Interference Detection for Subdivision Surfaces

Accurate and robust interference detection and ray-tracing of subdivision surfaces requires safe linear approximations. Approximation of the limit surface by the subdivided control polyhedron can be both inaccurate and, due to the exponential growth of the number of facets, costly. This paper shows how a standard intersection hierarchy, such as an OBB tree, can be made safe and efficient for subdivision surface interference detection. The key is to construct, on the fly, optimally placed facets, whose spherical offsets tightly enclose the limit surface. The spherically offset facets can be locally subdivided and they can be efficiently intersected based on standard triangle-triangle interference detection.