On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Smooth and convex grid generation over general plane regions
Mathematics and Computers in Simulation
A concept for parametric surface fitting which avoids the parametrization problem
Computer Aided Geometric Design
Fitting Subdivision Surfaces to Unorganized Point Data Using SDM
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Automatic and interactive mesh to T-spline conversion
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Fitting solid meshes to animated surfaces using linear elasticity
ACM Transactions on Graphics (TOG)
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Technical Section: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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
Template-Based 3D Model Fitting Using Dual-Domain Relaxation
IEEE Transactions on Visualization and Computer Graphics
Solid mesh registration for radiotherapy treatment planning
ISBMS'10 Proceedings of the 5th international conference on Biomedical Simulation
Restricted Trivariate Polycube Splines for Volumetric Data Modeling
IEEE Transactions on Visualization and Computer Graphics
SMI 2012: Full As-conformal-as-possible discrete volumetric mapping
Computers and Graphics
Design and Analysis of Optimization Methods for Subdivision Surface Fitting
IEEE Transactions on Visualization and Computer Graphics
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
A content-aware bridging service for publish/subscribe environments
Journal of Systems and Software
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We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be implicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We apply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.