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 atlas basis boundary called canonical choose circle packing closed surface compact Riemann surface complex compute conformal mapping conformal structure conformally equivalent connected constant construct convert coordinates corresponding curvature curve defined Definition denoted differential discrete disk divisor domain edge element embedded energy equation Euclidean exists face field fixed point function Gaussian curvature genus genus g geodesic geometry given half-edge harmonic 1-form harmonic map holomorphic 1-form homology homotopy group hyperbolic induces input length linear loop manifold matrix meromorphic mesh method metric Möbius transformation namely normal operator oriented path planar plane positive preserving problem projective Proof Prove represented Ricci flow Riemann surface Riemannian metric shape shows smooth sphere Suppose tangent tangent vector texture Theorem topological uniformization unique unit universal covering space vector vertex vertices zero