JPH01154282A - Metaball display system - Google Patents

Abstract

PURPOSE:To execute the display at a high speed although it is two-dimensional by calculating the potential sum in each picture element by a potential function generated in accordance with metaball information which has been inputted and bringing it to gradation display. CONSTITUTION:A potential function generating part 1 generates a potential function [for instance, in the expression (1), p0 and (r) denote a value of a potential in the center of a metaball and a distance from the center of the metaball, respectively], based on metaball information (number of metaballs, center position, potential function, cross section information, etc.) which has been inputted. A potential calculating part 2 calculates a potential function, and derives the sum of potential values of each metaball with regard to each position (picture element) on the screen. A display part 3 displays the sum of the potential values related to each picture element by a gradation on the screen 4.

Description

[Detailed Description of the Invention] [Summary] Regarding the metaball display method for displaying metaballs, the purpose is to calculate the potential at each position of the metaball and display it in shading, and to display it at high speed. a potential function generation unit that generates a potential function based on the potential function, a potential calculation unit that calculates the sum of potentials at each position on the screen by each metaball by calculating this potential function, and a potential function generation unit that generates a potential function based on the potential function. The present invention includes a display section that displays the sum on the screen in a shading manner, and the display section is configured to display the metaballs on the screen in a shading manner.

(Industrial Application Field) The present invention relates to a metaball display method for displaying metaballs.

[Conventional technology]

Conventionally, in computer graphics, a metaball (concentration sphere) technique that applies a charge potential field has been known as a means of displaying a curved surface. This designates the position of each charge in three-dimensional space and displays a curved surface expressed in a field of certain dark values. Threshold (
By changing the straightness, you can express various shapes,
It is used in many situations.

However, video generation using metaballs is usually done using ray tracing, so parameters must be specified and
It takes a lot of time to find the shape. Moreover, since the shape of modeling using metaballs is difficult to predict, it is necessary to perform modeling multiple times while interactively changing parameters to generate a desired image. Therefore, for each pixel that is to be displayed three-dimensionally on the screen, ray tracing is used to sequentially find the intersection between the viewpoint and the metaball and the normal line at this intersection, and calculate the angle of the light source illuminating the metaball. If the shading was calculated one by one from the above, it would take a long time, for example, more than 10 minutes, to obtain one screen, making it difficult to quickly generate a desired image.

The present invention aims to calculate the potential at each position of a metaball, display it in shading, and display it at high speed.

[Means for solving problems]

Means for solving the problem will be explained with reference to FIG.

In FIG. 1, a potential function generation unit 1 generates a potential function based on input metaball information.

The potential calculation unit 2 calculates the sum of the potentials by calculating each generated potential function for each position on the screen.

The display section 3 displays the metaball on the screen 4 in a shade corresponding to the sum of the potentials calculated by the potential calculation section 2.

The screen 4 is for displaying metaballs (density spheres) and the like.

[Effect]

In the present invention, as shown in FIG. 1, a potential function generation unit 1 generates a potential function based on input metaball information, and a potential calculation unit 2 calculates this potential function at each position on a screen 4. The sum of the potentials is calculated, and the display unit 3 displays the calculated sum of the potentials on the screen 4 in shading.

Therefore, it is possible to display an overview of the metaball corresponding to the input metaball information in two-dimensional shading at extremely high speed.

〔Example〕

Next, the configuration and operation of one embodiment of the present invention will be explained in detail using FIGS. 1 to 3.

In FIG. 1, the potential function generation unit 1 generates each metaball to be displayed in shading on the screen 4 based on input metaball information (number of metaballs, center position, potential function, cross section information, etc.). Potential functions such as the following equation (1) are generated respectively.

pi ”I)6 esu2 ・・・・・・・・・・・・f
i+Here, p represents the potential value to be displayed in gradation on the screen 4, po represents the potential value (charge) at the center of the metaball, and r represents the distance from the center of the metaball.

The potential calculation unit 2 calculates the potential function generated by the potential function generation unit 1, for example, equation (11), calculates the potential value of each metaball for each position (pixel) on the screen 4, and calculates the sum. be.

The display unit 3 displays the sum of Bo/-/Noyal for each position on the screen 4 calculated by the potential calculation unit 2.
It is displayed on the screen 4 in shading (Figure 3 (b)).
.

Next, follow the steps shown in the flowchart in Figure 2 to
The operation of the structure shown in FIG. 1 will be explained in detail with reference to the drawings.

In FIG. 2, ■ in the figure indicates a state in which the number of metaballs and the center position are set. This can be seen, for example, in Figure 3 (a).
As shown in the figure, this means setting the center position (marked with an X in the figure) of the metaballs A and B, and the center position of the metaballs A and B shown (cut along a certain plane). ing. It should be noted that if the metaballs are displayed as line drawings as shown in FIG. 3(a), the designer will not be able to understand the complex shapes.

■ in the figure indicates a state in which a cross section is specified.
As shown in Figure 3 (a) explained in , metaball A,
This means that when specifying the position of B, the cross-sectional information (Zo) is also used to specify the position at which the metaballs A and B are to be cut.

■ in the figure indicates a state in which potential calculation is performed.

This is done by calculating the potential function generated by the settings of ■ and ■ in the figure, for example, using equation (1), and then calculating the sum of the potentials at each position on the screen 4 using, for example, the C language shown in Figure 3 (c). It means to calculate (described later).

■ in the figure indicates a state in which gradation is displayed. This is shown in the figure.
This means that the sum of the potentials calculated at each position on the screen 4 is displayed in shading, for example, as shown in FIG. 3 (b).

■ in the figure indicates a state in which it is determined whether the metaball displayed in shading on the screen 4 is the image desired by the designer. Change the number, position, etc. of metaballs with ■, and
Repeat. If YES, you can get an overview of the high-speed metaball shading displayed by ■ and ■ in the figure, so next, perform well-known ray tracing of the metaball, which takes time, in ■, and @ in the figure. A state in which a three-dimensional object is displayed on the screen 4 is shown.

As mentioned above, by calculating the sum of potentials by metaballs and displaying this on screen 4 in 7 scales,
It becomes possible to display metaballs at extremely high speed.

FIG. 3(a) shows a line drawing of a cross section with metaballs A and H. In the figure, 6x'' is the center position of metaballs A and B.

FIG. 3 (b) shows an example of metaball display according to the present invention. As mentioned above, this is done by placing charges at the center positions of metaballs A and H, finding the sum of potentials at each position, and It is displayed in shading. This results in
Compared to the case where the images generated by Metaballs A and B are displayed three-dimensionally by ray tracing, the images are displayed extremely quickly and the desired image can be determined while interactively changing the position, number, etc. of Metaballs ASB. It becomes possible to do so.

Then, the final image of the three-dimensional object can be generated by performing well-known ray tracing, which requires a lot of time.
” Figure 3 (c) shows an example of the program already described using the C language for calculating the sum of potentials (in L) for each pixel (vol) on the screen 4. A brief explanation will be given below. .

In FIG. 3(C), the first line for (for each metaball) means that the calculation processing from the second line to the seventh line is performed for each metaball.

The second line “f or (0≦x SX)” is shown in Fig. 3 (
As shown in b), from 0 to X in the X direction on screen 4.
This means that the arithmetic processing from the third row to the sixth row is performed on the pixels in the section up to.

"for(0≦y≦Y)" in the third line is the fourth and fifth line for pixels in the section from 0 to Y in the y direction on the screen 4, as shown in FIG. This means that the arithmetic processing in the row is performed.

1nt=+IIeta(x,y);' in the 4th line is
Coordinate (x.

Calculate the value of the potential at the position of y). For example, use the formula (
11.

5th line vol (x) (Y) = vol (x
) (y)+1ntH'' means that when a plurality of metaballs exist, the sum of potentials due to these metaballs is calculated for each pixel.

The above program calculates the sum of potentials for each pixel on the screen 4. The metaball display according to the present invention shown in FIG. 3(B) is performed by displaying the calculated potential sum in shading on the screen 4.

〔Effect of the invention〕

As explained above, according to the present invention, the sum of potentials at each pixel on the screen is calculated using a potential function generated in response to input metaball information, and this sum of potentials is displayed in shading on the screen. Because it uses a display configuration, metaballs can be displayed on the screen extremely quickly in shading. As a result, the display of metaballs, which would otherwise require a huge amount of time, can be displayed extremely quickly, albeit in a two-dimensional manner, to the extent that the designer can understand, and various metaballs can be displayed interactively through trial and error. It becomes possible to quickly generate a desired video (scene).

[Brief explanation of the drawing]

FIG. 1 is a block diagram of one embodiment of the present invention, FIG. 2 is a flowchart explaining the operation of the present invention, and FIG. 3 is a diagram explaining the operation of the present invention. In the figure, 1 represents a potential function generation section, 2 a potential calculation section, 3 a display section, 4 a screen, and 5 a change section. OJ Kidney'Month's Movement vL August 70-Nayat 2nd Figure

Claims (1)

[Claims] A metaball display method for displaying metaballs includes a potential function generation unit (1) that generates a potential function based on specified metaball information, and a screen (1) that calculates this potential function and displays each metaball. 4)
A potential calculation unit (2) that calculates the sum of potentials at each position above; and this potential calculation unit (2).
and a display section (3) that displays the sum of the potentials calculated by on the screen (4) in a shaded manner, and the display section (3) displays the metaballs on the screen (4) in a shaded manner. A metaball display method characterized by being configured to.