Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees
Computational Geometry: Theory and Applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Metamorphosis of Arbitrary Triangular Meshes
IEEE Computer Graphics and Applications
One-to-one piecewise linear mappings over triangulations
Mathematics of Computation
Computer Aided Geometric Design
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
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
Cross-parameterization and compatible remeshing of 3D models
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
On the optimality of spectral compression of mesh data
ACM Transactions on Graphics (TOG)
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
Iso-charts: stretch-driven mesh parameterization using spectral analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Face transfer with multilinear models
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2005 Papers
Non-Euclidean Spring Embedders
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Spherical manifolds for adaptive resolution surface modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Duplicate-skins for compatible mesh modelling
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Face transfer with multilinear models
ACM SIGGRAPH 2006 Courses
Surface modeling and parameterization with manifolds
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A Riemannian approach to graph embedding
Pattern Recognition
Parameterizations of digital surfaces homeomorphic to a sphere using discrete harmonic functions
Pattern Recognition Letters
Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Modeling sphere-like manifolds with spherical Powell--Sabin B-splines
Computer Aided Geometric Design
Parameterizations of digital surfaces homeomorphic to a sphere using discrete harmonic functions
Pattern Recognition Letters
Technical Section: Pseudo surface-texture synthesis
Computers and Graphics
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Surface parameterization via aligning optimal local flattening
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Conformal spherical representation of 3D genus-zero meshes
Pattern Recognition
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
An image processing approach to surface matching
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Quasi-isometric parameterization for texture mapping
Pattern Recognition
Quasi-isometric parameterization for texture mapping
Pattern Recognition
An efficient approximation of arbitrary curves and surfaces using intersecting polylines and meshes
Advances in Engineering Software
Texture mapping on 3D surfaces using clustering-based cutting paths
International Journal of Computational Science and Engineering
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer-Aided Design
Optimizing Surface Triangulation Via Near Isometry with Reference Meshes
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Polynomial splines over hierarchical T-meshes
Graphical Models
A genus oblivious approach to cross parameterization
Computer Aided Geometric Design
Edge based parameterization for tubular meshes
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
Hardware Accelerated Per-Texel Ambient Occlusion Mapping
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Computer Aided Geometric Design
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
ACM SIGGRAPH ASIA 2009 Courses
Fast Spherical Mapping for Genus-0 Meshes
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Morphing planar graphs in spherical space
GD'06 Proceedings of the 14th international conference on Graph drawing
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Technical Section: Mesh reconstruction by meshless denoising and parameterization
Computers and Graphics
ACM SIGGRAPH 2010 Courses
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
SIAM Journal on Scientific Computing
Graph attribute embedding via Riemannian submersion learning
Computer Vision and Image Understanding
SMI 2011: Full Paper: Parallel computation of spherical parameterizations for mesh analysis
Computers and Graphics
Feature-based 3D morphing based on geometrically constrained spherical parameterization
Computer Aided Geometric Design
Elements of geometry processing
SIGGRAPH Asia 2011 Courses
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
3D active shape models using gradient descent optimization of description length
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
New 3d fourier descriptors for genus-zero mesh objects
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Geometry compression using spherical wavelet
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Discrete conformal shape representation and reconstruction of 3d mesh objects
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Feature-Constrained texturing system for 3d models
KES'05 Proceedings of the 9th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
Consistent spherical parameterization
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Shape-based retrieval of articulated 3d models using spectral embedding
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Texture synthesis using incremental patches
Edutainment'06 Proceedings of the First international conference on Technologies for E-Learning and Digital Entertainment
Meshing point clouds using spherical parameterization
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Efficient texture mapping by homogeneous patch discovery
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Ricci flow-based spherical parameterization and surface registration
Computer Vision and Image Understanding
Harmonic parameterization by electrostatics
ACM Transactions on Graphics (TOG)
FIMH'13 Proceedings of the 7th international conference on Functional Imaging and Modeling of the Heart
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Computer-Aided Design
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Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not too distorted and do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection to spectral graph theory and show how to compute these parameterizations.