Bærentzen, Jakob Andreas5; Gravesen, Jens5; Anton, François6; Aanæs, Henrik5
1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Mathematics, Technical University of Denmark4 Geometry, Department of Mathematics, Technical University of Denmark5 Department of Applied Mathematics and Computer Science, Technical University of Denmark6 National Space Institute, Technical University of Denmark
Foundations, Algorithms, and Methods
Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first be processed before it is useful. This Guide to Computational Geometry Processing 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. This is balanced with an introduction to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and 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 Graduate students will find this text a valuable, hands-on guide to developing key skills in geometry processing. The book will also serve as a useful reference for professionals wishing to improve their competency in this area.