Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
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Classical surface parameterization algorithms often place singularities in order to enhance the quality of the resulting parameter map. Unfortunately, singularities of positive integral index (as the north pole of a sphere) were not handled since they cannot be described with piecewise linear parameter functions on a triangle mesh. Preprocessing is needed to adapt the mesh connectivity. We present an extension to the QuadCover parameterization algorithm [1], which allows to handle those singularities. A singularity of positive integral index can be resolved using bilinear parameter functions on quadrilateral elements. This generalization of piecewise linear functions for quadrilaterals enriches the space of parameterizations. The resulting parameter map can be visualized by textures using a rendering system which supports quadrilateral elements, or it can be used for remeshing into a quad mesh.