Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
ACM Transactions on Graphics (TOG)
Axioms and variational problems in surface parameterization
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
A fast multigrid algorithm for mesh deformation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Adaptive deformations with fast tight bounds
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Handle-aware isolines for scalable shape editing
ACM SIGGRAPH 2007 papers
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Axioms and variational problems in surface parameterization
Computer Aided Geometric Design
Estimating the Laplace-Beltrami operator by restricting 3D functions
SGP '09 Proceedings of the Symposium on Geometry Processing
Parameterizing subdivision surfaces
ACM SIGGRAPH 2010 papers
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
Interactive and anisotropic geometry processing using the screened Poisson equation
ACM SIGGRAPH 2011 papers
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
Journal of Scientific Computing
Meshing point clouds using spherical parameterization
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Efficient preconditioning of laplacian matrices for computer graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner.