Low-dimensional rank-1 lattices in computer image synthesis

A computer program product operable in a digital computer processor adapted to enable the generation of synthetic images, the computer program product comprising computer readable program instructions encoded in a computer readable medium, the computer readable program instructions comprising:

• first computer program instructions encoded in the computer readable medium and executable by the computer processor to enable the computer processor to select a rank-1 lattice corresponding to points in the synthetic image to be generated;
• second computer program instructions encoded in the computer readable medium and executable by the computer processor to enable the computer processor to generate a data structure for efficient access to data stored in points of the rank-1 lattice, the data structure comprising the number n of lattice points, generator vector g, s basis vectors, and indices of the basis vectors, wherein the basis vectors are lattice points, and
• third computer program instructions encoded in the computer readable medium and executable by the computer processor to enable the computer processor to generate, using the rank-1 lattice, digital output representative of a synthetic image, wherein the generating comprises using the layout of rank-1 lattice points to represent textures of arbitrary dimension.

A subsystem, operable in a digital processing system operable to generate synthetic images, the subsystem comprising:

• a lattice selection module operable to select a rank-1 lattice corresponding to points in the synthetic image to be generated,
• a first generating module operable to generate a data structure for efficient access of data stored in points of the rank-1 lattice, the data structure comprising the number n of lattice points, generator vector g, s basis vectors, and indices of the basis vectors, wherein the basis vectors are lattice points, and
• a second generating module operable to generate, using the rank-1 lattice, digital output representative of a synthetic image, wherein the generating comprises using the layout of rank-1 lattice points to represent textures of arbitrary dimension.