Topology preserving algorithms for implicit surfaces simplifying and sewing

Abstract

Two discretization methods for implicit surfaces are presented: the Non-Compact Dual Simplification and the Sewing Octree. They work with surfaces polygonalized with Dual Contouring, an adaptive method which uses an octree. The Non-Compact Dual Simplification (NDS) preserves the topology of simplified non-compact surfaces. This method can be used for non-compact as well as for compact surfaces in the case the polygonalization region does not contain the latter ones. The Sewing Octree is a method to glue two or more octrees that share faces or edges and contain portions of the surface polygonalized with Dual Contouring. These methods can be employed either independently or coupled, by dividing the original cube in two or more cubes, making the polygonalization, simplifying these regions with NDS, if necessary, and glueing the resulting surfaces with the Sewing Octree. We assure that, with this procedure, the resulting surface and the original one share the same topology. © 2014 Springer International Publishing.