Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Signal-specialized parametrization
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Anisotropic Centroidal Voronoi Tessellations and Their Applications
SIAM Journal on Scientific Computing
Signal-specialized parameterization for piecewise linear reconstruction
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete Tensorial Quasi-Harmonic Maps
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Building triangulations using ε-nets
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Surface remeshing in arbitrary codimensions
The Visual Computer: International Journal of Computer Graphics
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
SIAM Journal on Numerical Analysis
Integral invariants for robust geometry processing
Computer Aided Geometric Design
ACM SIGGRAPH 2009 papers
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Semi-regular quadrilateral-only remeshing from simplified base domains
SGP '09 Proceedings of the Symposium on Geometry Processing
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Generation of bi-monotone patches from quadrilateral mesh for reverse engineering
Computer-Aided Design
Feature-aware partitions from the motorcycle graph
Computer-Aided Design
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Quadrangulation methods aim to approximate surfaces by semiregular meshes with as few extraordinary vertices as possible. A number of techniques use the harmonic parameterization to keep quads close to squares, or fit parametrization gradients to align quads to features. Both types of techniques create near-isotropic quads; feature-aligned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions. A complementary approach is to allow for anisotropic elements, which are well-known to have significantly better approximation quality. In this work we present a simple and efficient technique to add curvature-dependent anisotropy to harmonic and feature-aligned parameterization and improve the approximation error of the quadrangulations. We use a metric derived from the shape operator which results in a more uniform error distribution, decreasing the error near features.