Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
An effective approach to pose invariant 3D face recognition
MMM'11 Proceedings of the 17th international conference on Advances in multimedia modeling - Volume Part I
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
Modeling 3D articulated motions with conformal geometry videos (CGVs)
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Texture mapping subdivision surfaces with hard constraints
The Visual Computer: International Journal of Computer Graphics
Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization
Journal of Scientific Computing
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Mesh parameterization is a fundamental technique in computer graphics. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. Firstly, we deduce an exact analytical differential formula to represent area distortion by curvature change in the discrete conformal mapping, giving a dynamic Poisson equation. Our result shows the curvature map is invertible. Furthermore, we give the explicit Jacobi matrix of the inverse curvature map. Secondly, we formulate the task of computing conformal parameterizations with least area distortions as a constrained nonlinear optimization problem in curvature space. We deduce explicit conditions for the optima. Thirdly, we give an energy form to measure the area distortions, and show it has a unique global minimum. We use this to design an efficient algorithm, called free boundary curvature diffusion, which is guaranteed to converge to the global minimum. This result proves the common belief that optimal parameterization with least area distortion has a unique solution and can be achieved by free boundary conformal mapping. Major theoretical results and practical algorithms are presented for optimal parameterization based on the inverse curvature map. Comparisons are conducted with existing methods and using different energies. Novel parameterization applications are also introduced.