This book reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. Features: presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations; reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces; examines techniques for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses point location databases and convex hulls of point sets; investigates the reconstruction of triangle meshes from point clouds, including methods for registration of point clouds and surface reconstruction; provides additional material at a supplementary website; includes self-study exercises throughout the text.An obvious way of estimating the curvature of a triangle mesh is based on fitting a smooth surface to the mesh. Finding a global surface that fits the mesh is a difficult problem. ... Fortunately, any smooth surface can be represented locally as a height function f (u, v) where u and v are coordinates in an estimated tangent plane ... good surface to use is the paraboloid given by f(u, v) = 12(au2 +2buv+ cv2 ) .
|Title||:||Guide to Computational Geometry Processing|
|Author||:||J. Andreas Bærentzen, Jens Gravesen, Francois Anton, Henrik Aanæs|
|Publisher||:||Springer Science & Business Media - 2012-05-31|