Domain construction for volumetric cross-parameterization

•A novel patch construction algorithm to approximate an intersection-free surface.•An automatic construction algorithm to construct curved polyhedra as base-domains.•To establish the constrained cross-parameterization between three-manifold models.

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.

Graphical abstractVolumetric cross-parameterization can be established among models with different shapes. Given the prescribed anchor points, the entire solid model can be decomposed into curved polyhedral cells having the same connectivity as that of the common base-domains. By the volumetric cross-parameterization, interior structures of the cylinder model can be transferred across all the models (bottom row).Figure optionsDownload full-size imageDownload high-quality image (419 K)Download as PowerPoint slide