Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic Local Search: Foundations & Applications
Stochastic Local Search: Foundations & Applications
ACM SIGGRAPH 2004 Papers
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
IEEE Transactions on Visualization and Computer Graphics
Technical Section: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Technical Section: Feature-aligned harmonic volumetric mapping using MFS
Computers and Graphics
Steinitz theorems for orthogonal polyhedra
Proceedings of the twenty-sixth annual symposium on Computational geometry
Hexahedral shell mesh construction via volumetric polycube map
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Direct-Product Volumetric Parameterization of Handlebodies via Harmonic Fields
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Generalized PolyCube Trivariate Splines
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Editable polycube map for GPU-based subdivision surfaces
I3D '11 Symposium on Interactive 3D Graphics and Games
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping
Computers and Graphics
SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology
Computers and Graphics
Embedding a triangular graph within a given boundary
Computer Aided Geometric Design
Surface Mesh to Volumetric Spline Conversion with Generalized Polycubes
IEEE Transactions on Visualization and Computer Graphics
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PolyCubes, or orthogonal polyhedra, are useful as parameterization base-complexes for various operations in computer graphics. However, computing quality PolyCube base-complexes for general shapes, providing a good trade-off between mapping distortion and singularity counts, remains a challenge. Our work improves on the state-of-the-art in PolyCube computation by adopting a graph-cut inspired approach. We observe that, given an arbitrary input mesh, the computation of a suitable PolyCube base-complex can be formulated as associating, or labeling, each input mesh triangle with one of six signed principal axis directions. Most of the criteria for a desirable PolyCube labeling can be satisfied using a multi-label graph-cut optimization with suitable local unary and pairwise terms. However, the highly constrained nature of PolyCubes, imposed by the need to align each chart with one of the principal axes, enforces additional global constraints that the labeling must satisfy. To enforce these constraints, we develop a constrained discrete optimization technique, PolyCut, which embeds a graph-cut multi-label optimization within a hill-climbing local search framework that looks for solutions that minimize the cut energy while satisfying the global constraints. We further optimize our generated PolyCube base-complexes through a combination of distortion-minimizing deformation, followed by a labeling update and a final PolyCube parameterization step. Our PolyCut formulation captures the desired properties of a PolyCube base-complex, balancing parameterization distortion against singularity count, and produces demonstrably better PolyCube base-complexes then previous work.