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Geometric computations with interval and new robust methods : applications in computer graphics, GIS and computational geometry /
This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers comp...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester :
Horwood Publishing,
2003.
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| Colección: | Horwood Publishing series in computer science.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; ABOUT OUR AUTHORS; Geometric Computations with Interval and New Robust Methods: Applications in Computer Graphics, GIS and Computational Geometry; Copyright Page; Table of Contents; List of Figures; List of Tables; Preface; Chapter 1. Introduction; 1.1 Errors in Numerical Computations; 1.2 Geometric Computations; 1.3 Problems in Geometric Computations Caused by Floating Point Computation; 1.4 Approaches to Controlling Errors in Geometric Computations; 1.5 The Interval Analysis Approach; 1.6 Global Interval Aspects; 1.7 The Exact Sign of Sum Algorithm (ESSA).
- 1.8 Arithmetic Filters1.9 Computer Implementations; Chapter 2. Interval Analysis; 2.1 Introduction; 2.2 Motivation for Interval Arithmetic; 2.3 Interval Arithmetic Operations; 2.4 Implementing Interval Arithmetic; 2.5 Further Notations; 2.6 The Meaning of Inclusions for the Range; 2.7 Inclusion Functions and Natural Interval Extensions; 2.8 Combinatorial Aspects of Inclusions; 2.9 Skelboe's Principle; 2.10 Inner Approximations to the Range of Linear Functions; 2.11 Interval Philosophy in Geometric Computations; 2.12 Centered Forms and Other Inclusions; 2.13 Subdivision for Range Estimation.
- 2.14 SummaryChapter 3. Interval Newton Methods; 3.1 Introduction; 3.2 The Interval Newton Method; 3.3 The Hansen-Sengupta Version; 3.4 The Existence Test; Chapter 4. The Exact Sign of Sum Algorithm (ESSA); 4.1 Introduction; 4.2 The Need for Exact Geometric Computations; 4.3 The Algorithm; 4.4 Properties of ESSA; 4.5 Numerical Results; 4.6 Merging with Interval Methods, Applications; 4.7 ESSA and Preprocessing Implementation in C; Chapter 5. Intersection Tests; 5.1 Introduction; 5.2 Line Segment Intersections; 5.3 Box-Plane Intersection Testing; 5.4 Rectangle-Triangle Intersection Testing.
- 5.5 Box-Tetrahedron Intersection Testing5.6 Ellipse-Rectangle Intersection Testing; 5.7 Intersection Between Rectangle and Explicitly Defined Curve; 5.8 Box-Sphere Intersection Test; Chapter 6. The SCCI-Hybrid Method for 2D-Curve Tracing; 6.1 Introduction; 6.2 The Parts of the SCCI-Hybrid Method; 6.3 Examples; Chapter 7. Interval Versions of Bernstein Polynomials, B�ezier Curves and the de Casteljau Algorithm; 7.1 Introduction; 7.2 Plane Curves and Bernstein Polynomials; 7.3 Interval Polynomials and Interval Bernstein Polynomials; 7.4 Real and Interval B�ezier Curves.
- 7.5 Interval Version of the de Casteljau AlgorithmChapter 8. Robust Computations of Selected Discrete Problems; 8.1 Introduction; 8.2 Convex-Hull Computations in 2D; 8.3 Exact Computation of Delaunay and Power Triangulations; 8.4 Exact and Robust Line Simplification; Bibliography; Index.