Patent ID: 7167175

Claim:
A computer program product for use in connection with a computer to provide a computer graphics system for generating a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer program product comprising a computer-readable medium having encoded thereon: A. a sample point generator module configured to enable the computer to generate a set of sample points, at least one sample points being generated using at least one dependent sample, the at least one dependent sample comprising at least one element of a low-discrepancy sequence offset by at least one element of another low-discrepancy sequence; and B. a function evaluator module configured to enable the computer to generate at least one value representing an evaluation of a′ selected function at one of the sample points generated by said sample point generator, the value generated by the computer corresponding to the pixel value, wherein the sample point generator is configured to generate at least one sample point having two-dimensions, the at least one dependent sample being defined by an element of a two-dimensional Hammersley point set defined as, for sample point “i”, ( j / N , ⁢ Φ b ⁡ ( i ) ) , for selected base “b” and integer “N,” where Φ b (x) is a radical inverse function given by Φ b ⁢ : ⁢ ⁢ N 0 -> I x = ∑ j = 0 ∞ ⁢ a j ⁡ ( x ) ⁢ b j ↦ ∑ j = 0 ∞ ⁢ a j ⁡ ( x ) ⁢ b - j - 1 , where (a j ) j=0 ∞ is the representation of “x” in integer base “b”, wherein the sample point generator is configured to generate the at least one sample point with the other of said low-discrepancy sequence being defined by (Φ b′ (i), Φ b″ (i)) for selected integer “i” where (b′) and (b″) are selected bases, with b′, b″≠b, wherein the sample point generator is configured to generate the at least one sample point with the other of said low-discrepancy sequence being defined by (Φ b′ (i,σ b′), Φ b″ (i,σ b″ )) where σ is a selected integer permutation, and wherein the sample point generator is configured to generate the at least one sample point using a recursive integer permutation starting with permutation σ 2 =(0,1) for base b=2, in which a sequence of permutations is defined as follows: (i) for base “b” even, a permutation σ b is generated by first taking values of 2σ b/2 and appending values of 2 ⁢ σ b 2 + 1 , and (ii) for base “b” odd, a permutation σ b is generated by taking values of σ b,i , incrementing each value that is greater than or equal to b - 1 2 by one, and inserting value b - 1 2 in the middle of the permutation.