JP2003030683A - Rough surface light reflection circuit - Google Patents

Abstract

PROBLEM TO BE SOLVED: To plot highly real computer graphics video images in real time by making the reflection characteristic model of a fine object surface (rough surface) into a circuit. SOLUTION: A rough surface light reflection circuit calculates mirror reflection components on the rough surface by turning diffusion cosθ and mirror reflection cosα components obtained from a normal, a light source incident angle and a view point angle to input variables and respectively using a 2/cosθ table 2.1, a 2/cosγ table 2.2, a cosα×D (α) table 2.3, a k×ρ (λ, θ) table 2.4, multipliers 2.8, 2.10 and 2.13, a subtractor 2.5 and multiplexers 2.6 and 2.12.

Description

Description: TECHNICAL FIELD [0001] The present invention relates to a computer graphics rendering circuit for drawing rough surface shading (light / dark) in consideration of surface roughness caused by light reflection. About. By making the circuit of the present invention an LSI, it is applied to real-time visualization of a virtual reality system such as a simulation and a game. [Prior Art] Light reflection modeling is the most important technique in 3D computer graphics for realistically representing an image and obtaining geometrical perception. Although some techniques for drawing a light reflecting object using a specific algorithm have been developed, Phong shading is a typical example of rendering in polygon notation. When implementing these technologies in VLSI, it is generally necessary to divide the surface of the object into polygons, define the surface normals at the vertices of each polygon, and interpolate these at the rendering stage. ing. In general, these implementations had problems such as the normalization of normal vectors for each interpolation and the need for complex hardware circuits for calculating the direction cosine. As a method of solving this problem, an algorithm that expresses the normal of the surface and the unit vector of the light source by horizontal and vertical angles in polar coordinates, first interpolates this, and then performs a predetermined operation to omit the normalization calculation Was developed by the present inventors. In Japanese Patent Application Nos. 7-102904 and 9-155684 and U.S. Pat. No. 5,900,881, as a method for obtaining a specular reflection component, a surface normal and a light source vector are written in polar coordinates, interpolated, and then a multiplier and an adder are used. In this case, a diffuse reflection component is multiplied, and further subtracted by a light source vector. The circuit of the invention described above simplifies the circuit in that the interior of the surface is interpolated at polar coordinate angles and then converted to orthogonal coordinate normal vectors, which eliminates the need for normalization of normal vectors for each interpolation. Is planned. Von shading model is generally (1)
It is expressed by an equation. Here, let the incident light Ip to the viewpoint, the diffuse reflection coefficient Id, the specular reflection coefficient Is, the unit vector L of the light source, the surface normal N, and the viewpoint unit vector be V. m of cos α is a specular reflection index. However, these von shading models are based on an inference method in which the surface is a uniform plane and does not take into account the irregular reflectance and light wavelength characteristics on the surface caused by surface roughness. On the other hand, a Cook / Torrence model is known as a model of the surface roughness. This expresses the specular reflection component Rs by the following equation (2). Here, ρ (λ, θ), D (α), H, and V are reflectances that also have a Fresnel function of an object whose variable is the angle θ formed by the incident angle of the light source and the surface normal and the wavelength of light. L and V, a luminance distribution function using the angle α between the light reflection angle and the viewpoint direction as a variable
And a line-of-sight unit vector.
In the equation (2), the attenuation rate G is represented by a vector, and the minimum value among the three terms in parentheses is used for determining the luminance. To find this, we define these vectors at each vertex of the polygon, interpolate the interior of the polygon using vectors,
When the expression (2) is calculated using the vector components, it is necessary to normalize each of the vector components.
The circuitization of the equation has the problem that it is a much more complicated circuit than the Phong shading circuit. The present invention calculates the light reflection luminance on the rough surface, which is difficult to circuit as described above, and calculates the inner product value of the diffuse component and the specular reflection component from the value obtained by interpolating the polar coordinate system component. , To simplify the circuit of the specular reflection component. [Means for Solving the Problem] In the von shading model using the polar coordinates of the normal, light incident angle and viewpoint angle, the vertex of each polygon is determined in order to determine the luminance of the surface. Coordinate values (x, y, z), surface normals at vertices (Nh, Nv), and angles (Lh, L
v) and an angle (Eh, Ev) with the viewpoint are defined.
Here, the surface normal, the unit vector of the incident light, and the viewpoint vector are expressed by horizontal and vertical angles as polar coordinates (subscripts mean horizontal h and vertical v). These values are linearly interpolated at all points inside the polygon, and the interpolated values are then converted to the diffuse reflection component cos θ and the specular reflection component cos α using equations (3) and (4). Ask. The inner product cosγ formed by the surface normal and the viewpoint direction is By expanding Expression (2) using Expressions (3) to (8), Expression (9) is obtained as a specular reflected light component on the rough surface. In equation (9), the minimum value is selected from the three items in the brackets []. The specular reflection component is assumed to be Ispec. In the present invention, the interpolated values Lh, Lv, Nh, Nv, Eh, and Ev are expressed by equations (5) to (8), and the direction cosine cos θ formed by the surface normal and the light incident angle, the reflection angle and the viewpoint The direction cosine cosα formed by the direction and the angle co formed by the normal and the viewpoint
Find sγ. In the equation (9), the reflectance ρ (λ, θ)
Has a characteristic peculiar to a substance with respect to a light incident angle, and a distribution function D (α) is given by a function such as Gauss or Beckman. In the present invention, ρ (λ, θ) and D (α) represent addresses cos θ, respectively. And cosα RAM
Consist of a table. ρ (λ, θ) is ρ
(Λ, cos θ), and D (α) is, for example, a cos ⁿ α value.
α) is stored. n and k are determined by the surface characteristics of the object. As a result, the specular reflection component of the equation (9) is obtained by using only the cos θ, cos α, and cos γ obtained by the Phong shading circuit as input variables in the RAM table,
It can be easily configured with a ROM table, a multiplier, and the like. [Example] FIG. 1 shows the direction cosine cos θ of the angle θ formed by the surface normal and the incident angle of the light source, and the direction cosine cos α of the angle α formed by the mirror reflection angle of the incident light and the viewpoint direction. The following shows a circuit for obtaining. In FIG. 1, the horizontal and vertical angles, where the surface normal, the light source incident angle, and the viewpoint direction are polar coordinates, are N, respectively.
h, Nv, Lh, Lv and Eh, Ev, which are converted from polar coordinates to rectangular coordinates by the conversion circuits 1.1, 1.3, and 1.3, respectively, at rectangular coordinates Nx, Ny, Nz, Lx, L
y, Lz and Vx, Vy, Vz. The conversion circuit is composed of a trigonometric function table and a multiplier according to equations (5)-(7). Cos θ and cos α are calculated according to equations (3) and (4) as multipliers 1.4, 1.5, 1.6, adders 1.7, 1.8, and a multiplier 1.9 having a double scale. , 1.10, 1.11, subtractors 1.12, 1.1
3, 1.14, multipliers 1.15, 1.16, 1.17,
It can be configured using adders 1.18 and 1.19. Here, cos θ is obtained from adder 1.8 and cos α
Is output from the adder 1.18. The inner product cosγ between the surface normal and the viewpoint direction is obtained by multipliers 1.20, 1.21 and 1.22 and adders 1.23 and 1.14. In the rough specular reflection of the present invention, in the circuit of FIG.
After obtaining the values of θ, cosα, and cosγ from the surface normal, the light source incident angle, and the viewpoint angle, the reflectance, the attenuation rate, and the distribution rate are calculated, respectively. FIG. 2 shows a rough surface reflection circuit of the present invention. The specular reflection component is represented by Expression (9). In the circuit, cos θ is added to the memory tables 2.1 and 2.4, 2 / cos θ is stored in the table 2.1, and 2 / cos γ is stored in the table 2.2. On the other hand, the reflectance is stored for each color component in the memory table 2.4. For the reflectance ρ (λ, θ), the measured values of the reflection characteristics of the object for each color component are tabulated and read as cos θ. Therefore, the value converted into ρ (λ, cos θ) is actually stored. The distribution characteristic is Gauss, Beckman or cos
Values D (cos α) such as ⁿ α are tabulated in the memory 2.3 and read out with cos α. Further, 2 /
The cos θ is compared with 2 / cos γ, and the smaller value is selected by the multiplexer 2.6. This value is a multiplier 2.8
Is multiplied by cos α. This value is compared by the comparator 2.9 with 1 / cosγ, which has been set to で by the シ shifter 2.7, and the smaller one is selected by the multiplexer 2.12. Further, the output of the table 2.4 is multiplied by the output of the distribution ratio table 2.3 by the multiplier 2.10, and this value is further multiplied by the output of the multiplexer 2.12 by the multiplication circuit 2.13 to obtain the specular reflection component. Isp
ec. The reflectance ρ (λ, cos θ) is multiplied by the diffusion coefficient K1 by the multiplier 2.11 to obtain a diffusion component Idiff. From the above, the circuit of the present invention uses only cos α, cos θ and cos γ that can be shared with the conventional Phong shading as parameters for obtaining the rough surface characteristics, and makes a triangular function or an exponential function into a table. A rough surface shading circuit can be configured by a large-scale circuit. The memory tables 2.1 and 2.2 can also use a ROM (read only). [Effect of the Invention] According to the present invention, an object having delicate reflection characteristics can be rendered in real time.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 Diffuse and specular reflection component circuit of the present invention [Description of symbols] 1.1 Polar normal / rectangular coordinate conversion circuit for surface normal 1.11
Multiplier 1.2 Polar / Cartesian coordinate conversion circuit for light source 1.12
Subtractor 1.3 Line-of-sight polar / rectangular coordinate conversion circuit 1.13
Subtractor 1.4 Multiplier 1.14
Subtractor 1.5 Multiplier 1.15
Multiplier 1.6 Multiplier 1.16
Multiplier 1.7 Adder 1.17
Multiplier 1.8 Adder 1.18
Adder 1.9 Multiplier 1.19
Adder 1.10 Multiplier 1.20
Multiplier 1.21 Multipliers 1, 23
Adder 1.22 Multiplier 1.24
Adder [FIG. 2] Diffusion and specular reflection component circuit of the present invention [Description of symbols] 2.1 2 / cos θ table 2.8
Multiplier 2.2 2 / cosγ table 2.9
Comparator 2.3 D (cosα) table 2.10
Multiplier 2.4 k × ρ (λ, cos θ) table 2.11
Multiplier 2.5 Subtractor 2.12
Multiplexer 2.6 Multiplexer 2.13
Multiplier 2.7 1/2 shifter

Claims (1)

Claims: 1. An object is represented by a light reflection model that defines the light reflection luminance of an object having a surface roughness by using respective components of a reflectance, a light distribution function, and a light attenuation function on a surface. The vertices of the polygon that defines the surface normal, light incident angle, and viewpoint angle,
In a light reflection circuit that calculates the respective components of the light reflection model based on the values obtained by interpolating them inside the polygon, and determines the luminance of the surface on the rough surface,
Means for interpolating polygons using polar components consisting of horizontal and vertical angles, and the above-mentioned reflectance, reflected light distribution function and light attenuation function as surface normals, light incident vectors, and light reflection vectors. A rough surface light reflection circuit for obtaining a specular reflection component by using a storage element having, as an address, an inner product value formed by the surface vector and the viewpoint vector, and the respective inner product values formed by the surface normal and the viewpoint vector.