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Curve and Surface Reconstruction Algorithms with Mathematical Analysis

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ISBN-10: 0521863708

ISBN-13: 9780521863704

Edition: 2006

Authors: Tamal K. Dey

List price: $88.99
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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…    
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Book details

List price: $88.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/16/2006
Binding: Hardcover
Pages: 232
Size: 6.00" wide x 9.25" long x 0.75" tall
Weight: 0.946
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