Computational Conformal Geometry
Computational conformal geometry is an emerging inter-disciplinary field, with applications to algebraic topology, differential geometry and Riemann surface theories applied to geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation, and many other engineering fields.This new volume presents thorough introductions to the theoretical foundations—as well as to the practical algorithms—of computational conformal geometry. These have direct applications to engineering and digital geometric processing, including surface parameterization, surface matching, brain mapping, 3-D face recognition and identification, facial expression and animation, dynamic face tracking, mesh-spline conversion, and more.
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Homology and Cohomology
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algorithm angles basis boundary called canonical chain homotopy choose circle packing closed surface compact complex compute conformal mapping connected construct 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 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 original output parameterization path planar plane positive preserving problem projective Prove relation represented Ricci flow Riemann surface shape shortest shown shows smooth sphere spline Suppose tangent tangent vector texture Theorem topological unique unit universal covering space vector vertex vertices visualized zero