Computational Conformal Geometry

algorithm angles basis boundary called canonical chain homotopy choose circle packing compact complex compute conformal mapping connected construct convert coordinates corresponding curvature curve data structure defined Definition denoted differential discrete domain edge embedded energy equation equivalent Euclidean exists face field fixed function Gaussian curvature genus genus g geodesic geometry given graph half-edge handle harmonic 1-form harmonic map holomorphic 1-form homology homotopy group hyperbolic induced input length linear loop manifold matrix mesh method metric minimal Möbius transformation namely normal operator oriented output parameterization path planar plane positive preserving problem projective Prove relation represented Ricci flow Riemann surface shape shortest shows smooth sphere spline Suppose tangent tangent vector texture Theorem topological unique unit universal covering space vector vertex vertices zero