Guide to computational geometry processing: foundations, algorithms, and methods

✍ Scribed by Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs (auth.)

• Publisher: Springer-Verlag London
• Year: 2012
• Tongue: English
• Leaves: 330
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XVIII
Front Matter....Pages 11-11
Introduction....Pages 1-10
Front Matter....Pages 11-11
Vector Spaces, Affine Spaces, and Metric Spaces....Pages 13-43
Differential Geometry....Pages 45-64
Finite Difference Methods for Partial Differential Equations....Pages 65-79
Front Matter....Pages 81-81
Polygonal Meshes....Pages 83-97
Splines....Pages 99-117
Subdivision....Pages 119-141
Curvature in Triangle Meshes....Pages 143-158
Mesh Smoothing and Variational Subdivision....Pages 159-177
Parametrization of Meshes....Pages 179-190
Simplifying and Optimizing Triangle Meshes....Pages 191-211
Spatial Data Indexing and Point Location....Pages 213-225
Convex Hulls....Pages 227-240
Triangle Mesh Generation: Delaunay Triangulation....Pages 241-261
3D Surface Registration via Iterative Closest Point (ICP)....Pages 263-275
Surface Reconstruction using Radial Basis Functions....Pages 277-286
Volumetric Methods for Surface Reconstruction and Manipulation....Pages 287-308
Isosurface Polygonization....Pages 309-320
Back Matter....Pages 321-325

✦ Subjects

Math Applications in Computer Science; Symbolic and Algebraic Manipulation; Computer Graphics; Artificial Intelligence (incl. Robotics); Image Processing and Computer Vision; Computer-Aided Engineering (CAD, CAE) and Design