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E-raamat: Computational Geometry With Independent And Dependent Uncertainties

(The Hebrew Univ Of Jerusalem, Israel), (The Hebrew Univ Of Jerusalem, Israel)
  • Formaat: 160 pages
  • Ilmumisaeg: 11-Aug-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811253850
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  • Formaat: 160 pages
  • Ilmumisaeg: 11-Aug-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811253850
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"This comprehensive compendium describes a parametric model and algorithmic theory to represent geometric entities with dependent uncertainties between them. The theory, named Linear Parametric Geometric Uncertainty Model (LPGUM), is an expressive and computationally efficient framework that allows to systematically study geometric uncertainty and its related algorithms in computer geometry. The self-contained monograph is of great scientific, technical, and economic importance as geometric uncertainty is ubiquitous in mechanical CAD/CAM, robotics, computer vision, wireless networks and many other fields. Geometric models, in contrast, are usually exact and do not account for these inaccuracies. This useful reference text benefits academics, researchers,and practitioners in computer science, robotics, mechanical engineering and related fields"--

This Comprehensive Compendium Describes A Parametric Model And Algorithmic Theory To Represent Geometric Entities With Dependent Uncertainties Between Them. The Theory, Named Linear Parametric Geometric Uncertainty Model (Lpgum), Is An Expressive And Computationally Efficient Framework That Allows To Systematically Study Geometric Uncertainty And Its Related Algorithms In Computer Geometry. The Self-Contained Monograph Is Of Great Scientific, Technical, And Economic Importance As Geometric Uncertainty Is Ubiquitous In Mechanical Cad/Cam, Robotics, Computer Vision, Wireless Networks And Many Other Fields. Geometric Models, In Contrast, Are Usually Exact And Do Not Account For These Inaccuracies. This Useful Reference Text Benefits Academics, Researchers, And Practitioners In Computer Science, Robotics, Mechanical Engineering And Related Fields.

Preface viii
About the Authors ix
Acknowledgments xi
1 Introduction
1(12)
1.1 Background
1(2)
1.2 Literature Review
3(6)
1.3 Goals
9(1)
1.4 Overview and Novelty
9(2)
1.5 Book Organization
11(2)
2 The Linear Parametric Geometric Uncertainty Model
13(10)
2.1 Basic Definitions
13(1)
2.2 LPGUM Coordinate
14(1)
2.3 LPGUM Point and Vector
15(2)
2.4 LPGUM Line and Edge
17(2)
2.5 LPGUM Three-Point Circle
19(2)
2.6 Summary
21(2)
3 The Envelopes of Uncertain Points, Lines and Circles
23(32)
3.1 LPGUM Coordinate and Point
23(2)
3.2 LPGUM Line
25(13)
3.3 LPGUM Three-Point Circle
38(15)
3.4 Summary
53(2)
4 Half-Plane Point Retrieval Queries
55(14)
4.1 Background
55(3)
4.2 Half-Plane Point Retrieval Queries
58(9)
4.3 Summary
67(2)
5 Euclidean Minimum Spanning Trees
69(28)
5.1 Background
69(2)
5.2 Uncertain EMST: Definitions and Properties
71(5)
5.3 Pairwise Uncertain Edge Weight Comparison
76(6)
5.4 Uncertain EMST Stability Test
82(12)
5.5 The Weight of an Uncertain EMST
94(1)
5.6 Summary
95(2)
6 Voronoi Diagram and Delaunay Triangulation
97(34)
6.1 Background
97(4)
6.2 Voronoi Diagram and Delaunay Triangulation of LPGUM Points
101(9)
6.3 LPGUM Bisectors
110(2)
6.4 Intersection of Two Independent LPGUM Lines
112(3)
6.5 Properties of an Independent Uncertain Voronoi Diagram Vertex
115(2)
6.6 Stable Uncertain Voronoi Diagram Construction
117(4)
6.7 Point Location Queries in a Stable Uncertain Voronoi Diagram
121(8)
6.8 Dynamic Stable Uncertain Voronoi Diagram
129(1)
6.9 Summary
130(1)
7 Conclusion
131(4)
7.1 Summary
131(2)
7.2 Open Problems
133(2)
References 135(6)
Index 141