关键词: 参数曲面, Hausdorff距离, 三角面片, 层次包围盒

Abstract: In view of the high computational complexity and less related calculation methods between surfaces, a triangular patch bounding box method is proposed to compute approximate Hausdorff distance rapidly between parametric surfaces. Triangular patches discretized from surface is a good way to approach the surface, so the Hausdorff distance between surfaces can be approximated by the Hausdorff distance between triangles. In order to improve computational efficiency, bounding box technology is used to eliminate the invalid triangles in the process of computing. At the same time, in order to further simplify the distance calculation between two triangles, an approximate calculation method of sampling points is put forward and the error is under control. The experiments show that the proposed method is simpler, easier to implement and has a higher exclusion rate compared with the surface surrounded bounding box method, also the computational efficiency is significantly improved without affecting the results, so the method has a wide application value.

Key words: parametric surfaces, Hausdorff distance, triangular patches, hierarchical bounding volumes