Grid Creation Strategies for Efficient Ray Tracing

Both theoretical analysis and practical experience have shown that when ray tracing a well-behaved model with N geometric primitives, the lowest ray tracing times using a grid acceleration structure occurs when the grid has 0(N) cells. This paper extends the theoretical analysis in two ways and then experimentally verifies that analysis for several geometric models. The first extension is to examine how model characteristics influence the choice of the number of cells in a grid, with models made of long thin primitives being of particular interest. For such models, the lowest trace times come when O(N
^1.5
) cells are used, but may not always be practical due to the super-linear memory usage. The second extension is to nested grids where a grid cell may itself contain another grid. For the case of scattered data such as exploding particles, nesting is not helpful. For the case of tessellated manifolds with compact triangles, O(N
^0.6
) cells at top level is optimal if only one level of nesting is allowed. For d levels of nesting, O(N
^3/(3+2d)
) is optimal for the top level. For long thin primitives, O(N) cells at the top level is optimal when one level of nesting is allowed, but this again comes at the cost of super-linear memory usage.