Automatic Semi-regular Mesh Construction from Adaptive Distance Fields

This paper describes a method to construct semi-regular meshes for a surface S de ned by the zero set of a trivariate function F(x,y,z), representing a distance eld de nition of S. An adaptive distance eld (ADF) de nition of S is obtained by constructing, adaptively, an octree decomposition of F's domain. The vertices of the octree-based de nition of S lie either on the positive or negative side of S (or on S). Octree cells that are intersected by S are identi ed, and the faces of these cells that lie on the outside of S are projected onto S. The result is a quadrilateral mesh to which various procedures are applied that lead to an improved mesh containing a much smaller number of extraordinary vertices, i.e., non-valence-four vertices.