Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Applied numerical linear algebra
Applied numerical linear algebra
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Local Control for Mesh Morphing
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Hierarchical Least Squares Conformal Map
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
ACM SIGGRAPH 2004 Papers
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Numerical Recipes: The Art of Scientific Computing with IBM PC or Macintosh
Numerical Recipes: The Art of Scientific Computing with IBM PC or Macintosh
A fast multigrid algorithm for mesh deformation
ACM SIGGRAPH 2006 Papers
Graphical Models - Special issue on SPM 05
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Interactive mesh deformation using equality-constrained least squares
Computers and Graphics
Random walks for mesh denoising
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Preserving form features in interactive mesh deformation
Computer-Aided Design
Multi-scale capture of facial geometry and motion
ACM SIGGRAPH 2007 papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Automatic rigging and animation of 3D characters
ACM SIGGRAPH 2007 papers
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Automatic and interactive mesh to T-spline conversion
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Dual evolution of planar parametric spline curves and T-spline level sets
Computer-Aided Design
Random walks for feature-preserving mesh denoising
Computer Aided Geometric Design
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
ACM SIGGRAPH 2009 papers
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Regularisation of 3D Signed Distance Fields
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Flexible simulation of deformable models using discontinuous Galerkin FEM
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Boneless pose editing and animation
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
ACM Transactions on Graphics (TOG)
Freeform vector graphics with controlled thin-plate splines
Proceedings of the 2011 SIGGRAPH Asia Conference
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Preserving form-features in interactive mesh deformation
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
Least squares quasi-developable mesh approximation
Computer Aided Geometric Design
Updated sparse cholesky factors for corotational elastodynamics
ACM Transactions on Graphics (TOG)
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
Repoussé: automatic inflation of 2D artwork
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Template deformation for point cloud fitting
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
Fast simulation of mass-spring systems
ACM Transactions on Graphics (TOG)
Geodesics in heat: A new approach to computing distance based on heat flow
ACM Transactions on Graphics (TOG)
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The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more specifically to sparse, symmetric, and positive definite systems, that allow for a numerically robust and efficient solution. In this paper we discuss and evaluate the use of sparse direct solvers for such kind of systems in geometry processing applications, since in our experiments they turned out to be superior even to highly optimized multigrid methods, but at the same time were considerably easier to use and implement. Although the methods we present are well known in the field of high performance computing, we observed that they are in practice surprisingly rarely applied to geometry processing problems.