Multiresolution Normal Mesh Approximation of Implicit Surfaces
Normal mesh is a now new fundamental surface description, which is multiresolution mesh where each level can be written as a normal offset from a coarser version.In this paper,we presented an algorithm to create normal mesh approximations for implicit surfaces.This algorithm begins from a coarse base mesh created from implicit surface by a space-division based polygonization method,firstly. The base mesh is then optimized by a smoothing procedure, and the aspect ratios of long and narrow triangles in the mesh are improved remarkably. Subsequently, the facets of the base mesh are subdivided normally and iteratively, and the vertices newly created are located on the implicit surface along certain normal by employing interval arithmetic technique. Finally, a piecewise-linear approximation mesh is obtained, and it is a normal mesh with subdivision connectivity and provides implicit surface a multiresolution description, naturally.The mesh also has much fewer data with respect to the traditional non-regular polygonization in sense of same approximation error.The algorithm can be used in the context of multilevel drawing, progressive transmission or other relative geometric processing of implicit surfaces.