extends from one point, and one new rectangular surface is added between each two adjacent ridge lines. After the addition of the quadrilateral surface, the above conditions are also maintained.

[Region Division Processing Method] In the region division processing method according to the present invention, a region (target region) to be processed in a two-dimensional or more shape is divided into a plurality of predetermined polygon regions (polygons). A region dividing processing method for performing a dividing process on the target region, wherein an arbitrary point included in a boundary line (frame line) between the target region and a region having a shape other than the target region is one or two points. A part (frame line area) of the target area, which is in contact with the frame line, is divided into a plurality of the polygon areas so as to be included in the polygon area. A part that is not divided into regions (undivided region) is divided into one or more polygonal regions.

[Medium] The medium according to the present invention comprises:
A program for dividing a region to be processed (target region) in a shape having dimensions or more into a plurality of predetermined polygonal regions (polygonal regions), the program comprising: a target region; a shape other than the target region; A portion of the target region that is in contact with the frame line so that an arbitrary point included in a boundary line (frame line) with the region is included in one or more of the polygonal regions according to a predetermined rule. A frame region dividing step of dividing the frame region into a plurality of the polygon regions; and a part (undivided region) of the target region that is not divided into the polygon regions. And an undivided region dividing step of dividing the polygonal region.

[0027]

Embodiments of the present invention will be described below.

FIG. 1 is a diagram exemplifying a region to be processed which is divided into a plurality of rectangular planes by the region dividing process according to the present invention. As illustrated in FIG. 1, the processing target area (the area indicated by hatching in FIG. 1) is surrounded by an area other than the processing target area (non-processing target area). There may be a non-processing area inside, and the boundary line (frame) between the processing area and the non-processing area surrounding it is also referred to as an outer frame, and the processing area and the processing area are inside the processing area. A frame that separates the region to be processed (inner hole) from the processing target is also referred to as an inner frame. In some cases, a shape is given to a non-process target area.

The outer frame and the inner frame illustrated in FIG. 1 are a set of vertices and a ridge connecting between the two vertices (see FIGS. 2 and 8).
Etc.) and is composed of an ordered set closed, and one edge line is G1 continuous (tangential continuous, that is, one time differentiable) or more (G1 continuous or more means not only once but also twice) (The above differentiation is also possible). Further, two curves adjacent to the vertex satisfy continuity of G0 or more (that is, positions are not separated). In the cusp illustrated in FIG. 1, two curves adjacent to the vertex are G
A vertex that does not satisfy the continuity, that is, a vertex in which two curves are bent and connected is defined.

In the area dividing process according to the present invention, a three-dimensional shape designed by a CAD device or the like as shown in FIG. 1 is given, and the surface of the three-dimensional shape is subjected to processing such as display processing. When a target processing target area is designated, this processing target area is divided into quadrangular areas (quadrilateral faces) so that a curved surface patch suitable for smooth connection can be attached. In other words, the region division processing according to the present invention is performed to solve the problem of filling the processing target region with a set of tensor product surface patches connected smoothly in the outer frame and the inner frame. (Information indicating which surface patch and which other surface patch are adjacent) is created.

The tensor surface patch is a surface defined by the following equation using two variables u and v.
By specifying a value (u0, v0) in the variables u and v by the following equation, the XYZ coordinate values of one point S (u0, v0) on the curved surface can be obtained.

[0032]

S (u, v) = [X (u, v) Y (u, v) Z
(U, v)] (0 <= u, v <= 1) where X (u, v), Y (u, v), Z (u, v)
Is a function that returns a scalar value, and [XYZ] indicates a three-dimensional vector.

In the region dividing process according to the present invention, a tensor product surface patch (hereinafter simply referred to as a “surface patch”) that satisfies the following rule 2 such as a Bezier surface patch or a NURBS surface patch so as to completely fill the region to be processed. Is interpolated. That is, first, in the area division processing according to the present invention, the processing target area is filled with a tensor product surface patch.

Further, the area dividing process according to the present invention
Further, in order to make adjacent curved surface patches satisfy continuity of G1 continuity (tangent continuity continuity) or more inside the region and at the region boundary, “in the vertex set constituting the set of interpolated square surfaces, , An arbitrary vertex on the outer frame or the inner frame. If the vertex is not a vertex, the number of interpolated quadrangular faces adjacent to the vertex is 2 ”. Topological information including vertices, ridge lines, surfaces, and the like of the region as components is divided into a plurality of quadrilateral surfaces (quadrilateral meshes).

FIG. 2 is a diagram exemplifying four to six adjacent quadrangular faces sharing one vertex in the processing target area. As illustrated with the symbol (a) in FIG. 2, when four quadrangular faces are adjacent to each other while sharing a vertex, it is relatively easy to connect the four quadrangular faces to G1 continuous. is there. As illustrated in FIG. 2 with symbols (b) and (c), when n> 4, the condition for connecting adjacent quadrangular faces to G1 continuity becomes considerably complicated. Many reports have already been made on the conditions for achieving this. In these reports, it is stated that G1 continuity is achieved by inputting an initial curved surface shape representing an outline of the shape and modifying the curved surface shape so as to satisfy a predetermined condition.

FIG. 3 is a diagram exemplifying two to four adjacent quadrangular faces sharing one point on the outer frame (FIG. 1). FIG.
As illustrated in the example, a vertex shared by a plurality of quadrangular faces is
When the object is on the frame line (outer frame or inner frame) and the three-dimensional shape is also given to the non-processing area, the plurality of quadrangular surfaces as illustrated in FIG. It is necessary to maintain G1 continuity on the line. further,
If the shape of the non-processing area is given, if the shape of the frame line is changed, a gap is created between the processing area and the non-processing area, and G0 continuity on the frame line is reduced. I can't keep it. Therefore, in this case, the shape of the frame cannot be changed.

As described above, when there is a restriction that the shape of the frame line cannot be changed, in the case illustrated in FIGS. 3B and 3C, the G1 continuity between the quadrangular surfaces in the processing target area is improved. It is difficult to achieve. On the other hand, as illustrated in FIG. 3A, when the processing target area is divided such that the number of ridge lines extending from the frame line toward the inside of the processing target area is always one, the square surface in the processing target area is divided. It is easy to achieve G1 continuity between them. In the area dividing process according to the present invention, as illustrated in FIG. 3A, the processing target area is divided into quadrilateral faces so that the number of ridge lines extending from the frame line toward the inside of the processing target area is always one. By doing so, it is easy to maintain G1 continuity on the processing target region and the frame line.

As shown in FIG. 3 (a), if at most one ridge line extends inward from an arbitrary point on the frame line, the reason why the quadrangular surfaces are continuously connected to each other is as follows. The reason why this becomes easy will be further described. In addition,
This is because 'WH Du, FJM Schmitt, On the G1
continuity ofpiecewise Bezier surfaces: a review
with new results, Computer Aided Design, Vol. 22,
No. 9, pp. 556-573, 1990. (Reference 4) 'and the like.

FIG. 4 is a diagram exemplifying two adjacent quadrangular faces sharing the point V on the frame line. As illustrated in FIG. 3A, if only one ridgeline extends inward from an arbitrary point on the frame line, the point V on the frame line is shared as illustrated in FIG. The set of two adjacent quadrangular faces is only one set (SA, SB). On the other hand, FIG.
In the case shown in (b), there are two sets of square faces,
In the case shown in FIG. 3C, there are three sets of square faces. That is, for one square surface extending from the frame line toward the inside of the processing target area, there is a set of square surfaces on both sides.

As illustrated in FIG. 4, two square surfaces S
Assuming that a ridge line shared by A and SB is a ridge line C, a tangent vector PA in a direction crossing the ridge line C of the square surface SA at the point V and a tangent vector PB in a direction crossing the ridge line C of the square surface SB in the point V are as follows: In the case shown in FIG. 3A, according to the definition of the tangent vector, at points on the frame other than the apex, the frame is G1 continuous (tangent continuous).
, The symbols PA, the vectors PA,
PB is in the same direction. However, in the case shown in FIG. 3B, the vectors PA and PB are directed in different directions, as illustrated by adding the symbol (b) to FIG. Similarly,
Also, in the case shown in FIG. 3C, the vectors PA and PB face different directions as shown in FIG. 4B. As described above, when two or more ridge lines extend from one point on the frame line, the directions of the vectors PA and PB are not the same, and it is difficult to make the tangent planes of the square surfaces SA and SB continuous. .

That is, as illustrated in FIG. 4A, the tangent vectors PA, P of the square surfaces SA, SB at the point V
When the directions of B are the same, the continuity between the quadrangular surfaces in the direction crossing the ridge line C and the continuity between the quadrangular surfaces in the direction along the ridge line C can be treated as independent. If the directions of the vectors PA and PB are not the same,
When the directions of PA and PB are different as in B), the relationship between the continuity between the quadrangular surfaces in the direction crossing the ridge line C and the continuity between the quadrangular surfaces in the direction along the ridge line C Occurs,
They cannot be treated as independent. If point V is inside the area, G at point V
Although it is possible to maintain one continuity, FIG.
As shown in (c), when the point V exists on the frame line,
It is very difficult to maintain G1 continuity at point V because the continuity at two or three ridgelines around point V is interrelated and the shape of the frame cannot be changed. is there.

[First Embodiment] A first embodiment of the present invention will be described below.

[CAD Apparatus 1] FIG. 5 is a diagram showing a configuration of a CAD apparatus 1 for realizing the area dividing process according to the present invention. As shown in FIG. 5, the CAD device 1 includes a CPU 10 including a microprocessor, a memory and peripheral circuits thereof (not shown), an input device including a tablet 120, a keyboard 122, a mouse 124, and the like necessary for the CAD operation. A display device 14 such as a CRT device, an output device 16 such as a printer and a plotter, and an HDD, FD
A storage device 18 for recording / reproducing data to / from a recording medium 180 such as a D / MO device and a CD device. That is, the CAD device 1 is provided with a general computer and an input device 12 and an output device 1 suitable for the CAD device.
6 is adopted.

[CAD Program 2] FIG. 6 is a diagram showing a configuration of a CAD program 2 for realizing the area dividing process according to the present invention. As shown in FIG. 6, the CAD program 2 includes a mesh processing unit 3, an input unit 20, and a CAD unit 22.
And an image generation unit 24. The mesh processing unit 3 includes a mesh generation unit 30 and a surface patch generation unit 36
Consists of The CAD program 2 is, for example, a recording medium 180 (FIG. 5) or a network (not shown).
The program is loaded into the memory in the CPU 10 of the CAD apparatus 1 via the CPU and executed, and executes the area dividing process according to the present invention.

[Input Unit 20] In the CAD program 2, the input unit 20 outputs a C image according to the shape image displayed on the display device 14, a GUI (Graphic User Interface), or the like.
An operation performed by the operator of the AD program 2 on the input device 12 is accepted, and the accepted operation is output to the mesh generation unit 30, the CAD unit 22, and the image generation unit 24 of the mesh processing unit 3. That is, the input unit 20
The design operation performed by the operator of the CAD device 1 (CAD program 2) on the input device 12 (FIG. 5) is accepted and output to the CAD unit 22 as CAD input data. The input unit 20 is performed by the operator on the input device 12 and designates a region (processing target region) to be subjected to processing such as display processing, among the three-dimensional surface created by the CAD unit 22. Upon accepting the operation, target area data indicating the processing target area is output to the mesh generation unit 30 of the mesh processing unit 3.

[Mesh Generation Unit 30] FIG. 7 is a diagram showing a configuration of the first mesh generation unit 30 shown in FIG.
FIG. 8 is a diagram exemplifying a processing target area on a three-dimensional surface input from the CAD unit 22 to the mesh generation unit 30 shown in FIG. FIG. 9 is a diagram illustrating a quadrangular mesh generated by the mesh generation unit 30 illustrated in FIG. As shown in FIG. 7, the mesh generation unit 30
Initial mesh generation unit 300 and mesh addition unit 320
Consists of The mesh generation unit 30 uses these components to process a processing target area (illustrated in FIG. 8) indicated by target area data input from the input unit 20, of the three-dimensional surface designed by the CAD unit 22. 2 shown in Table 1 below
According to the two rules (rules 1 and 2), the area is divided into quadrangular areas (square planes; hereinafter, a set of square planes described below with reference to FIG. 10 is also referred to as a quadrilateral mesh), and FIG.
The mesh data indicating the quadrangular mesh obtained as a result of the processing as shown in FIG. Note that the mesh generation unit 30 creates a quadrilateral mesh so as to satisfy the rules shown in Table 2 below.

[0047]

Table 1 (Table 1: Division rule) Rule 1-1: An arbitrary point on the boundary line (frame line) between the processing target area and an area other than the processing target area (non-processing target area)
Be included in one or two square faces. Rule 1-2: A point where a frame line is geometrically broken (a break point, hereinafter referred to as a vertex) is defined by two square faces,
Alternatively, it must be included in a number of quadrilaterals according to the angle of the apex.

[0048]

[Table 2: Rules for creating square faces] Rule 2: Each square face has four curves or straight ridges,
These four edges include four vertices that are geometrically folded and connected, and the quadrilateral faces share the vertices and the edges.

[Initial mesh generator 300] FIG.
FIG. 9 is a diagram exemplifying a plurality of quadrangular faces (quadrangular meshes) obtained by the initial mesh generation unit 300 shown in FIG. 7 by dividing the processing target area shown in FIG. 8; In the mesh generation unit 30, the initial mesh generation unit 300 indicates, for example, the surface of a three-dimensional shape in the processing target region illustrated in FIG. 8, and an element size function input from the CAD unit 22,
In addition, based on the target area data input via the input unit 20, the three-dimensional shape surface indicated by the element size function in the processing target area indicated by the target area data is set as shown in FIG. According to 1-2, the image is divided into a plurality of quadrilateral surfaces satisfying the above rule 2, and initial mesh data indicating the quadrilateral mesh obtained as a result of the division is output to the mesh adding unit 320.

[Mesh Addition Unit 320] FIG.
FIG. 11 is a diagram illustrating an example of a process in which the mesh adding unit shown in FIG. 10 further adds a quadrangular surface to the quadrangular mesh illustrated in FIG. 10. The mesh adding unit 320 satisfies the rule 1-1 of Table 1 above for a quadrangular mesh (exemplified in FIG. 10) in the processing target area indicated by the initial mesh data input from the initial mesh generating unit 300. Add more square faces as shown. That is, the mesh adding unit 320 exemplifies the ridge lines of the quadrangular surface (FIG. 10) extending from the frame lines (the outer frame and the inner frame) to the inside of the processing target region, as illustrated by hatching in FIG. 11. By creating a ridge line connecting points on each of two adjacent ridge lines, a quadrangular surface satisfying the above rule 2 is added to a region (frame region) in contact with the frame line. The mesh adding unit 320 adds the quadrangular surface to the frame region as described above, and converts the mesh data indicating the quadrangular mesh that satisfies the rules 1-1, 1-2 and 2 into a curved surface patch generating unit. 36 (FIG. 6).

FIG. 12 shows the mesh addition unit 3 shown in FIG.
20 is a flowchart showing a process (S10) for adding a quadrilateral surface. The processing content of the mesh adding unit 320 will be described in more detail with reference to FIG. FIG.
As shown in the figure, in step 100 (S100),
The mesh adding unit 320 determines whether or not the process of adding a rectangular surface has been completed for all the frame lines (outer frame and inner frame: FIG. 8 and the like) included in the processing target region. If the process of adding a quadrilateral surface has been completed for all the frame lines, the mesh adding unit 320 ends the process. Otherwise, the process of adding the quadrilateral surface has not been completed at that time. One of the frame lines is selected as a processing target, and S10
Proceed to step 2.

In step 102 (S 102), the mesh adding section 320 makes an area in the processing target area which is in contact with the frame currently being subjected to the quadrilateral plane addition processing (frame area; see the hatched portion in FIG. 11). It is determined whether or not to add a quadrangular surface, in other words, whether or not all the quadrangular surfaces to be added along the target frame line have been added. When a quadrangular surface is added (when all the quadrangular surfaces to be added along the frame line have not been added), the mesh adding unit 320 proceeds to the process of S104, and otherwise returns to the process of S100. .

In step 104 (S104), the mesh adding unit 320 determines whether or not this step (S104) is selected from among the quadrangular faces tangent to the frame line selected as the processing target.
Is selected as a processing target. Further, the mesh adding unit 320 creates a new ridge line that continuously connects two points on two ridge lines extending from the frame line out of the four ridge lines of the quadrangular surface selected as the processing target, as shown in FIG. , A square surface satisfying the above rule 2 is added, and the process returns to S102.

[Surface Patch Generation Unit 36] The surface patch generation unit 36 (FIG. 6) is based on the mesh data input from the mesh addition unit 320 of the mesh generation unit 30 and the element size function outside the processing target area. , A surface patch is interpolated with respect to the mesh data, and mesh data (mesh geometric data) in which the surface patch is interpolated is output to the image generation unit 24.

The operation of the curved surface patch generator 36 will be further described. First, the curved surface patch generation unit 36 determines, for example, 'K. Ho
-Le, Finite Element Mesh Generation Methods: a Rev
iew and Classification, Computer Aided Design, Vo
l. 20, No. 1, 1989 (Reference 5) 'and the like, using a method called Laplacian smoothing, determine the positions of the vertices of the quadrangular mesh in the processing target region so as to enable smooth connection. Move. Further, the curved surface patch generation unit 36 includes, for example, 'J. Peters, C1-Surface Splin
es, SIAM J. Numer. Anal., Vol. 32, No 2, pp645-66
6, 1995 (Reference 6) ', a surface patch is generated by adjusting the positions of the vertices of the quadrilateral mesh so that the quadrilateral mesh satisfies the G1 continuity, and mesh geometry showing a smooth curved surface. The data is output to the CAD unit 22 and the image generation unit 24 as data.

[CAD Unit 22] The CAD unit 22 receives, via the input unit 20, a design operation (CAD input data) performed by the operator on the input device 12 (FIG. 5), and responds to the received CAD input. Create a three-dimensional shape. Further, the CAD unit 22 outputs an element size function for determining the size of the quadrangular surface to be generated to the mesh generation unit 30 of the mesh processing unit 3. Also, the CAD unit 22
Outputs CAD output data indicating the final three-dimensional shape designed based on the mesh geometric data and CAD input data input from the curved surface patch generation unit 36 to the storage device 18 and the output device 16. Storage device 1
The output device 8 and the output device 16 record the CAD output data on the recording medium 180 or print out the shape indicated by the CAD output data.

[Image Generation Unit 24] The image generation unit 24 processes the mesh geometric data input from the curved surface patch generation unit 36, and displays an image showing the surface of the three-dimensional shape obtained as a result of the design by the CAD unit 22. Generate data. The image generation unit 24 generates display data by combining the GUI image or the like generated by the input unit 20 with the generated image data, and outputs the display data to the display device 14. Display device 14
Displays the display data input from the image generation unit 24 and shows it to the operator.

[Overall Operation of CAD Program 2 in First Embodiment] The overall operation of the CAD program 2 in the first embodiment will be described below. In the CAD program 2 (FIG. 6), the CAD unit 22 processes CAD input data input from the input unit 20 according to an operation of an operator, and designs a three-dimensional shape. Further, the initial mesh generation unit 300 (FIG. 7) of the mesh generation unit 30
Processing target area specified by the operator (illustrated in FIG. 8)
Is divided into a plurality of quadrangular faces satisfying the rule 2 according to the rule 1-2, and initial mesh data indicating the quadrangular mesh (exemplified in FIG. 10) obtained as a result of the division is transmitted to the mesh adding unit 320. Output.

The mesh adding unit 320 processes the initial mesh data input from the initial mesh generating unit 300, and generates a square mesh (FIG. 10) according to the rule 1 shown in Table 1 above.
Further, a square surface is added so as to satisfy 1. That is, the mesh adding unit 320 performs the quadrilateral plane adding process shown in FIG. 12, and hatches the quadrangular plane frame area extending from the quadrilateral mesh (FIG. 10) as illustrated in FIG. 11. To the above rule 1
Mesh data indicating a quadrangular mesh (illustrated in FIG. 9) satisfying -1, 1-2 and Rule 2 is output to the surface patch generation unit 36 (FIG. 6).

The surface patch generation unit 36 interpolates the surface patch to the mesh data based on the mesh data input from the mesh addition unit 320 of the mesh generation unit 30 and the element size function outside the processing target area. , And outputs the mesh data (mesh geometric data) in which the curved surface patch is interpolated to the image generation unit 24.

The image generation unit 24 includes a curved surface patch generation unit 36
Processing the mesh geometry data input from
Image data indicating the surface of the three-dimensional shape obtained as a result of the design by the unit 22 is generated and displayed on the display device 14. Further, the CAD unit 22 generates a CAD representing a final three-dimensional shape designed based on the mesh geometric data input from the curved surface patch generation unit 36 and the CAD input data.
The output data is recorded on the storage device 18 or printed out on the output device 16.

[Modification] Hereinafter, a modification of the first embodiment will be described.

[Addition of Quadrilateral Surface] FIG. 13 is a diagram illustrating a case where a quadrilateral surface is not added to a frame line in a modification of the process of the mesh adding unit 320 (FIG. 7) of the first embodiment. FIG. 14 shows a mesh adding unit 320 according to the first embodiment.
FIG. 9 is a diagram illustrating a case where a quadrilateral surface is added to a frame line in a modification of the process of FIG. 7. Note that the processing of the mesh adding unit 320 (FIG. 7) is performed by counting the number of quadrangular faces that are points (vertexes) that overlap the corners of the quadrangular faces on the frame line and that share points other than the vertices (normal vertices). However, when the count result is 2 at all the normal vertices as illustrated in FIG. 13, it is determined that the quadrangular surface is not added, and as illustrated in FIG. It may be changed so that a quadrilateral surface is added only to a normal vertex shared by more than two quadrilateral surfaces.

FIG. 15 shows the mesh addition unit 3 of the first embodiment.
FIG. 20 is a diagram illustrating an example of a process of adding a quadrangular surface related to a vertex in a modification of the process of FIG. 20 (FIG. 7). In this case, the mesh adding unit 320 may perform the same determination as the above-described normal vertex when determining whether or not to add a new quadrangular surface for the apex on the frame (see FIG. 8 and the like). Alternatively, the mesh adding unit 320 may determine whether to add a quadrilateral surface in consideration of the angle formed by the frame line with the vertex as the vertex. That is, the mesh adding unit 32
As shown in FIG. 15, 0 is adjusted so that the number of square surfaces including the apex becomes 1 when the angle with the apex as the apex is about 90 degrees or less, and the angle becomes 180 degrees. If the center is considerably larger than 90 degrees and smaller than 270 degrees, the number of quadrilateral meshes sharing the apex is adjusted to be 2, and the angle is substantially larger than 180 degrees around 270 degrees. When the angle is large and substantially smaller than 360 degrees, the number of quadrangular surfaces sharing the apex is adjusted to be 3. When the angle is close to 360 degrees, the number of quadrangular surfaces sharing the apex is adjusted. The number of square faces is adjusted so that becomes 4. When the number of quadrangular faces sharing the apex is changed according to the angle formed by the frame line at the apex, the CAD program 2 can optimize the dividing process near the apex, Can be displayed more smoothly.

[Mesh Shape] The case where the processing target area on the three-dimensional surface is divided into a plurality of quadrangular faces has been described above as a specific example. However, the area dividing processing method according to the present invention is not necessary. Accordingly, the present invention can be applied to divide a processing target region having a triangular shape into regions having other shapes (such as a triangle and a pentagon).

[Process of Surface Patch Generation Unit 36] In the CAD program 2, the surface patch generation unit 3
6 has been described as a specific example in which the positions of the vertices of the quadrangular mesh in the processing target area are moved using Laplacian smoothing. The curved surface patch generation unit 36, for example, has It is also possible to use the method disclosed in U.S. Pat.

[Effects] FIGS. 16 to 25 show specific examples of a set of curved surface patches, and the effects obtained when the area dividing process according to the present invention is performed will be described. FIG. 16 to FIG.
FIG. 13 is a diagram illustrating a quadrilateral mesh and a curved surface patch generated when there is no quadrilateral surface adding process by the mesh adding unit 320 (FIG. 7) illustrated in FIG. 12. In addition, FIG.
FIG. 18 shows a processing process in the surface patch generation unit 36 (FIG. 6), and FIG. 19 shows a surface patch finally generated by the surface patch generation unit 36. FIG. 20 shows a surface patch created without applying the region division processing according to the present invention.
FIG. 20 is a diagram showing a normal line of a curved surface patch in a portion circled in FIG. 19.

As in the conventional case, when mesh data generated without adding a quadrangular surface by the mesh adding unit 320 is input, the curved surface patch generating unit 36
Through the processing steps shown in FIG. 8, the surface patch illustrated in FIG. 19 is generated. The normals of the plurality of curved surface patches at the boundary between the curved surface patches (thick lines) shown in FIG. 19 do not face the same direction as illustrated in FIG. Therefore, it is understood that the curved surface patch generation unit 36 generates the curved surface patch bent at the boundary portion when the mesh adding unit 320 does not perform the addition processing of the quadrangular surface.

FIGS. 21 to 24 are diagrams exemplifying a quadrangular mesh and a curved surface patch generated when the quadrangular surface adding process is performed by the mesh adding unit 320 (FIG. 7) shown in FIG. FIGS. 21 to 23 show processing steps in the surface patch generation unit 36 (FIG. 6).
Indicates a G1 continuous surface patch finally generated by the surface patch generation unit 36. FIG. 25 is a diagram showing a normal line of a curved surface patch of a portion indicated by a circle in FIG. 24 among the curved surface patches created by applying the area dividing process according to the present invention.

On the other hand, when the area dividing process according to the present invention is applied and mesh data generated by adding a quadrilateral surface by the mesh adding unit 320 is input, the curved surface patch generating unit 36 is configured as shown in FIGS. Through the processing steps as shown, the surface patch illustrated in FIG. 24 is generated. FIG.
The normals of the plurality of curved surface patches at the boundary between the curved surface patches (thick lines) shown in FIG. 4 face the same direction as illustrated in FIG. As can be seen by comparing FIG. 20 and FIG. 25, when the process of adding a quadrangular surface by the mesh adding unit 320 is performed, unlike the case where this process is not performed, the curved surface patch generating unit 36
However, it can be seen that a curved surface patch that is not bent even at the boundary portion is generated.

[Second Embodiment] The CAD shown in FIG.
A second embodiment of the present invention in which the first mesh processing unit 3 of the program 2 is replaced with a second mesh processing unit 4 will be described.

[Mesh Processing Unit 4] FIG. 26 is a diagram showing a configuration of the second mesh generation unit 34 shown in FIG.
As shown in parentheses in FIG. 6, the mesh processing unit 4
The first mesh generation unit 30 of the mesh processing unit 3 is replaced with a second mesh generation unit 34 different from the first mesh generation unit 30. As shown in FIG. 26, the mesh generation unit 34 includes a frame mesh generation unit 340 and a second mesh generation unit 34. It comprises a mesh adding unit 360.

[Frame Mesh Generation Unit 340] FIGS. 27 and 28 are first and second views illustrating the processing of the frame mesh generation unit 340 shown in FIG. When the processing target region illustrated in FIG. 8 is input to the frame mesh generation unit 340, the frame mesh generation unit 340 first sets rules 1-1, 1 along the outer frame as illustrated in FIG. When a quadrangular surface that satisfies −2 and 2 is created and quadrangular surfaces are created in all of the frame regions of the outer frame, as illustrated in FIG. 28,
A similar quadrangular surface is created along the inner frame, and initial mesh data indicating the created quadrangular surface is added to the mesh adding unit 360.
Output to

Hereinafter, with reference to FIG. 29, the processing of the frame mesh generation section 340 will be further referred to. FIG. 29 is a flowchart showing the processing (S20) of the frame mesh generation unit 340 shown in FIG. As shown in FIG. 29, in step 200 (S200), the frame mesh generation unit 340
Determines whether or not the process of creating a quadrilateral surface has been completed for all the frame lines included in the processing area. When the process of creating a quadrangular surface has been completed for all the frame lines, the frame mesh generation unit 340 ends the process. Otherwise, the frame mesh generation unit 340 sets unprocessed frame lines as processing targets. Then, the process proceeds to S202.

In step 202 (S202), the frame mesh generation section 340 divides the processing target frame line equally as shown in FIGS. 27 and 28, or
If the frame line has a peak, the space between the peaks is equally divided.

In step 204 (S204), the frame mesh generation unit 340 creates a quadrangular surface with the line segments obtained by the processing in S202 as ridges on the frame, and returns to the processing in S200.

[Mesh Addition Unit 360] FIG.
FIG. 7 is a diagram showing a quadrangular mesh generated by a mesh adding unit 360 shown in FIG. Similar to the initial mesh generation unit 300 shown in FIG. 7, the mesh addition unit 360 divides the processing target region other than the frame region with the quadrilateral surface as illustrated in FIG. 28 into a plurality of quadrilateral surfaces. 30 to generate a quadrilateral mesh as illustrated in FIG.
6 (FIG. 6).

[Overall Operation of CAD Program 2 in Second Embodiment] The overall operation of the CAD program 2 in the second embodiment will be described below. In the CAD program 2 (FIG. 6), the CAD unit 22 processes CAD input data input from the input unit 20 according to an operation of an operator, and designs a three-dimensional shape. Further, the frame mesh generation unit 340 (FIG. 7) of the mesh generation unit 30 applies the rules 1-1, 1-2, and 2 to the frame region of the processing target region (exemplified in FIG. 8) specified by the operator. 27 and FIG. 28, the mesh is divided into a plurality of quadrangular faces, and initial mesh data indicating the result is output to the mesh adding section 360.

The mesh adding unit 360 processes the initial mesh data input from the frame mesh generating unit 340, and divides the processing target area other than the frame line area into one or more quadrangular faces satisfying the rule 2. Then, the final quadrangular mesh (FIG. 30) illustrated in FIG.
6 (FIG. 6).

The surface patch generation unit 36 interpolates a surface patch to the mesh data based on the mesh data input from the mesh addition unit 320 of the mesh generation unit 30 and the element size function outside the processing target area. , And outputs the mesh data (mesh geometric data) in which the curved surface patch is interpolated to the image generation unit 24.

The image generation unit 24 includes a curved surface patch generation unit 36
Processing the mesh geometry data input from
Image data indicating the surface of the three-dimensional shape obtained as a result of the design by the unit 22 is generated and displayed on the display device 14. Further, the CAD unit 22 generates a CAD representing a final three-dimensional shape designed based on the mesh geometric data input from the curved surface patch generation unit 36 and the CAD input data.
The output data is recorded on the storage device 18 or printed out on the output device 16.

Note that the processing of the CAD program 2 in the second embodiment can be modified in the same manner as that shown in the first embodiment. Further, the effect of the region division processing according to the present invention described with reference to FIGS. 16 to 25 can also be obtained by the processing of the CAD program 2 in the second embodiment.

[0083]

As described above, according to the region dividing processing apparatus and method of the present invention, it is determined whether or not a polygonal region to be processed is convex, and a shape to be processed is determined. Regardless of the n-dimensional (three-dimensional) shape and the geometrical conditions of the polygonal region, such as whether or not it is closed, the processing target region is divided into a plurality of polygonal regions so that the surface patch can be smoothly interpolated. Can be divided. Also,
ADVANTAGE OF THE INVENTION According to the area division | segmentation processing apparatus and its method concerning this invention, a curved surface patch is interpolated smoothly, without restricting the n-dimensional (three-dimensional) shape of a process target to a specific shape, such as a hexahedron. Can be divided into a plurality of polygonal regions. Further, according to the region division processing apparatus and method of the present invention, a smooth curved surface patch can be interpolated without changing the boundary of the shape to be processed.

[Brief description of the drawings]

FIG. 1 is a diagram exemplifying a processing target region divided into a plurality of quadrangular surfaces by a region dividing process according to the present invention.

FIG. 2 is a diagram exemplifying four to six adjacent quadrangular faces sharing one vertex in a processing target area;

FIG. 3 is a diagram showing an example in which two points adjacent to each other share one point on the outer frame (FIG. 1).
It is a figure which illustrates four square surfaces.

FIG. 4 is a diagram exemplifying two adjacent quadrangular faces sharing a point V on a frame line;

FIG. 5 is a CAD for realizing a region dividing process according to the present invention;
FIG. 2 is a diagram illustrating a configuration of an apparatus.

FIG. 6 is a CAD for realizing a region dividing process according to the present invention;
FIG. 3 is a diagram showing a configuration of a program.

FIG. 7 is a diagram illustrating a configuration of a mesh generation unit illustrated in FIG. 6;

8 is a diagram exemplifying a processing target area on a three-dimensional surface input to the mesh generation unit from the CAD unit shown in FIG. 6;

FIG. 9 is a diagram illustrating a quadrilateral mesh generated by a mesh generation unit shown in FIG. 6;

10 is a diagram exemplifying a plurality of quadrangular surfaces (quadrangular meshes) obtained by the initial mesh generation unit shown in FIG. 7 by dividing the processing target region shown in FIG. 8;

11 is a diagram illustrating a process in which the mesh adding unit illustrated in FIG. 7 further adds a quadrangular surface to the quadrangular mesh illustrated in FIG. 10;

FIG. 12 is a flowchart showing a process (S10) of adding a quadrangular surface by the mesh adding unit shown in FIG. 7;

FIG. 13 is a diagram exemplifying a case in which a quadrangular surface is not added to a frame line in a modification of the process of the mesh adding unit (FIG. 7) of the first embodiment.

FIG. 14 is a diagram exemplifying a case where a quadrilateral surface is added to a frame line in a modification of the process of the mesh adding unit (FIG. 7) of the first embodiment.

FIG. 15 is a diagram illustrating an example of a process of adding a quadrangular surface related to a vertex in a modification of the process of the mesh adding unit (FIG. 7) of the first embodiment.

16 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is no quadrilateral surface adding process by the mesh adding unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) It is a 1st figure which shows a process.

17 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is no quadrilateral surface addition processing by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) It is a 2nd figure which shows a process.

18 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is no quadrilateral surface addition processing by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) It is a 3rd figure which shows a process.

19 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is no quadrilateral surface addition process by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) This shows a finally generated surface patch.

FIG. 20 is a diagram showing the normal line of the curved surface patch of a portion indicated by a circle in FIG. 19 among the curved surface patches created without applying the region division processing according to the present invention.

21 is a diagram exemplifying a quadrilateral mesh and a curved surface patch generated when there is a quadrangular surface adding process by the mesh adding unit (FIG. 7) shown in FIG. 12, wherein the curved surface patch generating unit (FIG. 6) It is a 1st figure which shows a process.

22 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is a quadrilateral surface addition process by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) It is a 2nd figure which shows a process.

23 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is a quadrilateral surface addition process by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) It is a 3rd figure which shows a process.

24 is a diagram exemplifying a quadrilateral mesh and a surface patch generated when there is a quadrilateral surface addition process by the mesh addition unit (FIG. 7) shown in FIG. 12, wherein the surface patch generation unit (FIG. 6) This shows a finally generated surface patch.

FIG. 25 is a diagram showing a normal line of a curved surface patch of a portion indicated by a circle in FIG. 23 among curved surface patches created by applying the area dividing process according to the present invention.

FIG. 26 is a diagram illustrating a configuration of a second mesh generation unit illustrated in FIG. 6;

FIG. 27 is a first diagram illustrating a process of a frame mesh generation unit illustrated in FIG. 26;

FIG. 28 is a second diagram illustrating the processing of the frame mesh generation unit illustrated in FIG. 26;

FIG. 29 is a flowchart showing processing (S) performed by the frame mesh generation unit shown in FIG. 26;
It is a flowchart which shows 20).

FIG. 30 is a diagram illustrating a quadrangular mesh generated by the mesh adding unit illustrated in FIG. 26;

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... CAD device 10 ... CPU 12 ... Input device 120 ... Tablet 122 ... Keyboard 124 ... Mouse 14 ... Display device 16 ... Output device 18 ... Storage device 180 ... Recording medium 2 ... CAD program 20 ... Input unit 22 ... CAD unit 24 ... Image generation unit 3,4 ... Mesh processing unit 30, 34 ... Mesh generation unit 300 ··· Initial mesh generation unit 320 ··· Mesh addition unit 340 ··· Frame mesh generation unit 360 ··· Mesh addition unit 36 ··· Curved surface patch generation unit

 ──────────────────────────────────────────────────の Continuing from the front page (72) Inventor Atsushi Yamada 1623-14 Shimotsuruma, Yamato-shi, Kanagawa Prefecture Within the Tokyo Research Laboratory, IBM Japan, Ltd. (72) Inventor Tomotake Furuhata, Yamato-shi, Kanagawa 1623-14 Tsuruma IBM Japan, Ltd. Tokyo Basic Research Laboratories (72) Inventor Takayuki Ito 1623-14 Shimotsuruma, Yamato-shi, Kanagawa Japan IBM Japan Ltd., Tokyo Basic Research Laboratory F-term (Reference) 5B046 DA02 FA06 FA18 GA01 5B080 AA11 AA15

Claims (11)

[Claims] 1. An area division processing apparatus for dividing an area (target area) to be processed in a shape of two or more dimensions into a plurality of predetermined polygonal areas (polygonal areas), According to a predetermined rule, an arbitrary point included in a boundary line (frame line) between a region and a region having a shape other than the target region is included in one or more of the polygonal regions. And the part (frame line area) in contact with the frame line,
A frame region dividing means for dividing the polygonal region into a plurality of polygonal regions; and a part (undivided region) of the target region which is not divided into the plurality of polygonal regions is converted into one or more polygonal regions. And an undivided area dividing unit for performing a dividing process. 2. The frame line area dividing means according to claim 1, wherein the frame line area dividing means divides the frame line area so that an arbitrary point of the frame line is included in one or two polygonal areas. Area division processing device. 3. The method according to claim 1, wherein the frame region dividing means includes any one or more of the polygonal regions including any point other than the break point of the frame line, and the number of break points of the frame line is two. 2. The region division processing device according to claim 1, wherein the frame region is divided so as to be included in the polygon region. 4. The frame line area dividing means sets the frame line area to a number of the polygonal areas according to an angle formed at a break point of the frame line so that the break point of the frame line is shared. 2. The region division processing device according to claim 1, wherein the region division processing is performed. 5. The frame region dividing means divides the frame region of the target region into a plurality of polygon regions, and the undivided region dividing device divides the frame region into a plurality of polygon regions. 5. The region division processing device according to claim 1, wherein the undivided region other than the frame region is divided into the plurality of polygon regions. 6. The undivided area dividing means divides the target area into a plurality of the polygonal areas, and the frame area dividing means comprises the polygonal line among arbitrary points included in the frame line. The area division according to any one of claims 1 to 4, wherein the frame region is divided into a plurality of the polygon areas so that points other than the above are included in one or two of the polygon areas. Processing equipment. 7. The frame region dividing means connects one point included in each of the two ridge lines of the polygonal region adjacent to each other including one point included in the frame line, The region division processing device according to claim 6, wherein the polygon region is added. 8. The area division according to claim 1, wherein said two-dimensional shape or more is a three-dimensional shape, and each of said plurality of polygonal regions shares a vertex with another polygonal region. Processing equipment. 9. The plurality of polygonal areas are quadrangular areas each sharing a vertex with another polygonal area.
3. The area division processing device according to 1. 10. An area division processing method for dividing an area (object area) to be processed in a shape of two or more dimensions into a plurality of predetermined polygonal areas (polygonal areas), wherein: An arbitrary point included in a boundary line (frame line) between a region and a region having a shape other than the target region is included in one or two of the polygon regions.
A portion (frame line region) in contact with the frame line is divided into a plurality of polygon regions, and a portion (undivided region) of the target region that is not divided into the plurality of polygon regions is defined as 1 An area division processing method for performing division processing on one or more polygonal areas. 11. A program for dividing an area (object area) to be processed in a shape of two or more dimensions into a plurality of predetermined polygonal areas (polygonal areas), wherein According to a predetermined rule, any point included in a boundary line (frame line) with an area having a shape other than the target area is included in one or more of the polygonal areas. The part that touches the border (border area)
A frame region dividing step of dividing the polygon region into a plurality of polygon regions; and a part (undivided region) of the target region that is not divided into the plurality of polygon regions is converted into one or more polygon regions. And a non-divided area dividing step of dividing the medium.