Patent ID: 7236171

Claim:
A computer program product comprising computer program instructions executable by a computer to provide a computer graphics system for generating a pixel value for an image using a selected ray-tracing methodology in which simulated rays are shot from the pixel into a scene, the simulated rays representing paths of simulated photons, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the pixel value being useable by the computer to enable the computer to generate a display-controlling electrical output in response to the pixel value, the computer program product comprising a computer-readable medium having encoded thereon: A. subdomain generator, program instructions, encoded on the computer-readable medium and executable by the computer to enable the computer to, for a query point “x” in the scene, and a selected number “k” of photons, generate a set of “M” subdomains D i on a disk D of radius r(B k (x)) centered at the query point “x” that is tangent to a minimal sphere around point “x” that encompasses “k” photons, such that ⋃ i = 0 M - 1 ⁢ D i = D ⁢ ⁢ and ⁢ ⁢ D i ⋂ D j ≠ 0 ⁢ ⁢ for ⁢ ⁢ i ≠ j , ⁢ where ⁢ ⁢  D i  =  D  M = π ⁢ ⁢ r 2 ⁡ ( B k ⁡ ( x ) ) M ; B. subdomain photon evaluator program instructions, encoded on the computer-readable medium and executable by the computer to enable the computer to identify the subset P of subdomains which contain a point X i|D where P = { D i ❘ D i ⋂ { x i ⁢  D  ⁢ i ∈ B k ⁡ ( x ) } ≠ 0 } , where X i|D refers to a position of photon “i” projected onto the disk D along its angle of incidence ω i , C. area value generator program instructions, encoded on the computer-readable medium and executable by the computer to enable the computer to generate an area value A according to A = π ⁢ ⁢ r 2 ⁡ ( B k ⁡ ( x ) ) ⁢  P  M , where |P| refers to the number of sub-domains in the subset P; and D. radiance value generator program instructions, encoded on the computer-readable medium and executable by the computer to enable the computer to generate a radiance value L r (x,ω) along selected angle ω in accordance with, L _ r ⁡ ( x , ω ) ≈ 1 A ⁢ ∑ i ∈ B k ⁡ ( x ) ⁢ f r ⁡ ( ω i , x , ω ) ⁢ Φ i , where Φ i represents the energy of the “i-th” photon.