C0 Generalized Coons Volumes over Arbitrary Polyhedra

摘要

Transfinite interpolation is a fundamental theme in geometric modeling. The most well-known transfinite interpolation volume is the Coons volume. However, the topology of Coons volumes is restricted to hexahedra, which significantly limits their applications. In this paper, we generalize the Coons volume from hexahedral topology to arbitrary polyhedral topologies via generalized barycentric coordinates. We prove that the proposed generalized Coons volume possesses several desirable geometric properties and demonstrate its applications in computer graphics.