Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
A taxonomy for conjugate gradient methods
SIAM Journal on Numerical Analysis
Surface fitting with hierarchical splines
ACM Transactions on Graphics (TOG)
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th 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
Multiresolution signal processing for meshes
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
Multiresolution hierarchies on unstructured triangle meshes
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Dynamic remeshing and applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
SMI '03 Proceedings of the Shape Modeling International 2003
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Hierarchical Least Squares Conformal Map
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
Interactive mesh deformation using equality-constrained least squares
Computers and Graphics
3D triangular mesh optimization in geometry processing for CAD
Proceedings of the 2007 ACM symposium on Solid and physical modeling
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Towards flattenable mesh surfaces
Computer-Aided Design
An incremental approach to feature aligned quad dominant remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Pattern computation for compression garment
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Using the CAT for 3D Sketching in Front of Large Displays
SG '08 Proceedings of the 9th international symposium on Smart Graphics
Pattern computation for compression garment by a physical/geometric approach
Computer-Aided Design
Feature aligned quad dominant remeshing using iterative local updates
Computer-Aided Design
Markerless reconstruction and synthesis of dynamic facial expressions
Computer Vision and Image Understanding
Non-uniform differential mesh deformation
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Versatile rigid-fluid coupling for incompressible SPH
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
OpenFlipper: an open source geometry processing and rendering framework
Proceedings of the 7th international conference on Curves and Surfaces
Vertex location optimisation for improved remeshing
Graphical Models
Rationalization of Triangle-Based Point-Folding Structures
Computer Graphics Forum
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
Computer Graphics Forum
Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes
Computer Graphics Forum
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
Statistical surface recovery: a study on ear canals
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Topology aware quad dominant meshing for vascular structures
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Robust fairing via conformal curvature flow
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Local fairing with local inverse
Proceedings of Graphics Interface 2013
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Providing a thorough mathematical foundation, multiresolution modeling is the standard approach for global surface deformations that preserve fine surface details in an intuitive and plausible manner. A given shape is decomposed into a smooth low-frequency base surface and high-frequency detail information. Adding these details back onto a deformed version of the base surface results in the desired modification. Using a suitable detail encoding, the connectivity of the base surface is not restricted to be the same as that of the original surface. We propose to exploit this degree of freedom to improve both robustness and efficiency of multiresolution shape editing.In several approaches the modified base surface is computed by solving a linear system of discretized Laplacians. By remeshing the base surface such that the Voronoi areas of its vertices are equalized, we turn the unsymmetric surface-related linear system into a symmetric one, such that simpler, more robust, and more efficient solvers can be applied. The high regularity of the remeshed base surface further removes numerical problems caused by mesh degeneracies and results in a better discretization of the Laplacian operator.The remeshing is performed on the low-frequency base surface only, while the connectivity of the original surface is kept fixed. Hence, this functionality can be encapsulated inside a multiresolution kernel and is thus completely hidden from the user.