On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Simplification of tetrahedral meshes
Proceedings of the conference on Visualization '98
ACM SIGGRAPH 2004 Papers
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Hexahedral mesh generation constraints
Engineering with Computers - Special Issue: 5th Symposium on Trends in Unstructured Mesh Generation in 2006. Guest Editor: Steven J. Owen
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Hexahedral shell mesh construction via volumetric polycube map
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
General planar quadrilateral mesh design using conjugate direction field
Proceedings of the 2011 SIGGRAPH Asia Conference
Boundary aligned smooth 3D cross-frame field
Proceedings of the 2011 SIGGRAPH Asia Conference
Integer-grid maps for reliable quad meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Optimizing polycube domain construction for hexahedral remeshing
Computer-Aided Design
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Decomposing a volume into high-quality hexahedral cells is a challenging task in geometric modeling and computational geometry. Inspired by the use of cross field in quad meshing and the CubeCover approach in hex meshing, we present a complete all-hex meshing framework based on singularity-restricted field that is essential to induce a valid all-hex structure. Given a volume represented by a tetrahedral mesh, we first compute a boundary-aligned 3D frame field inside it, then convert the frame field to be singularity-restricted by our effective topological operations. In our all-hex meshing framework, we apply the CubeCover method to achieve the volume parametrization. For reducing degenerate elements appearing in the volume parametrization, we also propose novel tetrahedral split operations to preprocess singularity-restricted frame fields. Experimental results show that our algorithm generates high-quality all-hex meshes from a variety of 3D volumes robustly and efficiently.