Parameterization Of Volume Bounded By High Genus Surface

Volumetric parameterization plays an important role in computer graphics,some example applications include volumetric morphing,template fitting,structured remeshing,cage-based deformations,trans-fer of interior structures or volumetric textures,compatible meshing via volumetric correspondences,and the mapping to regular grids for parallel volumetric computations.In this paper,we generalize the surface foliation algorithm to the volume,and propose the volume foliation algorithm to realize the volume parameterization.The method is capable of handling volumes with more complicated topologies,such as a volume with a single high genus boundary surface,the method is based on solving harmonic maps from the volume to a weighted graph,like conventional harmonic map-ping algorithms,it has unique solution,and is stable;furthermore,the whole algorithm pipeline is automatic.Hence the method is both rig-orous and practical.