Guide to computational geometry processing: 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 locationdatabases and convex hulls of point sets; investigates the reconstruction of triangle meshes from point clouds, including methods for registration of pointclouds and surface reconstruction; provides additional material at a supplementary website; includes self-study exercises throughout the text. INDICE: 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.

• ISBN: 978-1-4471-4074-0
• Editorial: Springer
• Encuadernacion: Cartoné
• Fecha Publicación: 08/06/2012
• Nº Volúmenes: 1
• Idioma: Inglés