Domain construction for volumetric cross-parameterization

We present an algorithm in this paper for constructing volumetric domains with consistent topology to parameterize three-manifold solid models having homeomorphic topology. The volumetric parameterizations generated by our approach share the same set of base domains and are constrained by the corresponding anchor points. Our approach allows users to control interior mappings by specifying interior anchor points, and the anchor points are interpolated exactly. With the help of a novel construction algorithm developed in this work, the volumetric cross-parameterization computed by our method demonstrates its functionality in several examples.