- Full 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.
- Table of Contents
Table of Contents
- 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.
- 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.
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