JPH0765205A - 3D shape display - Google Patents

Abstract

(57) [Summary] [Object] To provide a three-dimensional shape display device capable of easily displaying a desired shape. [Structure] The three-dimensional shape data stored in the shape data management unit 2 is calculated by a deformation amount calculation unit 3 in accordance with a deformation process instructed by a user through the input unit 1, and the three-dimensional shape data is calculated by the shape data operation unit 4. Change the original shape data. The triangle division processing unit 5 recursively divides the triangles forming the triangular shape according to the transformation processing. The display data calculation unit 6 calculates display data based on the three-dimensional shape data stored in the shape data management unit 2, and displays the deformed shape on the display unit 7.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a three-dimensional shape display device, and more particularly to a three-dimensional shape display device for interactively deforming a three-dimensional shape.

[0002]

2. Description of the Related Art In order to interactively deform a three-dimensional shape in computer graphics or a CAD system, a method of expressing the three-dimensional shape as a set of triangles and moving the vertices of the triangles to deform the shape. There is.
In the method disclosed in Japanese Patent Application Laid-Open No. 4-24876, a three-dimensional object surface is two-dimensionally developed, control points are placed on a two-dimensional parameter space, and two-dimensional parameters connecting the control points are used as the above-mentioned modification method. By dividing the space into multiple triangle regions and given the amount of movement of the vertices, by linearly interpolating the amount of movement of the points in the triangular region, the amount of movement of the control points that are the vertices of the triangle. Looking for.

Further, as another shape transformation method, Japanese Patent Laid-Open No. Hei 1
In the method disclosed in Japanese Patent Publication No. 297771, a grid having a plurality of grid points is defined on the xy plane, and at least one of the plurality of grid points is selected as a reference point. When a movement amount in the z-axis direction is given, the grid points around the reference point are moved based on the movement amount of the reference point, and the movement amount of the reference point is propagated to the surrounding grid points. The grid points are being moved.

[0004]

In the conventional three-dimensional shape apparatus that uses the above-mentioned deformation method, it is necessary to explicitly indicate the vertex to be moved, and therefore the movement target is required to realize the desired deformation. It was necessary to explicitly specify all the vertices that would be required, and the operation was complicated. Further, since a calculation method for obtaining the movement amount of the surrounding vertices based on the designated movement amount of the vertices is specified, the versatility is low and an arbitrary shape cannot be easily input. Furthermore, when the amount of movement of the vertices becomes large, the triangle becomes too coarse to represent the shape after movement, and it is not possible to display the detailed deformation state, and it is possible to display any shape. There wasn't.

An object of the present invention is to solve the above problems, and an object thereof is to provide a three-dimensional shape display device capable of easily displaying a desired shape.

[0006]

A three-dimensional shape display device according to claim 1 is a shape display means for displaying a shape in a three-dimensional space by a plurality of triangles, and a moving means for moving constituent points forming the triangle. And dividing means for further dividing the triangle into a plurality of triangles according to the amount of movement of the constituent points.

A three-dimensional shape display device according to a second aspect inputs a shape display device for displaying a shape in a three-dimensional space by a plurality of triangles and an instruction mark for instructing movement of constituent points forming the triangle. Input means, a movement amount calculation means for obtaining a movement amount of the constituent point by a function represented by a distance between the indicator sign and the constituent point and a predetermined parameter, and a movement amount of the constituent point is controlled by changing the parameter. The control unit includes a control unit and a moving unit that moves the constituent point according to the amount of movement of the constituent point.

A three-dimensional shape display device according to a third aspect of the present invention is a shape display means for displaying a shape in a three-dimensional space by a plurality of triangles, and a normal vector at a constituent point forming the triangle is a normal line of surrounding triangles. It includes a calculating means for calculating as a weighted average by the area of the vector, and a processing means for performing a predetermined display process on the shape by using the normal vector calculated by the calculating means.

[0009]

In the three-dimensional shape display device according to the first aspect, the triangle for displaying the shape in the three-dimensional space is further divided into a plurality of triangles according to the amount of movement of the constituent points. Can be displayed.

In the three-dimensional shape display device according to the second aspect, the amount of movement of the constituent point can be controlled by changing the parameter of the function, so that the deformation of the shape due to the movement of the constituent point can be changed by changing the parameter of the function. It can be controlled arbitrarily.

In the three-dimensional shape display device according to the third aspect, the predetermined display processing is performed by using the normal vectors at the constituent points calculated as the weighted average by the areas of the normal vectors of the surrounding triangles. Even when the triangle is locally finely divided, a normal vector according to the area of the triangle can be used, and good display processing can be performed.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A three-dimensional shape display device according to an embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing the configuration of a three-dimensional shape display device according to an embodiment of the present invention.

In FIG. 1, the three-dimensional shape display device includes an input unit 1, a shape data management unit 2, a deformation amount calculation unit 3, a shape data operation unit 4, a triangulation processing unit 5, a display data calculation unit 6, and a display. The unit 7 and the control unit 8 are included.

The input unit 1 receives an input from a user,
Input data such as an operation command is output to the control unit 8. The shape data management unit 2 manages the three-dimensional shape data represented by the set of triangles output from the shape data operation unit 4. The deformation amount calculation unit 3 is based on the control command of the control unit 8,
The amount of deformation of the shape data managed by the shape data management unit 2 is calculated and output to the shape data operation unit 4. The shape data operation unit 4 operates the shape data stored in the shape data management unit 2 based on the control command from the control unit 8. The triangle division processing unit 5 divides a triangle forming a three-dimensional shape into a plurality of triangles based on the shape data stored in the shape data management unit 2 based on a control command from the control unit 8. It is output to the shape data operation unit 4.
The display data calculation unit 6 calculates display data from the shape data stored in the shape data management unit 2 based on the control command of the control unit 8, and displays the display data.
Output to. The display unit 7 displays a shape corresponding to the display data calculated by the display data calculation unit 6 based on the control command from the control unit 8. The control unit 8 is connected to each block and controls the operation of each block.

Next, the operation of the above three-dimensional shape display device will be described. FIG. 2 is a flowchart for explaining the operation of the three-dimensional shape display device shown in FIG.

First, in step S1, the amount of movement of each vertex is calculated in the deformation amount calculation unit 3 based on the deformation method instructed by the user in the input unit 1.

Next, in step S2, the shape data operating unit 4 changes the coordinates of each vertex stored in the shape data managing unit 2 based on the amount of movement of each vertex calculated in step S1.

Next, in step S3, the triangulation processing unit 5 refers to the shape data stored in the shape data management unit 2 to check the necessity of dividing the triangle representing the shape data.

Next, in step S4, the triangles to be divided are divided. Next, in step S5, the triangles adjacent to the divided triangles, which will be described later, are processed.

Next, in step S6, the display data calculation unit 6 refers to the shape data stored in the shape data management unit 2 to perform shading processing, for example,
The normal vector at each vertex required for displaying a shape such as Guro shading is calculated as a weighted average by the areas of the normal vectors of the surrounding triangles.

Next, in step S7, the shape is displayed on the display unit 7 based on the shape data and the like created by the above processing.

Next, the process of checking the necessity of dividing the triangle in step S3 shown in FIG. 2 will be described in detail. FIG. 3 is a flowchart for explaining the check processing of the necessity of dividing the triangle in step S3 shown in FIG.

First, in step S8, the inner product of the normal vector of the triangle for checking the necessity of division and the normal vector of the adjacent triangle is calculated.

Next, in step S9, step S
The inner product calculated in step 8 is compared with a predetermined threshold value set in advance, and if the inner product is larger than the threshold value, step S
If not, the process proceeds to step S11.

Next, when it is determined in step S9 that the inner product is larger than the threshold value, in step S10, the division flag of the triangle for which the necessity of division is checked is turned on. When this division flag is ON, in step S4 shown in FIG. 2 described above, it is determined that the triangle is a division target and a predetermined division process is performed.

On the other hand, if it is determined in step S9 that the inner product is not greater than the threshold value, then in step S11 it is checked whether all triangles adjacent to the triangle whose necessity for division is checked are checked. To do. If you haven't checked all triangles,
The process proceeds to step S8, and the subsequent processing is continued. If all triangles are checked, the process proceeds to step S12.

Next, in step S12, it is confirmed whether or not the necessity of division has been checked for all triangles. If the necessity of division is not checked for all triangles, the process proceeds to step S8 and the subsequent processes are continued. If the check is completed for all triangles, the process ends.

The above-mentioned processing for checking the necessity of dividing the triangle is an example, and it may be a processing for checking the necessity of dividing another triangle, such as simply comparing the area of the triangle with a predetermined value.

Next, the division of triangles and the processing of triangles adjacent to the divided triangles in steps S4 and S5 shown in FIG. 2 will be described.

FIG. 4 is a flow chart for explaining the division of triangles and the processing of triangles adjacent to the divided triangles in steps S4 and S5 shown in FIG.

First, in step S13, it is determined whether or not the division flag of the triangle of interest is turned on. If it is turned on, the process proceeds to step S14, and if not, the process proceeds to step S19.

When the triangle division flag is on,
In step S14, the midpoints of the three sides of the triangle are generated.

Next, in step S15, the generated midpoints are connected and divided into four triangles.

Next, in step S16, it is confirmed whether or not the midpoints have been generated on the three sides of the triangle adjacent to the divided triangle. If the midpoint is generated because the surrounding triangles have already been divided, the process proceeds to step S18, and otherwise the process proceeds to step S17.

If no midpoint has been generated, step S
At 17, it is confirmed whether or not any of the sides of the triangle adjacent to the divided triangle is divided twice or more.
If it is divided, the process proceeds to step S18, and otherwise, the process proceeds to step S19.

If it is determined in step S16 that the midpoint has been generated, or if it is determined in step S17 that the midpoint has been divided twice or more, then in step S18,
Split adjacent triangles. This division processing is performed according to the processing of steps S14 and S15 already described.

Next, in step S19, it is determined whether or not the above processing has been performed for all adjacent triangles. If the processing is not completed, step S16
The process proceeds to step S20 and the subsequent processes are continued. If completed, the process proceeds to step S20.

Next, in step S20, it is determined whether or not the division flags have been checked for all triangles. If the check is not completed for all triangles, the process proceeds to step S13, and if it is completed, the process ends.

Next, the three-dimensional shape deformation state by the above processing will be described. FIG. 5 is a diagram illustrating a deformed state of a three-dimensional shape. In FIG. 5, the points indicated by ● are the vertices of each triangle, and the points indicated by × are the points of deformation.

First, as shown in FIG. 5 (a), when the deformation instructing point is designated, the movement amount of each vertex can be expressed by a function of the distance between the deformation instructing point and each vertex. , For example, can be expressed by the following formula.

[0041]

[Equation 1]

From the above equations, it is possible to express the range affected by the deformation by D, the spread of the deformation by a, and the magnitude of the entire deformation by k. Therefore, by changing each parameter, each vertex can be changed. It is possible to easily realize a desired three-dimensional shape deformation by controlling the movement amount. As a result,
The characteristics of the material of the shape to be deformed can also be expressed. The form of the above-mentioned function is arbitrary, and the point of transformation may be not only a point but also a line or a surface.

The amount of movement of each apex can be calculated by the above functional expression, and the amount of movement of each apex indicated by the arrow is calculated as shown in FIG. 5 (b).

When each vertex is moved based on the calculated amount of movement, the shape shown in FIG. 5C is obtained, and the three-dimensional shape can be deformed by designating one designated point.
The desired shape can be easily displayed. The state of deformation can be controlled by deforming each parameter of the above function.

Next, the effect of dividing a triangle according to the amount of movement will be described. FIG. 6 is a diagram for explaining the effect of dividing a triangle.

In FIG. 6 (a), when the vertex indicated by ● moves in the direction of the arrow, if it is moved without dividing the triangle, as shown in (b) of FIG. In some places, the angle between the triangles becomes small, resulting in a sharply pointed shape, which may result in deformation different from the shape intended by the user. However, in the three-dimensional shape display device of the present invention, since the triangles are divided according to the movement amount, it is possible to easily create a delicate shape intended by the user, as shown in (c) and (d) of FIG. Can be expressed in.

The timing of dividing the above triangles is not limited to the process of checking the necessity of dividing the triangles described with reference to FIG. It may be divided when the angle between the surfaces becomes equal to or larger than a certain value or when the user gives an instruction.

Next, the case of dividing one triangle into four triangles will be described. Figure 7 shows one triangle
It is a figure explaining the method of dividing into one triangle.

At the midpoint of each side of the triangle shown in FIG. 7A, vertices are generated as shown by ◯ as shown in FIG. 7B. Next, as shown in FIG. 7C, the vertices are reconnected to form four triangles. The same method can be used to further divide these divided triangles.

Next, the handling of triangles adjacent to the divided triangles will be described. FIG. 8 is a first diagram illustrating how to handle a triangle adjacent to a divided triangle.

When one of the adjacent triangles is divided as shown in FIG. 8A, the triangle is treated as two triangles separated by a broken line as shown in FIG. 8B.

FIG. 9 is a second diagram for explaining how to handle a triangle adjacent to a divided triangle. When handled as two triangles divided by a broken line as shown in FIG. 8B, even when the apex is moved in the direction shown by the arrow as shown in FIG. 9A, FIG. 9B
As shown in (2), since it is handled as two triangles divided by a broken line, it is possible to maintain flatness.

Next, the case of dividing a triangle in which one of the adjacent triangles is divided will be described. Figure 10
[Fig. 8] is a third diagram for explaining how to handle a triangle adjacent to a divided triangle. As shown in (a) of FIG. 10, when the vertices already exist, the existing vertices are used as shown in (b) of FIG. Do.

Next, the handling when two adjacent triangles are divided will be described. FIG. 11 is a diagram for explaining the handling when two adjacent triangles are divided.

As shown in FIG. 11A, when two adjacent triangles are divided, FIG. 11B,
Two treatments shown in (c) can be considered. Regarding display, which one is selected is arbitrary. When calculating the normal vector at each vertex, the calculation is performed for each vertex indicated by ○.

Next, a method of dividing a triangle in which two adjacent triangles are divided will be described. FIG. 12 is a diagram illustrating a method of dividing a triangle in which two adjacent triangles are divided. In this case, the two vertices that have already been generated are used, a new vertex is generated at the midpoint as shown by a circle for the side where no vertex exists, and triangles are divided using these vertices. In addition to the above method, the triangle may be divided when two of the adjacent triangles are divided. When all three adjacent triangles are divided, the already generated vertices are used to divide the triangle.

Next, the adjacent triangles are divided,
The handling when one of the triangles is further divided will be described. FIG. 13 is a diagram for explaining the handling when adjacent triangles are divided and one of them is further divided.

When division is performed as shown in FIGS. 13A to 13B, adjacent triangles are divided once as shown in FIG. 13C. In FIG.
Circles are newly generated vertices, and broken lines are the same as those shown in FIG.

Next, a method of calculating the normal vector of the vertices of a triangle as a weighted average by the areas of the normal vectors will be described. The weighted average by the area of the triangle of the normal vector can be calculated by the following formula.

[0060]

[Equation 2]

FIG. 14 shows a method of calculating the normal vector at the vertices of a partially divided triangle group using the above equation.
Shown in. The phase shown in (a) of FIG.
It is assumed that it is represented by a plurality of triangles as shown in (b). Here, the arrow shown in FIG. 14 is a normal vector of each triangle. When obtaining the normal vector at the point indicated by ◯ in FIG. 14B, the simple average of the normal vectors of the triangles belonging to the vertices of ◯ is obtained as shown in FIG. , The error may increase. Therefore, after adding the values obtained by multiplying the respective normal vectors by the area of the triangle as described above, and normalizing, the normal vector corresponding to the area of the triangle is obtained as shown in (d) of FIG. It is possible to calculate, display processing such as good shooting can be performed, and the shape can be displayed with high quality.

[0062]

According to the three-dimensional display device of the first aspect, the triangle for displaying the shape in the three-dimensional space is divided into a plurality of triangles according to the movement amount of the constituent points, and the fine deformation state is displayed. Therefore, it is possible to easily display a desired shape.

In the three-dimensional shape display device according to the second aspect, the deformation of the shape due to the movement of the constituent points can be controlled by changing the parameter of the function, so that the desired shape can be easily displayed. Becomes

In the three-dimensional shape display device according to the third aspect, good display processing can be performed by using the normal vectors at the constituent points calculated as the weighted average by the areas of the normal vectors of the surrounding triangles. Therefore, even if the triangle is locally finely divided, it is possible to easily display a desired shape.

[Brief description of drawings]

FIG. 1 is a block diagram illustrating a configuration of a three-dimensional shape display device according to an exemplary embodiment of the present invention.

FIG. 2 is a flowchart for explaining the operation of the three-dimensional shape display device shown in FIG.

FIG. 3 is a flowchart illustrating a check process of necessity of dividing the triangle shown in FIG.

FIG. 4 is a flowchart illustrating processing of dividing the triangle shown in FIG. 2 and processing of a triangle adjacent to the divided triangle.

FIG. 5 is a diagram illustrating a deformed state of a three-dimensional shape of the three-dimensional shape display device shown in FIG.

6A and 6B are diagrams illustrating an effect of dividing a triangle in the three-dimensional shape display device illustrated in FIG.

FIG. 7 is a diagram illustrating a method of dividing one triangle into four triangles of the three-dimensional shape display device shown in FIG.

FIG. 8 is a first diagram for explaining how to handle a triangle adjacent to a divided triangle of the three-dimensional shape display device shown in FIG.

9 is a second diagram for explaining how to handle a triangle adjacent to a divided triangle of the three-dimensional shape display device shown in FIG.

10 is a third diagram for explaining how to handle a triangle adjacent to a divided triangle in the three-dimensional shape display device shown in FIG.

FIG. 11 is a diagram for explaining the handling of the three-dimensional shape display device shown in FIG. 1 when two adjacent triangles are divided.

FIG. 12 is a diagram illustrating a method of dividing a triangle in which two adjacent triangles of the three-dimensional shape display device shown in FIG. 1 are divided.

FIG. 13 is a diagram for explaining the handling when the adjacent triangles of the three-dimensional shape display device shown in FIG. 1 are divided and one of the triangles is further divided.

14 is a diagram illustrating a method of calculating a normal vector at a vertex of a triangular group obtained by dividing a part of the three-dimensional shape display device illustrated in FIG.

[Explanation of symbols]

 1 Input Section 2 Shape Data Management Section 3 Deformation Calculation Section 4 Shape Data Operation Section 5 Triangulation Processing Section 6 Display Data Calculation Section 7 Display Section 8 Control Section

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification number Office reference number FI technical display location 7623-5L G06F 15/60 400 D

Claims (3)

[Claims] 1. A shape display means for displaying a shape in a three-dimensional space by a plurality of triangles, a moving means for moving a constituent point forming the triangle, and a triangle for displaying the triangle according to a moving amount of the constituent point. A three-dimensional shape display device further comprising a dividing means for dividing into a plurality of triangles. 2. A shape display device for displaying a shape in a three-dimensional space by a plurality of triangles, input means for inputting an instruction mark for instructing movement of constituent points forming the triangle, and the instruction mark. A movement amount calculation means for obtaining a movement amount of the constituent point by a function represented by a distance from the constituent point and a predetermined parameter; and a control means for controlling the movement amount of the constituent point by changing the parameter. A three-dimensional shape display device including: a moving unit that moves the constituent point according to the amount of movement of the constituent point. 3. A shape display means for displaying a shape in a three-dimensional space by a plurality of triangles, and a normal vector at a constituent point forming the triangle is calculated as a weighted average by areas of normal vectors of surrounding triangles. By using the calculating means and the normal vector calculated by the calculating means,
A three-dimensional shape display device including a processing means for performing a predetermined display process on the shape.