Guide to Computational Geometry Processing, 2012 Foundations, Algorithms, and Methods

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.

Provides a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics Presents an introduction to the theoretical and mathematical underpinnings of each technique Includes self-study exercises throughout the text, and supplies additional material at a supplementary website Includes supplementary material: sn.pub/extras