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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1-chain angles annulus atlas boundary called canonical circle packing circle packing metric closed 1-form closed surface cochain cohomology compact Riemann surface complex conformal geometry conformal mapping conformal parameterization conformal structure conformally equivalent conjugate continuous map coordinates curve cut graph deck transformation defined Definition deformation denoted differential dimensional divisor double covering edge embedded in R3 equation Euclidean finite fixed point following algorithm forall function fundamental domain fundamental group fundamental polygon Gauss map Gaussian curvature genus g geodesic harmonic 1-form harmonic energy harmonic map holomorphic 1-form homeomorphism homology homotopy class homotopy group induced input linear manifold matrix meromorphic method Mobius transformation normal oriented output plane Poincare quasi-conformal map Ricci flow Riemannian metric shortest loop simplicial splines Suppose surface Ricci flow tangent vector target curvature texture mapping Theorem topological disk topological spaces triangular mesh triangulation unique unit disk unit sphere universal covering space vector field vertex vertices zero points