Computer-Aided Geometric Design
A Totally Four-Dimensional Approach
Résumé
Computer graphics, computer-aided design, and computer-aided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computer-aided design systems although it contains elements that inevitably lead to an inaccurate, non-robust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an n-space problem is to be processed in n-space. The difficulties that accompany the division operation may be avoided if processing is conducted entirely in (n+1)-space. The paradigm attained through the logical extension of this approach, totally four-dimensional processing, is the subject of this book. This book offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system.
Contents
I: Problem Definitions- Problems of Euclidean Approach
- Homogeneous Coordinates
- Classical Projective Space
- Two-Sided Space
- Processing in Projective Spaces
- Transformations
- A Solution
- Geometric Definitions in General
- Geometric Element Definitions
- Homogeneous Curves
- Homogeneous Surfaces
- Basic Intersections
- 4 X 4 Determinant Methods
- The Homogeneous Determinant Method
- Geometric Newton-Raphson Method
- Exact Arithmetic
- Fundamentals of Topology
- Data Structures
- Euclidean and Affine
- Set Operations
- Polyhedron Subdivisions
- Reconstruction of 3-D Points
- Display Process
- Classical or Two-Sided?
- Various Tests
- Evaluations
- Role of Division Operations
- Various Interpretations
Appendix B: Various Geometries
Appendix C: Plane Determinant Method
Appendix D: Analytical Geometry in Vector Space
Appendix E: Proofs for Chapter 16
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | F. Yamaguchi |
| Parution | 18/11/2002 |
| Nb. de pages | 670 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 1257g |
| Intérieur | Noir et Blanc |
| EAN13 | 9784431703402 |
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