A Volumetric Parameterization Approach Based on Bounded-distortion Harmonic Energy

Volumetric parameterization is a basic and important problem for digital geometry processing and computer graphics. This paper presents a volumetric parameterization approach which is based on bounded-distortion harmonic energy. We take the tetrahedral mesh as input data and maps it to a solid sphere, in that way we can acquire a bijective simplicial map. Then we project the bijective simplicial map on the space of the bounded-distortion map, which means that we find a closet mapping that is featured with bijective and bounded-distortion. The resulting map is loss-distortion, bijective and non-flips.