JPH0721407A - Method for displaying picture - Google Patents

Abstract

PURPOSE:To attain a non-linear fog effect faithful to a landscape on the practical earth by high speed arithmetic processing without increasing the size of harware. CONSTITUTION:This picture display method generates display picture data on a two-dimensional screen from picture data consisting of three-dimensional information including depth information Z and displays a three-dimensional object on the two-dimensional screen. In the case of displaying an object so as to observe it faintly in accordance with a distance far from a visual point by mixing the color and brightness of an object, the color of fog and the brightness of air based upon a prescribed mixing coefficient to be a function of depth information Z, the mixing coefficient is generated from a hyperbola function.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image display method for displaying a three-dimensional image on a two-dimensional screen, such as computer graphics.
The present invention relates to an invention that enhances a three-dimensional visual effect by a so-called fog effect.

[0002]

2. Description of the Related Art In devices that apply computer graphics, such as graphic computers and game consoles,
It is required to realistically represent a three-dimensional object or background on a two-dimensional screen. Shading is often used as a realistic three-dimensional representation method on a two-dimensional screen. Shading is a method of making a three-dimensional (three-dimensional) object look by determining the position and direction of the light source, calculating what kind of light and shade (shadow) the object to be rendered can be drawn, and drawing it.

FIG. 7 illustrates the principle of shading. Here, for simplicity, the shading by the parallel light source will be described. In addition, the light source and the object have only brightness, and do not consider the color.

In the case of the parallel light source 1, the position of the light source is not given, but it has only the direction and strength. To calculate the strength of the shadow at the point of the object 2, the normal vector V of the object surface at that point is calculated.
The inner product of I and the light source vector VL representing the direction and strength of the light source is taken as the shadow strength. At this time, the negative value is replaced with 0.

As described above, since the shading due to shading is determined by the shape and orientation of the object, the same shading is given wherever the object is in space. Therefore, it is possible to express a clear space like space by shading alone, but it is difficult to express the actual landscape on the earth. This is because, in the actual landscape on the earth, light is attenuated by the atmosphere, and as shown in FIG.

Therefore, even in computer graphics, there is a case where the brightness of an object and the brightness of the atmosphere are mixed (blending) by using the distance from the viewpoint to the object so that the farther the object is, the more faint it looks. FIG. 9 illustrates one of these methods.

First, a point Pmax at which an object is completely invisible due to the atmosphere and a point Pmin at which the influence of the atmosphere does not appear are determined, and the distances from the viewpoint to these points are respectively set to Z.
Determine max and Zmin. Next, let Z (depth information) be the distance from the viewpoint to the position Pz of the object. The brightness of the object is L
0, and the brightness (darkness) of the atmosphere is L1, the brightness L of the object seen from the viewpoint is L = L0 * (Zmax-Z) / (Zmax-Zmin) + L1 * (Z-Zmin) / ( Zmax-Zmin) (Equation 1-1). That is, this is the brightness L of the object.
This is a method of linearly interpolating 0 and the brightness L1 of the atmosphere.

FIG. 9 is a graph showing the interpolation function (function of the mixing coefficient) IL (Z) = (Z-Zmin) / (Zmax-Zmin) (Equation 1-2) in this case. It is clipped to 0 from (= 0) to Zmin and to 1 from Zmax to infinity.

The perspective can be obtained also by the mixing coefficient by the interpolation by such a linear function, but the following can be understood when considering the attenuation of light by the actual atmosphere, that is, the fog effect.

The fog effect is a phenomenon in which fine water drops cover a space and a distant view is blurred. Physically considering this, the object is a distance dZ from the distance Z,
If you move a little away, there will be fine particles of water droplets between the distances, and the object will be covered by the water droplets.

Now, the brightness at the position of the distance Z of the object is L
And The ratio of water droplets floating in the air is a (a <1.0
), The color of the object is slightly blurred while moving away by a slight distance dZ, and becomes (1-a · dZ) × L (Equation 2).

If the color of the water droplet itself is L1, then the color of the water droplet is added by a.dZ.L1 (Equation 3). Therefore, the brightness (L + dL) of the object at the distance Z + dZ from the viewpoint is After all, L + dL = (1-a · dZ) L + a · dZ · L1 (Equation 4). When this is solved under the condition of L = L0 when Z = 0, L = (L0-L1) * exp (-a.Z) + L1 (Equation 5) L = L0 * exp (-a.Z) + L1 × (1-exp (−a · Z)) (Equation 6). This is the original color L0 at Z = 0 and L1 at Z = ∞.
, Are asymptotic exponential functions. FIG. 10 is a graph showing the exponential function {1-exp (-a · Z)}.

Here, as in the case of linear interpolation, Zma
When x and Zmin are set and Expression 6 is slightly modified to obtain Expression 7, the interpolation function INL (Z) becomes as shown in the graph of FIG.

L = L0 × (1−INL (Z)) + L1 × INL (Z) INL (Z) = (1-exp (−a (Z−Zmin))) ÷ (1−exp (−a (Zmax -Zmin))) (Equation 7)

[0015]

As is apparent from the comparison between FIG. 9 and FIG. 11, linear interpolation is far from the actual fog effect and is not realistic. In order to obtain a realistic fog effect, the mixing coefficient obtained by the non-linear interpolation given by (Equation 7) may be used, but the calculation of Equation 7 requires exponential calculation, which takes time, It was difficult with such a simple system.

In view of the above points, it is an object of the present invention to provide an image display method capable of performing a non-linear interpolation similar to the equation 7 at high speed and obtaining a realistic fog effect. Is.

[0017]

In order to solve the above problems, the present invention uses a hyperbolic function as an interpolation function.

That is, according to the present invention, display image data on a two-dimensional screen is generated from image data composed of three-dimensional information including depth information, and a three-dimensional object is displayed on the two-dimensional screen. In the image display method, the brightness of the object and the brightness of the atmosphere are mixed using a predetermined mixing coefficient that is a function of the depth information, and the more distant from the viewpoint, the more dimly displayed. , The above mixing coefficient is generated from a hyperbolic function.

[0019]

2 is a graph of a hyperbolic function of -1 / Z, where Z>
It is the 0 part. As is clear from FIG. 2, this is a convex function as in the graph (FIG. 11) of the interpolation function (exponential function) of Expression 7. As shown in FIG. 3, the function of FIG. 2 is translated by b in the Z direction and by c in the direction orthogonal to the Z direction to obtain the equation 7
By setting Zmax and Zmin similar to, it is possible to create an interpolating function IGL (Z) as shown below.

L = L0 × (1-IGL (Z)) + L1 × IGL (Z) (Equation 8-1) IGL (Z) = K / (Z + b) + c (K <0) (Equation 8-2) Z = Zmax, Z = Zmin in the interpolation function IGL (Z)
Is substituted, IGL (Zmin) = K / (Zmin + b) + c = 0 (Equation 8-3) IGL (Zmax) = K / (Zmax + b) + c = 1.0 (Equation 8-4) is obtained. Equations (8-3) and (8-4) are quadratic equations for b and c, but can be solved as follows if b with a small amount of parallel movement is selected.

[0021]

[Equation 1]

[0022]

[Equation 2] Here, K is a parameter that changes the curvature of the graph.

As is clear from a comparison between FIG. 3 and FIG. 11, the graph of the interpolation function IGL (Z) is very similar to the graph of the exact fog effect interpolation function INL (Z), and It can be seen that −2 is an approximation of Equation 7. Therefore, instead of the interpolation function INL (Z), the interpolation function IGL
By using (Z), it is possible to obtain an effect similar to the actual fog effect for the display image.

By the way, in the three-dimensional computer graphics to which the present invention is applied, when the object is drawn, the object is perspective-transformed from the three-dimensional space onto the two-dimensional screen screen, so that the three-dimensional coordinates of the object are viewed from the viewpoint. It is necessary to divide by the distance Z of, and many have a function of executing the division by Z at high speed.

Since the above-mentioned hyperbolic function divides by the distance Z, the present invention uses the division function for perspective transformation to approximately perform the above-mentioned nonlinear fog calculation. Realistic fog effect can be realized at high speed without increasing the hardware scale.

[0026]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the image display method according to the present invention will be described below with reference to the drawings. FIG. 4 is a block diagram showing an example of a system for carrying out an embodiment of the present invention. In this block diagram, among the graphic computers and game consoles to which the present invention mainly applies,
Only the part that executes three-dimensional computer graphics and draws is shown.

Prior to the description of FIG. 4, an outline of the image drawing processing by three-dimensional computer graphics will be described. In computer graphics, an object to be drawn is divided into small basic figures (polygons), and the shape, position, orientation, color, pattern, etc. of the polygons are given as polygon data that determines an image. The shape, position, and orientation of a polygon are determined by the coordinates of its vertices.

As the image drawing process, first, for example, the drawing data stored in the memory or the recording medium is read,
From the drawing data, the vertex coordinates of the small polygons forming the object and the brightness data are obtained. Next, for example, based on the viewpoint position information input from a predetermined input means, the screen that directly faces the viewpoint is hypothesized, and the vertex coordinates of the small polygon are converted into the coordinates on the screen.

The coordinate transformation of the vertex coordinates is a three-dimensional coordinate transformation process for transforming the orientation of the object based on the viewpoint, and a perspective according to the distance Z from the viewpoint to the object on the screen. Conversion (two-dimensional coordinate conversion) is performed. Three
The dimensional coordinate conversion is performed using a coordinate conversion matrix, and the perspective conversion is performed by a division operation using depth information (Z coordinate information) of the vertices.

The following equations 10-1 and 10-2 are calculations executed by perspective transformation. Here, X and Y are the X and Y coordinates of the three-dimensional space after the three-dimensional coordinate conversion, h is the distance from the viewpoint to the screen, and SX and SY are the X on the screen.
The coordinates are the Y coordinate.

SX = X × h / Z (Equation 10-1) SY = Y × h / Z (Equation 10-2) Then, the polygon is drawn on the video RAM according to the obtained converted vertex coordinate data. It is performed by the given brightness value. At this time, when the fog effect processing is performed, the above-described interpolation function is used to replace the brightness value of the small polygon.

FIG. 4 shows the configuration of an image processing system for performing the above processing at high speed. In the system of FIG. 4, the CPU 12, the main memory 13, the geometry processor 14, and the raster processor 15 are connected to the system bus 11, and the video RAM 16 is connected to the raster processor 15. The digital video signal read from the video RAM 16 is D /
It is converted into an analog video signal by the A converter, supplied to the display monitor device, and displayed on the screen.

The CPU 12 controls the entire system and transfers data between blocks via the system bus 11. Programs and data are stored in the main memory 13. The geometry processor 14 calculates coordinates for determining an image to be drawn from a given program or data and calculates pixel values (luminance or color). The raster processor 15 draws on the video RAM 16 using the calculation result of the geometry processor.

FIG. 5 shows a detailed configuration example of the geometry processor 14, in which the geometry processor 1
4 is a product-sum calculator 2 for coordinate conversion and pixel value calculation
1 and a divider 22. Divider 2
2 is used in this example for perspective transformation and fog effect interpolation calculations.

FIG. 1 is a flow chart showing an example of the procedure for calculating the fog effect according to the image display method according to the present invention. Here, a procedure for performing coordinate conversion, pixel value conversion, and perspective conversion is also shown.

[Step S1] First, the CPU 12 calculates the vertex coordinates and brightness of the small polygons forming the object in the three-dimensional space by the product-sum calculator 21 of the geometry processor 14 according to the program and data in the main memory 13. To do.

[Step S2] Next, in step S2, the geometry processor 14 makes the divider 22
Is used to perform the calculations of the above equations 10-1 and 10-2 to perform perspective transformation from the three-dimensional coordinates of the vertices of the small polygon to obtain the screen coordinates.

[Step S3] The interpolation function IGL (Z) is obtained from the Z coordinate of the three-dimensional coordinates of the vertices of the small polygon according to the above-mentioned equation 8-2. At that time, the geometry processor 14 calculates the interpolation function IGL (Z) using the perspective-dividing divider 22.

[Step S4] The brightness L of the object viewed from the viewpoint is calculated according to the equation 8-1 by the geometry processor 14
Calculate with. Then, the brightness L of the calculation result is replaced with the brightness of the small polygon to generate the fog effect.

[Step S5] Steps S1 to S4 are repeated for all the small polygons forming the object.

Next, FIG. 6 is a flow chart showing another embodiment of the image display method according to the present invention.

In this example, the constant b in the equation 8-2 is 0, that is, only Zmax is specified. Formula 8-1 to Formula 8-4 are respectively L = L0 * (1-IHL (Z)) + L1 * IHL (Z) (Formula 11-1) IHL (Z) = K / Z + c (Formula 11-2) IHL (Zmax) = K / Zmax + c = 1.0 (Equation 11-3) c = Zmax-K (Equation 11-4).

Here, IHL (Z) = K / Z + c = (K / h) × (h / Z) +
c. Therefore, in this case, not only the division function for perspective transformation can be used, but also the calculation result (h / Z) at the time of perspective transformation can be used to calculate the fog effect at higher speed.

The example of FIG. 6 differs from the example of FIG. 1 in that
Only step S3 is changed to step S3 '. In step S3 ′, the interpolation function IHL (Z) is obtained from the Z coordinate of the three-dimensional coordinates of the vertices of the small polygon according to the equation 11. At that time, the interpolation function IHL (Z) is calculated using the division result in the perspective transformation.

In the above description, for the sake of simplicity, only the luminance has been described. However, in the case of color display, by mixing the color of the object and the color of the fog,
The fog effect can be obtained. In that case, for example, the color of the object and the color of the fog are each composed of three primary colors, and the display color is determined by performing the above-described interpolation calculation for each primary color information.

[0046]

As described above, according to the image display method of the present invention, the interpolation function for generating the mixing coefficient for the fog effect which has the effect of increasing the reality of the image by computer graphics is used. By approximating using a hyperbolic function instead of an exponential function that accurately corresponds to the real one, a non-linear fog effect faithful to the actual landscape on the earth can be processed at high speed without increasing the hardware scale. Can be realized by

[Brief description of drawings]

FIG. 1 is a flow chart for explaining an embodiment of an image display method according to the present invention.

FIG. 2 is a diagram showing a part of an example of a graph of a hyperbolic function.

FIG. 3 is a diagram showing an example of a graph of an interpolation function by a hyperbolic function used in the present invention.

FIG. 4 is a block diagram showing a configuration example of a system for carrying out an embodiment of the present invention.

5 is a diagram showing a configuration example of a part of the system of FIG.

FIG. 6 is a flowchart for explaining another embodiment of the image display method according to the present invention.

FIG. 7 is a diagram illustrating shading.

FIG. 8 is a diagram illustrating a fog effect.

FIG. 9 is a diagram showing an example of a graph of a linear interpolation function.

FIG. 10 is a diagram showing an example of a graph of an exponential function.

FIG. 11 is a diagram showing an example of a graph of an interpolation function using an exponential function.

[Explanation of symbols]

 11 System Bus 12 CPU 13 Main Memory 14 Geometry Processor 15 Raster Processor 21 Sum of Products Calculator 22 Divider

Claims (3)

[Claims] 1. An image display method for generating display image data on a two-dimensional screen from image data composed of three-dimensional information including depth information and displaying a three-dimensional object on the two-dimensional screen. , The color and brightness of the object and the color of fog and the brightness of the atmosphere are mixed by using a predetermined mixing coefficient that is a function of the depth information, and the farther from the viewpoint, the more vague the display. And an image display method, wherein the mixing coefficient is generated from a hyperbolic function. 2. The image display method according to claim 1, wherein display image data on the two-dimensional screen is generated by performing a geometric operation including division using depth information from the image data including the three-dimensional information. Then, the image display method in which the division for calculating the hyperbolic function for generating the mixing coefficient is performed using the division function. 3. The image display method according to claim 2, wherein processing using the mixing coefficient is performed using a division result when the two-dimensional display image data is generated from the image data including the three-dimensional information. An image display method characterized by being performed.