Computational Geometry: Theory and Applications
2D-Shape Analysis Using Conformal Mapping
International Journal of Computer Vision
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
IEEE Transactions on Visualization and Computer Graphics
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Shape analysis of planar objects with arbitrary topologies using conformal geometry
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
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Conformal mapping plays an important role in Computer Graphics and Shape Modeling. According to Poincare's uniformization theorem, all closed metric surfaces can be conformally mapped to one of the three canonical spaces, the sphere, the plane or the hyperbolic disk. This work generalizes the uniformization from closed high genus surfaces to high genus surfaces with boundaries, to map them to the canonical spaces with circular holes. The method combines discrete surface Ricci flow and Koebe's iteration with zero holonomy condition. Theoretic proof for the convergence is given. Experimental results show that the method is general, stable and practical. It is fundamental and has great potential to geometric analysis in various fields of engineering and medicine.