Domain Mapping for Volumetric Parameterization using Harmonic Functions

Abstract

ABSTRACTVolumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the boundary of a 3D model (which is a surface). Volumetric parameterization is typically helpful in solving complicated geometric problems pertaining to shape matching, morphing, path planning of robots, and isogeometric analysis etc. A novel method is proposed in which a volume parameterization is developed by mapping a general non-convex (genus-0) domain to its topologically equivalent convex domain. In order to achieve a continuous and bijective mapping of a domain, first we use the harmonic function to establish a potential field over the domain. The gradients of the potential values are used to track the streamlines which originate from the boundary and converge to a single point, referred to as the shape center. Each streamline approaches the shape center at a ...