Hexahedral shell mesh construction via volumetric polycube map
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology
Computers and Graphics
SMI 2012: Full As-conformal-as-possible discrete volumetric mapping
Computers and Graphics
Constructing hexahedral shell meshes via volumetric polycube maps
Computer-Aided Design
PolyCut: monotone graph-cuts for PolyCube base-complex construction
ACM Transactions on Graphics (TOG)
Journal of Computational Physics
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Volumetric parameterization plays an important role for geometric modeling. Due to the complicated topological nature of volumes, it is much more challenging than the surface case. This work focuses on the parameterization of volumes with a boundary surface embedded in 3D space. The intuition is to decompose the volume as the direct product of a two dimensional surface and a one dimensional curve. We first partition the boundary surface into ceiling, floor and walls. Then we compute the harmonic field in the volume with a Dirichlet boundary condition. By tracing the integral curve along the gradient of the harmonic function, we can parameterize the volume to the parametric domain. The method is guaranteed to produce bijection for handle bodies with complex topology, including topological balls as a degenerate case. Furthermore, the parameterization is regular everywhere. We apply the proposed parameterization method to construct hexahedral mesh.