Guide to Computational Geometry Processing: Foundations, Algorithms, and Methods [Hardcover]

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.

From the book reviews:

The book consists of two partsMathematical Preliminaries and Computational Geometry Processing. Almost 70 pages of linear algebra, differential geometry and finite dilãƒ