Arithmetic research about Boolean operation of surfel model based on hierarchical bounding volumes

As CSG primitive, the point is not studied deeply in application of digital geometry. With no topology and adjacency of point models, it is unnecessary to keep consistent with the topology at the time of modeling, but it brings more difficulties to drawing and keeping the surface flow. Review the point model-based geometrical expressions, this paper puts forward a improved data structure of surfel, achieves the complicated surfel modeling with constructive solid geometry technique and brings forward the Boolean operators for the complicated surfel modeling. Based on the point modeling process, solves the quick intersection and lowers the time complexity of algorithm with the theory of hierarchical bounding volumes. This paper describes the intersection test with the grid-topological relations to further quicken the intersection test and puts forward that the time complexity of n primitives is reduced from O(n2) to O(logd-1 n + Kb) in the bounding box way of the Boolean operators based on the improved basic surfel data structures. (5 pages)