FAST HIERARCHICAL DISCRETIZATION OF PARAMETRIC BOUNDARY REPRESENTATIONS

Abstract

Prevalent discretization methods based on Delaunay triangulations and advancing fronts, which sample and mesh simultaneously, can guarantee well shaped triangles but at a fairly high computational cost. In this paper we present a novel and flexible two-part sampling and meshing algorithm, which produces topologically correct meshes on arbitrary boundary representations whose faces are represented parametrically, without requiring an initial coarse mesh. Our method is based on a hybrid spatial partitioning scheme driven by user-designed subdivision rules that combines the power of quadtree decomposition with the flexibility of the binary decompositions to produce meshes that favor prescribed geometric properties. Importantly, the algorithm offers a performance increase of approximately two orders of magnitude over Delaunay based methods and at least one order of magnitude over advancing front methods. At the same time, our algorithm is practically as fast as the computationally optimal algorithm based on a pure quadtree decomposition, but with a markedly better distribution in the regions with parametric distortion. The hierarchical nature of our surface decomposition is well suited to interactive applications and multithreaded implementation.