Patent ID: 7515151

Claim:
A method 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 method being executable by a computer processor of a computer graphics system to enable the computer graphics system to generate a displayable image using the selected ray-tracing methodology, the computer processor comprising computer hardware elements, the method comprising: A. for a query point “x” in the scene, and a selected number “k” of photons, generating, in the computer processor, 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. identifying, in the computer processor, the subset P of subdomains which contain a point x i|D P= D i |D i ∩{x i | D |iεB 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. generating, in the computer processor, 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. generating, in the computer processor, 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.