Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
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
Spanning Tree Seams for Reducing Parameterization Distortion of Triangulated Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Modeling sphere-like manifolds with spherical Powell--Sabin B-splines
Computer Aided Geometric Design
A genus oblivious approach to cross parameterization
Computer Aided Geometric Design
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Feature-based 3D morphing based on geometrically constrained sphere mapping optimization
Proceedings of the 2010 ACM Symposium on Applied Computing
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
Efficient parameterization of 3d point-sets using recursive dynamic base surfaces
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Cauchy's theorem and edge lengths of convex polyhedra
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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Parameterization of 3D mesh data is important for many graphics and mesh processing 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 3D triangle mesh onto the 3D 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 do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.