1. A method for reducing an amount of cache memory required to store a three-dimensional texture atlas, the method comprising: determining, using a processor, a mapping between regions of a three-dimensional triangle mesh and leaves in an octree, each region of the three-dimensional triangle mesh being mapped to a single leaf in the octree; grouping, using the processor, a plurality of triangles that form the three-dimensional triangle mesh into a plurality of groups of triangles based on the mapping, each triangle in the plurality of triangles being assigned to a particular group based on a spatial positioning of the triangle within a particular region of the three-dimensional triangle mesh that corresponds to a particular leaf in the octree; creating, using the processor, a plurality of texture tiles based on the plurality of groups of triangles, wherein at least one texture tile in the plurality of texture tiles is created by scanning a group of triangles that is within a three-dimensional bounding volume, wherein a length of each dimension of the three-dimensional bounding volume is less than or equal to 2 k , and wherein k equals a positive integer that limits the three-dimensional bounding volume to an octree leaf size plus a maximum triangle size; combining, using the processor, the plurality of texture tiles to form at least one three-dimensional texture atlas; and storing, using the processor, the at least one three-dimensional texture atlas in the cache memory.