Computational Conformal GeometryXianfeng David Gu, Shing-Tung Yau International Press, 2008 - 295 Seiten "Computational conformal geometry is an emerging inter-disciplinary field, which applies algebraic topology, differential geometry and Riemann surface theories in geometric modelling, computer graphics, computer vision, medical imaging, visualization, scientifice computations and many other engineering fields."--Back cover. |
Inhalt
Introduction | 1 |
Homotopy Group | 33 |
Homology and Cohomology | 51 |
Urheberrecht | |
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1-chain angles annulus 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 coordinates curve cut graph deck transformation defined Definition denoted differential double covering edge embedded equation Euclidean face finite fixed point forall function fundamental domain fundamental group fundamental polygon Gaussian curvature genus g geodesic harmonic 1-form harmonic energy harmonic map holomorphic 1-form homeomorphism homology homotopy group induced input linear M₁ manifold map f matrix meromorphic method Möbius transformation normal oriented plane Poincaré disk quasi-conformal map Ricci flow Riemann mapping Riemannian metric simplicial spline Suppose surface Ricci flow tangent vector target curvature Teichmüller texture mapping Theorem topological disk topological spaces triangular mesh triangulation unique unit disk unit sphere universal covering space vector field vertex vertices w₁ zero points ди