Patent ID: 6885370

Claim:
A computer graphics system for generating a pixel value for a pixel in an image, the pixel being representative of a point {right arrow over (x)} in a scene, the computer graphics system generating the pixel value to simulate global illumination for a plurality of colors, global illumination being represented by an evaluation of a function ƒ(x), the function ƒ(x) having the form f ⁢ ( x ) = g ⁢ ( x ) + ∫ 0 1 ⁢ K ⁢ ( x , y ) ⁢ f ⁢ ( y ) ⁢ ⁢ ⅆ y , where ƒ(x) (and similarly ƒ(y)) is an unknown function, and g(x) and K(x,y) are known functions, with K(x,y) serving as a “kernel” of the integral, the kernel K(x,y) including a function associated with at least two colors, the computer graphics system comprising: A. an estimator generator module configured to generate a selected number “N” of estimators ƒ (n) lds,RR (x) as f _ lds , RR ( n ) ⁡ ( x ) = ⁢ g ⁡ ( x ) + K ⁡ ( x , ξ 1 ( n ) ) ⁢ S 1 ( n ) + K ⁡ ( x , ξ 2 ( n ) ) ⁢ S 2 ( n ) + K ⁡ ( x , ξ 3 ( n ) ) ⁢ S 3 ( n ) + ⋯ ⁢ , where S i (n) are defined recursively as S 1 ( n ) := g ⁢ ( ξ 1 ( n ) ) , ⁢ S j + 1 ( n ) := Θ ⁡ ( M K ⁡ ( ξ j + 1 n , ξ j n ) , S j ( n ) - ξ j ′ ⁡ ( n ) ) M K ⁡ ( ξ j + 1 n , ξ j n ) , S j ( n ) ⁢ K ⁡ ( ξ j + 1 n , ξ j n ) ⁢ S j ( n ) , ⁢ with M A , B := { ∫ 0 ∞ ⁢ A λ ⁢ B λ ⁢ ⅆ λ ∫ 0 ∞ ⁢ B λ ⁢ ⅆ λ , if ⁢ ⁢ ∫ 0 ∞ ⁢ B λ ⁢ ⅆ λ > 0 0 , if ⁢ ⁢ ∫ 0 ∞ ⁢ B λ ⁢ ⅆ λ = 0 , and where Θ(x) represents the Heaviside function, and ξ 1 (n) , ξ′ 1 (n) , ξ 2 (n) , ξ′ 2 (n) , . . . , ξ L (n) , ξ′ L (n) , represent components of a predetermined multi-dimensional strictly deterministic low-discrepancy sequence and where “n” denotes a sequence index, the estimator generator module being configured to generate successive terms for each estimator ƒ (n) lds,RR (x) until it generates a term having the value zero; B. a luminance value module configured to generate a luminance value for the point in the scene as the average of said estimator values generated by said estimator generator module; and C. a pixel value generator module configured to use the luminance value generated for the point in the scene in generating the pixel value.