JPH08305890A - Method and device for phon shading - Google Patents

Abstract

PURPOSE: To make a drawing system easily turnable into hardware. CONSTITUTION: Angles θ1 and α1 determining the directivity of a light beam of every pixel are interpolated with the angles θa (∼θc) and αa (∼αc) of vertexes (DDAs 1 and 2), and reflected light vector quantities cosθ and cos<n> α are found by referring to function tables in a ROM 3 and a RAM 4 according to the obtained angles, and those are multiplied by diffusion and mirror surface reflection effective incident light intensity values Id and Is to find reflected light intensity values Id.cosθ and Is.cos<n> α(multipliers 5 and 6 and storage parts 10 and 11) and an ambient light intensity value Ia is added to them (adders 7 and 8) to calculate the total reflected light intensity I. Consequently, phon shading is actualized by a simple calculation. Consequently, the device can be easily turned into hardware and the arithmetic processing is speeded up.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a phon shading method and apparatus for three-dimensional computer graphics, which aims at high-quality drawing using a reflected light (diffuse, specular reflection) effect, and particularly to a drawing processor. Is what is used.

[0002]

2. Description of the Related Art As the performance of graphics LSIs increases year by year, it is required to improve beautiful drawing by smooth shading. When expressing the surface of an object as part of that method, individual highlights due to reflected light (the shiningly visible portion of a glossy object) have a great influence.

In the prior art, there are two drawing methods using Gouraud shading and phon shading to represent this highlight.

A drawing method by Gouraud shading will be described with reference to FIG. In the figure, a triangle is drawn at an arbitrary position in the drawing area, and each vertex of this triangle is represented by a, b, c.
And the brightness values represented by the three primary colors are set for each. For example, at vertex a, red has the strongest luminance value,
When blue has the strongest luminance value at the vertex b, the luminance value of each pixel in the triangle of the vertexes a → b is visually smoothly interpolated from red → purple → blue. This is a triangle drawing by Gouraud shading by interpolating the "brightness value" of each pixel by brightness calculation using a bilinear function.

[0005]

However, with Gouraud shading, even if smooth luminance values can be interpolated when a curved surface object is drawn, interpolation that partially illuminates is not possible regardless of surrounding luminance values. I'm having trouble drawing with high-definition highlights.

On the other hand, the phon shading provides such a high-quality highlight, and the drawing method by the phon shading will be described below with reference to FIGS. 6 and 7. In Phong shading, a normal vector is obtained by interpolating a certain object for each pixel, and the intensity of reflected light is obtained. This reflected light is affected by the configuration, orientation, shape and orientation of the object surface and the characteristics (material, etc.) of the light source, and is caused by the diffuse reflection that is uniformly radiated in any direction and is reflected on the surface of the object. Characterized by specular reflection. FIG. 6 shows a case where light is reflected at an arbitrary point A on a curved surface object, and illustrates diffuse reflection and specular reflection, and angles necessary for obtaining the reflected light intensities thereof. Here, θ1 is an angle formed by a vector from the point A toward the light source and a normal vector of the object surface, and is related to diffuse reflection. θ2
Is the angle formed by the reflected light and the normal vector, and α is the angle formed by the reflected light and the vector from the point A toward the line of sight, and is related to the specular reflection that is always affected by the observer's viewpoint.

The light source calculation of the reflected light of the phon shading uses the ambient light, diffuse reflection, and specular reflection of the environment (default value) of the object. The method of calculating the intensity (I) of the reflected light is obtained by the formula shown below.

I = La · Ka + L1 · Kd · cos θ + L1 · Ks · cos ⁿ α where La is ambient light intensity, Ka is ambient light diffuse reflection coefficient, L1 is intensity of incident light from the light source, and Kd is from the light source. Is the diffuse reflection coefficient of the incident light, Ks is the reflectance coefficient, and the n-th power is an index that approximates the dispersion of the specularly reflected light.

Further, cos θ and cos α are obtained by the following equations. Here, ↑ n (“↑” means a vector, and here, the vector n is shown), ↑ L, ↑ R, and ↑ S are shown in FIG.
Corresponding to each vector of
(Xn, Yn, Zn), L = (X1, Y1, Z1), R
= (Xr, Yr, Zr), S = (Xs, Ys, Zs).

[0010] cosθ = ↑ n · ↑ L = n · L / | n || L | = (Xn · X1 + Yn · Y1 + Zn · Z1) ÷ (Xs 2 + Yn 2 + Zn 2) 1/2 · (X1 2 + Y1 ² + Z1 ² ) ^1/2 cos α = ↑ R ・ ↑ S = R ・ S / | R |｜ S ｜ = (Xr ・ Xs + Yr ・ Ys + Zr ・ Zs) ÷ (Xr ² + Yr ² + Zr ² ) ^1/2・(Xs ² + Ys ² + Zs ² ) ^1/2 The problem of phon shading calculated using these equations will be described with reference to FIG. In FIG. 7, specular reflection as in FIG. 6 is performed on each pixel on the triangle. Taking each pixel of this vertex b → c as an example, ↑ L,
↑ S is fixed, but ↑ n changes by interpolating three components of x, y, and z, and ↑ R also changes by this change.
The problem is that normalization is required because | n | and | R | also change with this change, and the range in which the variable changes is infinite. It is repeated for each pixel using square root and division. It requires complicated calculations. Also, there is a problem that it is difficult to realize the system by hardware due to the large amount of calculation.

The present invention has been made in view of the above problems of the prior art, and an object of the present invention is to provide a smooth shading method and a device thereof which enable hardwareization of a drawing system. is there.

[0012]

According to the phon shading method of the present invention, in three-dimensional computer graphics in which an object is three-dimensionally displayed by a polygonal mesh, the normal line at each vertex of the polygonal mesh and the angle of the incident light ray. And calculating the first angle information indicating the angle between the incident ray and the normal line for each pixel located between the vertices in the polygon mesh, and the line-of-sight and reflection at each vertex of the polygon. Calculating second angle information indicating an angle between a line of sight of each pixel located between the vertices in the polygonal mesh and a reflected light ray based on an angle with the light ray; and diffusing the first angle information. In the reflection normalization coefficient,
Converting the second angle information into a specular reflection normalization coefficient, and an effective incident light intensity obtained by adding the diffuse reflection normalization coefficient and the incident light intensity to the object to the diffuse reflection coefficient to the object. The diffuse reflection intensity of the object is calculated by multiplying by, and the specular reflection normalization coefficient and the effective incident light intensity in which the specular reflection coefficient of the object is added to the incident light intensity of the object are multiplied to obtain the object The method further comprises the steps of obtaining a specular reflection intensity and calculating a reflected light intensity by adding the diffuse reflection intensity and the specular reflection intensity to the ambient light intensity of the object.

In converting the angle information into each coefficient,
When the first angle information is θ, the diffusion normalization coefficient is c
It is possible to use a diffuse reflection function table obtained as osθ, and use a specular reflection function table obtained as the specular reflection intensity cos ⁿ α, ^where α is the second angle information and n is the dispersion approximation index of the specular reflection light of the object. desirable.

Further, the phon shading device of the present invention is a three-dimensional computer graphics for three-dimensionally displaying an object by a polygon mesh, based on the normal line at each vertex of the polygon mesh and the angle of the incident light ray. The first angle information indicating the angle between the incident ray and the normal line for each pixel located between the vertices of the polygonal mesh is calculated by interpolation calculation, and the line of sight and reflection at each vertex of the polygonal mesh are calculated. Angle information interpolating means for calculating, by interpolation calculation, second angle information indicating the angle between the line of sight of each pixel located between the vertices in the polygonal mesh and the reflected ray based on the angle with the ray;
The first angle information is used as a diffuse reflection normalization coefficient, and the second
Angle information conversion means for respectively converting the angle information of the specular reflection normalization coefficient, and the effective incident light intensity obtained by adding the diffuse reflection normalization coefficient and the incident light intensity to the object to the diffuse reflection coefficient to the object. By multiplying the diffuse reflection intensity calculation means for obtaining the diffuse reflection intensity of the object by multiplying the specular reflection normalization coefficient and the incident light intensity on the object with the specular reflection coefficient of the object. Then, the specular reflection intensity calculation means for obtaining the specular reflection intensity of the object, and the total reflection light intensity from the object by adding the diffuse reflection intensity and the specular reflection intensity to the ambient light intensity of the object A reflected light intensity calculation means is provided.

The angle information interpolating means can be constituted by a digital differential analyzer.

This angle information conversion means is provided with a diffuse reflection function table for obtaining the diffusion normalization coefficient as cos θ, where the first angle information is θ, and the second angle information is α, the specular reflection light of the object. When the variance approximation index is n,
It is desirable to have a configuration having a specular reflection function table for obtaining the specular reflection intensity as cos ⁿ α.

R is used as the diffuse reflection function table.
RA with OM table as specular reflection function table
It can be configured to have an M table.

[0018]

According to the present invention, the angle information that determines the directionality of the light ray vector for each pixel is interpolated by the angle information of the vertex, and the reflected light ray vector amount for each pixel is obtained based on this interpolated angle information. Since the phon shading can be realized by a simple calculation in which the total reflected light intensity is calculated by adding these, the hardware can be easily realized.

That is, there is a drawing method by phon shading in order to make the drawing showing the highlight by the conventional Gouraud shading beautiful. However, the conventional interpolation calculation method at the time of drawing by phon shading interpolates the three components (x, y, z) of the normal vector and calculates the light source as the normal line and the incident light and the sight line and the reflection as shown in the above formula. It has complex operations that are processed by the inner product of light and the normalization calculation. In contrast to this conventional method, the present invention performs processing by angle interpolation between normal and incident light, line of sight and reflected light, and light source calculation (preferably calculation using a trigonometric function table), so that calculation can be simplified.

In the present invention, the intensity (I) of the reflected light is calculated by the following formula.

I = Ia + Idf1 (θ) + Isf2 (α) where Ia = LaKa, Id = L1Kd, Is =
L1 · Ks, f1 (θ) = cos θ (diffuse reflection normalization coefficient), f2 (α) = cos ⁿ α (specular reflection normalization coefficient)
Is.

Trigonometric functions f 1 (θ), f prepared in advance
A table for solving 2 (α) will be described with reference to FIG. In the figure, n is an index that approximates the dispersion of specularly reflected light, and the larger the value of n, the more metallic or glossy the surface. This figure shows cos ⁿ α in the range of the angle −π / 2 ≦ α ≦ π / 2 (excluding the range where the light source is in the shadow of the object). Among the A, B, and C curves with different n values, A is the angle between the normal and the incident light (θ), and B and C are the angle between the line of sight and the reflected light (α).
The cos ⁿ α for According to the present invention for obtaining the reflected light intensity (I) for each pixel by forming a table of trigonometric functions such as storing this angle and data corresponding thereto at each address and processing using the constants Ia, Id, Is. It is possible to realize high-quality drawing that can display highlights that make the most of the characteristics of conventional phon shading.

[0023]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the configuration of a phon shading device according to an embodiment of the present invention. In the figure, a DDA (digital differential analyzer) 1 uses a normal line na (~ nc) at each vertex of a polygonal mesh and an angle θa (~ θc) of an incident ray L to determine each vertex of the polygonal mesh. The first angle information indicating the angle θ1 between the incident ray and the normal line of each pixel located between them is calculated by interpolation calculation, and this first angle information is converted into address information for accessing the ROM 3 described below. Output. DDA2 is
Based on the angles αa to αc between the line of sight S and the reflected ray R at each vertex of the polygonal mesh, the angle α between the line of sight and the reflected ray of each pixel located between the respective vertices in the polygonal mesh
The second angle information indicating 1 is calculated by interpolation calculation and converted into address information for accessing the RAM 4 described below.

In the ROM 3, the incident light-normal angle θ 1 is
A function table for converting to sθ1 is stored. This table is read and accessed by the address information from the DDA1, and cosθ1 which is the conversion value of the first angle information is read. The RAM 4 stores a function table for converting the angle α formed by the line-of-sight vector S and the reflected light vector R into cos ⁿ α. This table stores a function table which is read out and accessed by the address information from the DDA 2 and converted into cos ⁿ α which is the conversion value of the second angle information. Here, the calculation of cos ⁿ α is performed by R
The AM is used because n varies depending on the material of the surface of the object, and the function table can be changed for each object.

An example of these tables is shown in FIG. The table shown in this figure is 0 ≦ α ≦ π in the curves A and B of FIG.
It shows data (cos ⁿ α1) stored at 32 addresses for each angle of / 2. FIG.
(A) is the data of cos α, (B) is the data of cos ⁿ α1 / n
= 5 is a table.

The storage unit 10 stores the effective diffuse incident light intensity Id (L
1 × Kd), and the multiplier 5 multiplies cos θ1 and its Id to obtain the diffuse reflected light intensity Id · cos θ
Ask for 1. The storage unit 11 stores the effective specular incident light intensity Is (L
1 × Ks), and the multiplier 6 multiplies cos ⁿ α and its Is to multiply the specular reflection light intensity Is.cos ^n.
Find α.

The adder 7 has a diffuse reflection light intensity Id .multidot.cos .theta.1 from the multiplier 5 and a specular reflection light intensity Is from the multiplier 6.
-Add cos ⁿ α. The storage unit 9 stores the ambient light intensity Id.
The adder 8 adds this Id and Id.cos .theta.1 + Is .cos ⁿ .alpha. From the adder 7 to obtain the total diffuse reflected light intensity I.

As described above, according to this embodiment,
The amount of calculation can be reduced. That is, in the conventional Phong shading, the reflected light intensity is obtained with a huge amount of calculation by the normal vector for each pixel and the calculation for normalization accompanying it, whereas in the present embodiment, the angle for each pixel is calculated. Since the reflected light intensity is obtained through interpolation of the angle information using the function table, the amount of calculation can be reduced, and the hardware to be realized can be simple in configuration.

Further, by using the hardware as described above, the interpolation for each pixel and the calculation of the reflected light intensity can be speeded up.

Further, although the light source is a parallel light beam in the above description, the advantage of the present invention is improved as the distance between the light source and the object is shorter. FIG. 4 compares the diffuse reflection at a point P1 near the light source on the plane object and a point P2 far from the light source. As shown in the figure, the angle θn formed by the vector from the arbitrary point P1 to the light source and the normal vector and the angle θn formed by the vector from the point P2 to the light source and the normal vector
m is very different. When the diffuse reflected light intensity is obtained by the conventional phon shading, it is necessary to interpolate the incident light ray vector for each pixel, and the enormous amount of calculation is further increased. However, in the present invention, the small amount of calculation of P1 and P2 is required. Can be increased.

As a result, more realistic and beautiful highlights can be obtained, the range of practicality is expected to be expanded due to the reduction of the calculation amount, and the speed can be further increased depending on the method.

[0032]

As described above, according to the present invention, the angle information for determining the directionality of the light ray vector for each pixel is interpolated by the angle information of the apex and each pixel is calculated based on the interpolated angle information. The total reflected light intensity is calculated by obtaining the reflected ray vector amount of
Since the phon shading can be realized by such a simple calculation, hardware implementation becomes easy.

[Brief description of drawings]

FIG. 1 is a block diagram showing the structure of a phon shading device according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing functions of diffusion and specular reflection which are the basis of the ROM or RAM function table configuration of the apparatus shown in FIG.

FIG. 3 is an explanatory diagram showing the configuration of a ROM or RAM function table of the device shown in FIG.

FIG. 4 is an explanatory diagram showing a state of change of an incident light vector for each pixel, which is taken into consideration in calculation of reflected light intensity by the apparatus shown in FIG.

FIG. 5 is an explanatory diagram showing conventional Gouraud shading.

FIG. 6 is an explanatory diagram showing a reflection phenomenon of an incident light ray on a curved surface object.

FIG. 7 is an explanatory diagram showing how the normal vector of each pixel changes in the calculation of reflected light intensity by the apparatus shown in FIG.

[Explanation of symbols]

 1, 2 DDA 3 ROM 4 RAM 5, 6 Multiplier 7, 8 Adder 9-11 Storage unit

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[Procedure amendment]

[Submission date] June 27, 1995

[Procedure Amendment 1]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 6

[Correction method] Change

[Correction content]

[Figure 6]

Claims (6)

[Claims] 1. In three-dimensional computer graphics for three-dimensionally displaying an object by a polygonal mesh, each vertex of the polygonal mesh is based on a normal line at each vertex of the polygonal mesh and an angle of an incident ray. The first angle information indicating the angle between the incident ray and the normal line for each pixel located between them is calculated, and based on the angle between the line of sight and the reflected ray at each vertex of the polygon, the polygon mesh Calculating second angle information indicating an angle between a line of sight of each pixel located between the vertices and a reflected ray; and using the first angle information as a diffuse reflection normalization coefficient and the second angle information.
Angle information of the specular reflection normalization coefficient, respectively, and multiplying the diffuse reflection normalization coefficient and the effective incident light intensity that adds the diffuse reflection coefficient to the object to the incident light intensity to the object. The specular reflection intensity of the object is obtained by multiplying the specular reflection normalization coefficient and the effective incident light intensity obtained by adding the specular reflection coefficient of the object to the specular reflection normalization coefficient. And a step of adding the diffuse reflection intensity and the specular reflection intensity to the ambient light intensity of the object to calculate the reflected light intensity. 2. When converting the angle information into each coefficient, when the first angle information is θ, the diffusion normalization coefficient is cos.
Using the diffuse reflection function table obtained as θ, and using the second angle information as α and the dispersion approximation index of the specular reflection light of the object as n, use the specular reflection function table obtained as cos ⁿ α for the specular reflection intensity. The phone shading method according to claim 1, wherein the phone shading method is used. 3. A three-dimensional computer graphics for three-dimensionally displaying an object by a polygon mesh, wherein each vertex of the polygon mesh is based on a normal line at each vertex of the polygon mesh and an angle of an incident ray. The first angle information indicating the angle between the incident ray and the normal line for each pixel located between the pixels is calculated by interpolation calculation, and based on the angle between the line of sight and the reflected ray at each vertex of the polygonal mesh, Angle information interpolation means for calculating, by interpolation calculation, second angle information indicating the angle between the line of sight of each pixel located between the vertices in the polygonal mesh and the reflected light ray, and the first angle information is diffuse reflection normal In the conversion factor, the second
Angle information conversion means for respectively converting the angle information of the specular reflection normalization coefficient, and the effective incident light intensity that takes into account the diffuse reflection normalization coefficient and the diffuse reflection coefficient to the object in addition to the incident light intensity to the object. And a diffuse reflection intensity calculating means for obtaining the diffuse reflection intensity of the object by multiplying the specular reflection normalization coefficient and the effective incident light intensity obtained by adding the specular reflection coefficient of the object to the incident light intensity of the object. Then, a specular reflection intensity calculating means for obtaining the specular reflection intensity of the object, and a total reflection light intensity from the object by adding the diffuse reflection intensity and the specular reflection intensity to the ambient light intensity of the object. A phone shading device comprising: reflected light intensity calculation means. 4. The phon shading device according to claim 3, wherein the angle information interpolating means is constituted by a digital differential analyzer. 5. The angle information conversion means outputs the first angle information as θ.
And a diffuse reflection function table for obtaining a diffusion normalization coefficient as cos θ, where α is the second angle information and n is the dispersion approximation index of the specular reflection light of the object, the specular reflection intensity is cos ⁿ α 5. The phon shading device according to claim 3, further comprising a specular reflection function table to be obtained. 6. The phon shading device according to claim 5, wherein a ROM table is provided as the diffuse reflection function table, and a RAM table is provided as the specular reflection function table.