Description
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. Part I: Mathematical Preliminaries Vector Spaces, Affine Spaces, and Metric Spaces Differential Geometry Finite Difference Methods for Partial Differential Equations Part II: Computational Geometry Processing Polygonal Meshes Splines Subdivision Curvature in Triangle Meshes Mesh Smoothing and Variational Subdivision Parametrization of Meshes Simplifying and Optimizing Triangle Meshes Spatial Data Indexing and Point Location Convex Hulls Triangle Mesh Generation: Delaunay Triangulation 3D Surface Registration via Iterative Closest Point (ICP) Surface Reconstruction using Radial Basis Functions Volumetric Methods for Surface Reconstruction and Manipulation Isosurface Polygonization
