A spherical volumetric parameterization approach based on large-scale distortion harmonic energy

Spherical volumetric parameterization is a basic and important problem in the fields of digital geometry processing and computer graphics. It is beneficial to the texture mapping and reconstruction of volume mesh. But some methods of spherical volumetric parameterization cannot guarantee the triangles and tetrahedrons without distortion after parameterization. Therefore, this paper presents an efficient algorithm to solve the problem of large-scale distortion spherical mappings of the tetrahedral mesh, the algorithm is based on harmonic energy. We first take the tetrahedral mesh as input data and map it to a solid sphere, which may generate lots of distortion. Then we project the simplicial map onto the space of the bounded-distortion map. In this way, we find a closet mapping that is bijective and reaches to non-distortion approximately. The resulting map is approximately non-distortion.