Abstract: A system is described for generating a plurality of identifiers, each associated with one of a like plurality of subdivision surfaces of a surface element, and for generating, using an identifier for a subdivision surface, coordinates for the subdivision surface. Each identifier includes one or more position codes. Each position code indicates the position of a subdivision surface at a respective level relative to the next higher level, so that successive position codes in the identifier indicate the positions of subdivision surfaces through successive subdivision levels. To generate coordinates for a subdivision surface from the identifier associated with the subdivision surface, the system sequences through successive position codes in the identifier to determine locations of the subdivision surfaces through the successive levels.

Abstract: A system is described for generating a plurality of identifiers, each associated with one of a like plurality of subdivision surfaces of a surface element, and for generating, using an identifier for a subdivision surface, coordinates for the subdivision surface. Each identifier includes one or more position codes. Each position code indicates the position of a subdivision surface at a respective level relative to the next higher level, so that successive position codes in the identifier indicate the positions of subdivision surfaces through successive subdivision levels. To generate coordinates for a subdivision surface from the identifier associated with the subdivision surface, the system sequences through successive position codes in the identifier to determine locations of the subdivision surfaces through the successive levels.

Abstract: A system is described for generating a plurality of identifiers, each associated with one of a like plurality of subdivision surfaces of a surface element, and for generating, using an identifier for a subdivision surface, coordinates for the subdivision surface. Each identifier includes one or more position codes. Each position code indicates the position of a subdivision surface at a respective level relative to the next higher level, so that successive position codes in the identifier indicate the positions of subdivision surfaces through successive subdivision levels. To generate coordinates for a subdivision surface from the identifier associated with the subdivision surface, the system sequences through successive position codes in the identifier to determine locations of the subdivision surfaces through the successive levels.

Abstract: A computer graphics system generates a pixel value for a pixel in an image, the pixel being representative of a point in a scene. The computer graphics system generates the pixel value by an evaluation of an integral of a selected function. The computer graphics system comprises a sample point generator and a function evaluator. The a sample point generator is configured to generate respective sets of sample points each associated with one of a series of rays in a ray trace configured to have a plurality of trace levels. The ray at at least one level can be split into a plurality of rays, with each ray being associated with a ray instance identifier. The sample point generator is configured to generate the sample points as predetermined strictly-deterministic low-discrepancy sequence to which a selected rotation operator is applied recursively for the respective levels.

Abstract: A computer graphics system generate a pixel value for a pixel in an image to simulate global illumination represented by an evaluation of an unknown function ƒ of the form f ? ( x ) = g ? ( x ) + ? 0 1 ? K ? ( x , y ) ? f ? ( y ) ? ? ? ? y , g(x) and K(x,y) known functions, with K(x,y) a “kernel” including a function associated with at least two colors.

Abstract: A system is described for generating a plurality of identifiers, each associated with one of a like plurality of subdivision surfaces of a surface element, and for generating, using an identifier for a subdivision surface, coordinates for the subdivision surface. Each identifier includes one or more position codes. Each position code indicates the position of a subdivision surface at a respective level relative to the next higher level, so that successive position codes in the identifier indicate the positions of subdivision surfaces through successive subdivision levels. To generate coordinates for a subdivision surface from the identifier associated with the subdivision surface, the system sequences through successive position codes in the identifier to determine locations of the subdivision surfaces through the successive levels.

Abstract: A computer graphics system generate a pixel value for a pixel in an image to simulate global illumination represented by an evaluation of an unknown function f of the form f(x)=g(x)+∫01K(x,y)f(y)dy,g(x) and K(x,y) known functions, with K(x,y) a “kernel” including a function associated with at least two colors.

Abstract: A computer graphics system generates a pixel value for a pixel in an image, the pixel being representative of a point in a scene. The computer graphics system generates the pixel value by an evaluation of an integral of a selected function. The computer graphics system comprises a sample point generator and a function evaluator. The a sample point generator is configured to generate respective sets of sample points each associated with one of a series of rays in a ray trace configured to have a plurality of trace levels. The ray at at least one level can be split into a plurality of rays, with each ray being associated with a ray instance identifier. The sample point generator is configured to generate the sample points as predetermined strictly-deterministic low-discrepancy sequence to which a selected rotation operator is applied recursively for the respective levels.