JP2003281568A - Image processor and processing method, storage medium and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To optionally deform a 3D polygonal model in a state where the smoothness of its surface is kept, following a user's operation in real time by use of a computer of consumer level. <P>SOLUTION: The image processing program divides each polygon to be divided which consists of three edges to be divided as polygons 1, 2, 3, 5, 6, and 7, as shown in Fig. 14, to four pieces on the basis of the calculated dividing positions of edges to be divided, and halves a polygon which is not the polygon to be divided but contains only one edge to be divided as polygon 4. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image processing apparatus and method, a recording medium, and a program, and in particular, a three-dimensional polygon mesh model displayed in a virtual space on a display is deformed following a user's operation. The present invention relates to an image processing apparatus and method suitable for use in a case, a recording medium, and a program.

[0002]

2. Description of the Related Art As a method of expressing a three-dimensional object (three-dimensional object) on a two-dimensional display by computer graphics, there is a method of displaying a three-dimensional polygon mesh model (hereinafter abbreviated as 3D polygon model). is there. The 3D polygon model represents a surface of a three-dimensional object by combining a plurality of polygons (polygons) such as triangles.

Conventionally, many methods for changing the shape of the displayed 3D polygon model have been proposed. For example, the document “TWS Sederberg and SRParry, Free-Form D
eformation of Solid Geometric Models, Computer Gra
phics (SIGGRAPH '86 Proceedings), pp.151-160, Aug.
1986. "discloses a method for deforming a 3D polygon model using an FFD (Free-Form Deformation) method.

In the FFD method, a rectangular space is assumed around the 3D polygon model to be deformed, the space is distorted by moving the vertices of the space, and the 3D polygon model is deformed corresponding to the distortion of the space. Is done.

Therefore, in the FFD method, in order to deform the 3D polygon model, the apex of the rectangular space provided around the 3D polygon model is moved instead of directly performing the deformation operation on the 3D polygon model. It is difficult to transform the 3D polygon model into a desired shape because the operation is performed.

As a method for solving such a problem, 3
There is a method of directly modifying the D polygon model.
Specifically, a method of designating the vertices of a polygon forming the surface of a 3D polygon model, simply moving the vertices to the position after the transformation, and further deforming the polygon including the vertices with the movement of the vertices. Exists.

However, in the method of simply moving the vertices of the polygon to the position after the deformation, when the amount of movement of the vertices is large, the edges of the polygon deformed by the movement of the vertices are conspicuously visible. .

For example, as shown in FIG. 1, by moving the vertex Pa of a 3D polygon model formed by combining a plurality of triangular polygons in the direction of the broken line arrow,
When the 3D polygon model is deformed, as shown in FIG. 2, the edges (indicated by thick lines in FIG. 2) of the triangular polygon deformed with the movement of the vertex Pa stand out,
The smoothness of the surface of the 3D polygon model was lost.

As a method of improving the smoothness of the surface of the 3D polygon model, there is a method of dividing all the polygons forming the surface of the 3D polygon model into a plurality of polygons. However, in this method, since all the polygons that form the surface of the 3D polygon model are targeted for division, the larger the number of polygons that form the surface of the 3D polygon model, the longer the time required for the division processing. Met.

[0010]

Therefore, a technique has been established in which a consumer-level computer can be used to follow a user's operation in real time to deform the 3D polygon model smoothly and arbitrarily like clay work. There were issues that were not addressed.

The present invention has been made in view of such a situation, and uses a consumer-level computer to follow a user's operation in real time to maintain a smooth surface of a 3D polygon model. The purpose is to be able to transform arbitrarily.

[0012]

An image processing apparatus of the present invention corresponds to a deformation area designating means for designating an arbitrary portion of a three-dimensional object as a deformation area, and a transformation area designated by the deformation area designating means. A moving vertex selecting means for selecting a vertex of a polygon forming a three-dimensional object as a moving vertex, a moving means for moving the position of the moving vertex by a predetermined moving amount, and a moving vertex deformed by the moving means moving the moving vertex. Among the polygons to be divided, polygons that satisfy a predetermined condition are designated as division target polygons, division target edge designation means for designating the edges forming the division target polygons as division target edges, and movement by the movement unit. Of the polygons that are deformed as the vertices move,
At present, it includes a division target polygon adding means for additionally designating a division target polygon that is not a division target polygon and has a plurality of division target edges, and a division means for dividing a polygon including a division target edge into a plurality of polygons. It is characterized by

The polygon may be a triangle.

The image processing apparatus of the present invention may further include setting means for setting the amount of movement of the moving vertex moved by the moving means.

When there is no polygon vertex in the deformation area designated by the deformation area designating means, the moving vertex selecting means divides the polygon included in the deforming area to generate a new moving vertex. be able to.

The image processing apparatus of the present invention may further include polygon reducing means for reducing the number of polygons increased by the processing of the dividing means.

According to the image processing method of the present invention, the three-dimensional object is designated in correspondence with the transformation area designating step of designating an arbitrary portion of the three-dimensional object as the transformation area and the transformation area designated in the processing of the transformation area designating step. A moving vertex selecting step of selecting the vertices of the polygons forming the moving vertex as a moving vertex; Among them, a division target polygon designating step for designating one that satisfies a predetermined condition as a division target polygon, a division target edge designating step for designating edges constituting the division target polygon as a division target edge, and a movement by the processing of the moving step Of the polygons that are deformed due to the movement of vertices, they are not currently the target polygons for division and Characterized in that it comprises a dividing step of dividing the division target polygon additional step of adding specify those having a plurality of target edges division target polygon, a polygon including a split target edge into a plurality of polygons.

The program of the recording medium of the present invention is a three-dimensional program corresponding to a deformation area designating step for designating an arbitrary portion of a three-dimensional object as a transformation area and a modification area designated in the processing of the transformation area designating step. A moving vertex selecting step of selecting the vertices of polygons forming an object as moving vertices, a moving step of moving the position of the moving vertices by a predetermined amount of movement, and deformation of the moving vertices due to movement of the moving vertices. Of the polygons, those that satisfy a predetermined condition are designated as the division target polygons, the division target edge designation step for designating the edges forming the division target polygons as the division target edges, and the movement step processing. Of the polygons that are deformed with the movement of the moving vertices, currently they are not the division target polygons, One, characterized in that it comprises a division target polygon additional step of adding specify those having a plurality of divided object edge division target polygon, and dividing step of dividing the polygon including the divided target edge into a plurality of polygons.

The program of the present invention configures a three-dimensional object in correspondence with a transformation area designating step for designating an arbitrary portion of the three-dimensional object as a transformation area and the transformation area designated in the processing of the transformation area designating step. The moving vertex selection step of selecting the vertex of the polygon to be moved as the moving vertex, the moving step of moving the position of the moving vertex by a predetermined moving amount, and the polygon deformed by the movement of the moving vertex by the processing of the moving step. , A division target polygon designating step for designating a polygon that satisfies a predetermined condition as a division target polygon, a division target edge designating step for designating edges constituting the division target polygon as a division target edge, Of the polygons that are deformed due to movement, currently they are not target polygons for division, and A division target polygon additional step of adding specify those having a plurality of elephants edge division target polygon, characterized in that to execute the dividing step of dividing the polygon including the divided target edge into a plurality of polygons in a computer.

In the image processing apparatus and method and the program of the present invention, the vertices of polygons forming the three-dimensional object are selected as the moving vertices corresponding to the designated deformation area, and are moved by a predetermined moving amount. . Of the polygons that are deformed with the movement of the moving vertex, those that satisfy a predetermined condition are designated as division target polygons, and the edges forming the division target polygons are designated as division target edges. Further, among the polygons that are deformed due to the movement of the moving vertex, those that are not the division target polygons at present and have a plurality of division target edges are additionally specified as the division target polygons. Further, the polygon including the division target edge is divided into a plurality of polygons.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. First, the outline of the present invention will be described with reference to FIG. FIG. 3 is an external view of a personal computer that operates as an image processing apparatus to which the present invention is applied by executing a predetermined application program (hereinafter referred to as an image processing program).

The personal computer 1 has a display 2 for displaying an image of a processing result, a pointer sensor 3 for detecting a user's operation, and a 3D polygon model sensor 5.

For example, the pointer sensor 3 operated by the user's right hand detects a three-dimensional movement operation in the real space using magnetism or ultrasonic waves, and outputs a movement operation signal indicating its own current position and angle. Output to the personal computer 1. Corresponding to this movement operation signal, display 2
The transformation area pointer 21 is moved in the virtual three-dimensional space displayed in.

Further, the pointer sensor 3 has a trigger button 4, detects a user's pressing operation on the trigger button 4, and outputs a corresponding pressing operation signal to the personal computer 1. In response to this push-down operation signal, the state in the deformation mode (described later) and the state in the non-deformation mode are alternately switched. Alternatively, the deformation mode may be set only while the trigger button 4 is pressed, and the deformation mode may not be set when the trigger button 4 is not pressed.

The shape of the pointer sensor 3 is preferably a shape (insertion stick type, pen type, etc.) that is reminiscent of the shape of the corresponding deformation area pointer 21 (that is, an arrow).
Not so.

For example, the 3D polygon model sensor 5 operated by the user's left hand detects a three-dimensional moving operation in the real space using magnetism or ultrasonic waves, and indicates the current position and angle of the user. The signal is output to the personal computer 1. The 3D polygon model 22 is moved in the virtual three-dimensional space displayed on the display 2 in response to this movement operation signal.

The external appearance (shape or pattern) of the 3D polygon model sensor 5 is preferably, but not limited to, the one that is associated with the external appearance (spherical shape in this case) of the corresponding displayed 3D polygon model 22.

Instead of the pointer sensor 3 and the 3D polygon model sensor 5, a general input device such as a keyboard, a mouse or a trackball provided in the personal computer 1 may be used.

By moving at least one of the pointer sensor 3 and the 3D polygon model sensor 22 in the real space, the user contacts the deformation area pointer 21 and the 3D polygon model 22 in the virtual three-dimensional space displayed on the display 2. Then, by pressing the trigger button 4 in that state, the deformation portion of the 3D polygon model 22 can be specified and the image processing apparatus can be set to the deformation mode. After that, by moving the deformation area pointer 21 in an arbitrary direction in the deformation mode, the deformation portion of the 3D polygon model 22 can be deformed in the moved direction.

In the following, the plurality of triangular polygons forming the 3D polygon model 22 will be simply referred to as polygons.

Next, FIG. 4 shows a personal computer 1.
The example of composition of is shown. This personal computer 1
Includes a CPU (Central Processing Unit) 31. An input / output interface 35 is connected to the CPU 31 via a bus 34. ROM (Read O
nly Memory) 32 and RAM (Random Access Memory) 33
Are connected.

In the input / output interface 35, in addition to the pointer sensor 3 operated by the user and the 3D polygon model sensor 4, an operation input unit 36 to which an input device such as a keyboard, a mouse and a trackball is connected and the display 2 are displayed. A display control unit 37 that generates a video signal, a storage unit 38 that includes a hard disk drive that stores various data such as programs and 3D polygon models, a communication unit 39 that communicates data via a network represented by the Internet, and a magnetic field. A drive 40 for reading / writing data from / to a recording medium such as a disk 41 to a semiconductor memory 44 is connected.

An image processing program for causing the personal computer 1 to operate as an image processing apparatus to which the present invention is applied includes a magnetic disk 41 (including a floppy disk) and an optical disk 42 (CD-ROM (Compact Disc-Read).
Only Memory), DVD (including Digital Versatile Disc)), magneto-optical disc 43 (including MD (Mini Disc)), or semiconductor memory 44 is supplied to the personal computer 1 and read by the drive 40. Installed in the hard disk drive built in the storage unit 38. The image processing program installed in the storage unit 38 is a CP corresponding to a command input by the user to the operation input unit 36.
It is loaded into the RAM 33 from the storage unit 38 and executed by a command from the U 31.

Next, the 3D polygon model deformation processing by the image processing program will be described with reference to the flowchart of FIG. It is assumed that the deformation area pointer 21 and the 3D polygon model 22 are already displayed on the display 2 by a predetermined operation by the user.

In step S1, the image processing program causes the pointer sensor 3 and the 3D polygon model sensor 5 to detect a user operation. Step S2
In, the image processing program determines whether or not the current state is the deformation mode, based on the pressing operation of the trigger button 4 provided on the pointer sensor 3 by the user. If it is determined that the deformation mode is not set, the process proceeds to step S3.

In step S3, the image processing program corresponds to the user's operation on the pointer sensor 3 and the 3D polygon model sensor 5, and the deformation area pointer 2 in the virtual three-dimensional space displayed on the display 2 is displayed.
Move the 1 and 3D polygon models 22.

In step S5, the image processing program determines whether or not to end the 3D polygon model deformation processing, based on whether or not a predetermined end condition is satisfied. Here, the predetermined termination condition is, for example, when the termination command is input from the user, the memory (RAM3
It refers to restrictions on software or hardware, such as when the remaining amount in 3) is insufficient.

Therefore, when the predetermined termination condition is not satisfied, it is determined that the 3D polygon model deformation processing is not terminated, the processing returns to step S1, and the subsequent processing is repeated, that is, the user's operation. The movement of the deformation area pointer 21 or the like corresponding to the operation or the deformation processing for the 3D polygon model 22 is continued.

When it is determined in step S2 that the current state is the deformation mode, the process proceeds to step S4. In step S4, the image processing program moves the deformation area pointer 21 and deforms the 3D polygon model 22 in accordance with the movement amount of the pointer sensor 3.

The details of this transformation process will be described with reference to the flowchart of FIG. In step S11, the image processing program executes 3D in a spherical deformation area 51 having a predetermined radius centered on the deformation area pointer 21 in the virtual three-dimensional space displayed on the display 2.
It is determined whether or not the vertices of polygons forming the polygon model 22 are present. The shape of the deformation area 51 is not limited to the spherical shape.

For example, as shown in FIG. 7, when it is determined that the vertices of the polygons forming the 3D polygon model 22 do not exist in the deformation area 51, the process is step S12.
Proceed to. In step S12, the image processing program determines the polygon (polygon in the case of FIG. 7) located closest to the deformation area pointer 21, and newly generates a vertex Pn in the deformation area 51 as shown in FIG. Then, the polygon is divided into three by designating it as a moving vertex.

If it is determined in step S11 that the vertices of the polygons forming the 3D polygon model 22 are present in the deformation area 51, as shown in FIG. 9, the vertices existing in the deformation area 51 are shown. Is designated as the moving vertex, and the process of step S12 is skipped.
In FIG. 9, the vertices (that is, the moving vertices) of polygons existing in the deformation area 51 are circled.

Further, the processing of step S11 is omitted so that the 3D polygon model 22 is placed in the transformation area 51.
Irrespective of whether or not the vertices of the polygons that make up the polygon exist, the polygon closest to the deformation area pointer 21 is determined, a vertex Pn is newly generated inside this polygon, and the polygon is divided into three parts. May be designated as the moving vertex.

In step S13, the image processing program moves the position of the moving vertex in response to the user's moving operation on the pointer sensor 3. Along with this, the polygon including the moving vertex is deformed.

In step S14, the image processing program focuses on all polygons including the moving vertex. In step S15, the image processing program selects a polygon satisfying a predetermined selection condition from among the polygons noted in step S14 as a division target polygon. The predetermined selection conditions include, for example, that the length of a side between vertices forming a polygon (hereinafter, referred to as an edge) is a predetermined threshold or more, the area of the polygon is a predetermined threshold or more, the polygon That is, the angle between the edges forming the above is equal to or more than a predetermined threshold value.

In step S16, the image processing program determines whether or not the polygon selected as the division target polygon in step S15 exists (that is, whether or not there is a polygon determined to satisfy a predetermined selection condition). judge. When it is determined that the selected polygon exists as the division target polygon, the polygon division processing is performed on the division target polygon.

Details of this polygon division processing will be described with reference to the flowchart of FIG. Step S
In 21, the image processing program designates all the edges of all the polygons currently selected as the division target polygons as the division target edges, and adds a flag indicating the division target edges. For example, in FIG.
When the polygons, ... Are selected as the division target polygons, as shown in the figure, all the edges forming the polygons, ... Are designated as the division target edges, and a flag indicating that they are the division target edges (see FIG. 11). In the following, circles will be used).

In step S22, the image processing program determines whether or not there is a polygon which is not currently selected as a division target polygon and which includes two division target edges. A polygon that is not currently selected as a division target polygon and includes two division target edges (for example, a polygon,
) Is present, the process proceeds to step S2.
Go to 3.

In step S23, the image processing program adds the polygons (polygons in FIG. 11) determined to exist in step S22 to the polygons to be divided. The process returns to step S21, and the subsequent processes are repeated. By repeating steps S21 to S23, as shown in FIG.
The edges forming the are also specified as the division target edges, and the polygons are also added to the division target polygons.
As shown in 3, the edges forming the polygon are also designated as the division target edges.

Then, in step S22, at present,
When it is determined that there is no polygon selected as the division target polygon and there is no polygon including two division target edges, the process proceeds to step S24.
In step S24, the image processing program determines the division position of each division target edge (that is, the position where a new vertex is generated).

Examples of the method of determining the division position of the division target edge include a method of calculating the middle of both ends of the division target edge as the division position, a method of using the Modified Butterfly method, and the like. Modified Butterf
For details of the ly method, see "Denis Zorin, Peter Schroder and
Wim Sweldens, ”Interpolating subdivision for meshe
s with arbitrary topology, ”in Proceedings of SIGG
RAPH 1996, ACM SIGGRAPH, 1996, pp.189-192 ".

In step S25, the image processing program, on the basis of the division position of the division target edge calculated in step S24, as shown in FIG. 14, three division targets such as polygons, ... In FIG. Each polygon to be divided consisting of edges is divided into four, and
A polygon including only one division target edge such as the polygon in 3 is divided into two.

In this way, after the polygon deformed by the movement of the selected vertex is divided, the process returns to step S18 in FIG. In step S18,
The image processing program performs polygon reduction processing on the polygons increased by the division processing in step S17.

Here, the polygon reduction processing is
This is a process for reducing the number of polygons forming the deformed 3D polygon model while maintaining the outer shape characteristics of the deformed 3D polygon model as much as possible, and is disclosed in, for example, Japanese Patent Laid-Open No. 9-231401. There is.

As described above, by executing the polygon reduction process, it is possible to suppress the decrease in the drawing speed when the number of polygons is increased, and the deformation process can be drawn in real time in response to the user's operation.

The polygon reduction process in step S18 may be omitted.

The process returns to step S5 in FIG. Then, in step S5, when the predetermined termination condition is satisfied, it is determined that the 3D polygon model deformation process is terminated, and the 3D polygon model deformation process is terminated. This is the end of the description of the 3D polygon model deformation processing.

As described above, according to the 3D polygon model transformation processing, for example, when the vertex is moved as shown in FIG. 15, only the edges of the polygons transformed along with the movement of the vertices stand out in FIG. Since it is divided as shown, it is possible to follow the user's operation in real time and deform the 3D polygon model while maintaining the smoothness of the surface.

Further, by appropriately performing polygon reduction processing, the number of polygons increased by the division of polygons can be suppressed, so that the load of the arithmetic processing by the CPU 31 is reduced. Therefore, it becomes easier to perform the deformation operation while drawing the deformation process of the 3D polygon model in real time.

The image processing apparatus to which the present invention is applied is
It may be realized not only by the personal computer executing the image processing program, but also by, for example, the home-use game machine executing the game program. Alternatively, the image processing device to which the present invention is applied can be realized as hardware.

In the present specification, the steps for writing the program recorded on the recording medium are not limited to the processing performed in time series according to the order described, but may be performed in parallel even if the processing is not necessarily performed in time series. Alternatively, it also includes processes that are individually executed.

[0062]

As described above, according to the present invention, a consumer-level computer is used to follow a user's operation in real time, and the 3D polygon model is arbitrarily deformed while maintaining the smoothness of the surface. It becomes possible to do.

[Brief description of drawings]

FIG. 1 is a diagram for explaining an example of a conventional method for deforming a 3D polygon model.

FIG. 2 is a diagram for explaining an example of a conventional method for deforming a 3D polygon model.

FIG. 3 is a diagram showing the execution of an image processing program.
1 is an external view of a personal computer 1 that operates as an image processing apparatus to which the present invention has been applied.

FIG. 4 is a block diagram showing an electrical configuration example of a personal computer 1.

FIG. 5 is a flowchart illustrating 3D polygon model deformation processing by an image processing program.

FIG. 6 is a flowchart illustrating a modification process of step S4 of FIG.

FIG. 7 is a diagram for explaining the process of step S11 of FIG.

FIG. 8 is a diagram for explaining the process of step S12 of FIG.

FIG. 9 is a diagram for explaining the process of step S11 of FIG.

FIG. 10 is a flowchart illustrating the polygon division processing in step S17 of FIG.

FIG. 11 is a diagram for explaining the processing of steps S21 to S23 of FIG.

12 is a diagram for explaining the processing of steps S21 to S23 of FIG.

13 is a diagram for explaining the processing of steps S21 to S23 of FIG.

FIG. 14 is a diagram for explaining the process of step S25 of FIG.

FIG. 15 is a diagram for explaining a processing result of 3D polygon model deformation processing by an image processing program.

FIG. 16 is a diagram for explaining a processing result of 3D polygon model deformation processing by an image processing program.

[Explanation of symbols]

1 personal computer, 2 display,
3 pointer sensor, 4 trigger button, 5 3D polygon model sensor, 21 deformation area pointer, 2
2 3D polygon model, 31 CPU, 41 magnetic disk, 42 optical disk, 43 magneto-optical disk, 44 semiconductor memory, 51 deformation area

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Claims (8)

[Claims] 1. An image processing apparatus for displaying a three-dimensional object using a plurality of polygons, the deformation area designating unit designating an arbitrary portion of the three-dimensional object as a deformation area, and the transformation area designating unit. A moving vertex selecting unit that selects a vertex of the polygon forming the three-dimensional object as a moving vertex corresponding to the deformation area; a moving unit that moves the position of the moving vertex by a predetermined moving amount; Of the polygons that are deformed as the moving vertex is moved by the moving means, a polygon to be divided that specifies a polygon that satisfies a predetermined condition as a polygon to be divided, and an edge that constitutes the polygon to be divided are to be divided. Edge-to-be-divided specifying means for specifying an edge, and before being deformed by the movement of the moving vertex by the moving means Among the above described polygons, at present, not the division target polygon, but a division target polygon adding means for additionally designating a polygon having a plurality of the division target edges to the division target polygon, and a plurality of the polygons including the division target edge. An image processing device, comprising: 2. The image processing apparatus according to claim 1, wherein the polygon is a triangle. 3. The image processing apparatus according to claim 1, further comprising setting means for setting a movement amount of the movement vertex moved by the movement means. 4. The moving vertex selecting means newly divides the polygon by dividing the polygon contained in the deformation area when the vertex of the polygon does not exist in the deformation area designated by the transformation area designating means. The image processing apparatus according to claim 1, wherein the image processing apparatus generates vertices. 5. The image processing apparatus according to claim 1, further comprising polygon reducing means for reducing the number of polygons increased by the processing of the dividing means. 6. An image processing method of an image processing device for displaying a three-dimensional object using a plurality of polygons, comprising: a transformation area designating step of designating an arbitrary portion of the three-dimensional object as a transformation area; A moving vertex selecting step of selecting a vertex of the polygon constituting the three-dimensional object as a moving vertex corresponding to the deformation area designated in the process of step, and moving the position of the moving vertex by a predetermined moving amount. And a division target polygon designating step of designating, as a division target polygon, a polygon that satisfies a predetermined condition among the polygons that are deformed by the movement of the movement vertex by the processing of the movement step. A dividing target edge specifying step of specifying an edge forming a polygon as a dividing target edge; Among the polygons that are deformed due to the movement of the moving apex by the process of step, the division target that is not the division target polygon at present and has a plurality of the division target edges is additionally specified as the division target polygon. An image processing method comprising: a polygon adding step; and a dividing step of dividing the polygon including the division target edge into a plurality of polygons. 7. A program for displaying a three-dimensional object using a plurality of polygons, comprising: a transformation area designating step of designating an arbitrary portion of the three-dimensional object as a transformation area; and a transformation area designating step. A moving vertex selecting step of selecting a vertex of the polygon forming the three-dimensional object as a moving vertex corresponding to the deformation area designated in the process, and a movement of moving the position of the moving vertex by a predetermined moving amount. A step of designating a polygon to be segmented that designates, as a polygon to be segmented, a polygon that satisfies a predetermined condition among the polygons that are deformed with the movement of the moving vertex by the process of the moving step; A dividing target edge designating step of designating a constituent edge as a dividing target edge, and the moving step of Of the polygons that are deformed due to the movement of the moving apex by the processing, the division target polygon addition that specifies the division target polygon that is not the division target polygon at present and has a plurality of division target edges A recording medium having a computer-readable program recorded thereon, comprising: a dividing step of dividing the polygon including the division target edge into a plurality of polygons. 8. A computer for displaying a three-dimensional object using a plurality of polygons, the deformation area designating step of designating an arbitrary portion of the three-dimensional object as a transformation area, and the modification area designating step. A moving vertex selecting step of selecting a vertex of the polygon forming the three-dimensional object as a moving vertex corresponding to the deformation area; a moving step of moving the position of the moving vertex by a predetermined moving amount; Among the polygons that are deformed by the movement of the moving apex by the movement step processing, a division target polygon designation step of designating a polygon that satisfies a predetermined condition as a division target polygon, and an edge forming the division target polygon By the division target edge designation step designated as the division target edge, and the processing of the moving step Among the polygons that are deformed with the movement of the moving vertex, the division target polygon adding step of additionally designating a polygon having a plurality of division target edges, which is not the division target polygon at present, to the division target polygon. A program for executing a dividing step of dividing the polygon including the division target edge into a plurality of polygons.