Curve and Surface Reconstruction Algorithms with Mathematical Analysis

Name: Curve and Surface Reconstruction Algorithms with Mathematical Analysis
Price: 93.48 USD
Availability: InStock
ISBN: 9780521863704

ISBN-10: 0521863708

ISBN-13: 9780521863704

Edition: 2006

Authors: Tamal K. Dey

List price: $95.99

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Description:

Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi and Delaunay based techniques, implicit surface based…

Book details

List price: $95.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/16/2006
Binding: Hardcover
Pages: 232
Size: 5.98" wide x 9.02" long x 0.67" tall
Weight: 1.122
Language: English



Preface



Basics



Shapes



Spaces and Maps



Manifolds



Complexes



Feature Size and Sampling



Medial Axis



Local Feature Size



Sampling



Voronoi Diagram and Delaunay Triangulation



Two Dimensions



Three Dimensions



Notes and Exercises


Exercises



Curve Reconstruction



Consequences of [epsilon]-Sampling



Crust



Algorithm



Correctness



NN-Crust



Algorithm



Correctness



Notes and Exercises


Exercises



Surface Samples



Normals



Approximation of Normals



Normal Variation



Edge and Triangle Normals



Topology



Topological Ball Property



Voronoi Faces



Notes and Exercises


Exercises



Surface Reconstruction



Algorithm



Poles and Cocones



Cocone Triangles



Pruning



Manifold Extraction



Geometric Guarantees



Additional Properties



Topological Guarantee



The Map [nu]



Homeomorphism Proof



Notes and Exercises


Exercises



Undersampling



Samples and Boundaries



Boundary Sample Points



Flat Sample Points



Flatness Analysis



Boundary Detection



Justification



Reconstruction



Notes and Exercises


Exercises



Watertight Reconstructions



Power Crust



Definition



Proximity



Homeomorphism and Isotopy



Algorithm



Tight Cocone



Marking



Peeling



Experimental Results



Notes and Exercises


Exercises



Noisy Samples



Noise Model



Empty Balls



Normal Approximation



Analysis



Algorithm



Feature Approximation



Analysis



Algorithm



Notes and Exercises


Exercises



Noise and Reconstruction



Preliminaries



Union of Balls



Proximity



Topological Equivalence



Labeling



Algorithm



Notes and Exercises


Exercises



Implicit Surface-Based Reconstructions



Generic Approach



Implicit Function Properties



Homeomorphism Proof



MLS Surfaces



Adaptive MLS Surfaces



Sampling Assumptions and Consequences



Influence of Samples



Surface Properties



Hausdorff Property



Gradient Property



Algorithm and Implementation



Normal and Feature Approximation



Projection



Other MLS Surfaces



Projection MLS



Variation



Computational Issues



Voronoi-Based Implicit Surface



Notes and Exercises


Exercises



Morse Theoretic Reconstructions



Morse Functions and Flows



Discretization



Vector Field



Discrete Flow



Relations to Voronoi/Delaunay Diagrams



Reconstruction with Flow Complex



Flow Complex Construction



Merging



Critical Point Separation



Reconstruction with a Delaunay Subcomplex



Distance from Delaunay Balls



Classifying and Ordering Simplices



Reconstruction



Algorithm



Notes and Exercises


Exercises


Bibliography


Index