Mathematical Methods for CAD

Couverture
Cambridge University Press, 13 août 1992 - 196 pages
This book sets out the fundamental elements of the theory of computational geometry and computer-aided design in a mathematically rigorous manner. Splines and Bézier curves are first tackled, leading to Bézier surfaces, triangulation, and box splines. The final chapter is devoted to algebraic geometry and provides a firm theoretical basis for anyone wishing to seriously develop and investigate CAD systems.
 

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Table des matières

Bsplines
9
Cubic splines
10
Fundamental properties
14
14 The Bspline basis of Pkrr+
20
15 Basic Algorithms for Bsplines
24
16 Approximation by a spline curve
31
17 Divided differences
34
Spline curves and Bézier curves
39
45 Triangular Bézier patches
109
46 Junction between Bézier patches
116
47 Base points of rational Bézier patches
119
48 Polyhedral splines
128
49 Box splines
138
Triangulations
147
51 Voronoï diagrams
148
52 Generalities about triangulations
152

22 Bsplines curves
42
23 Algorithms for spline curves
46
Interpolation and complements
67
32 Other properties of the matrix N
70
33 Matrix representation
72
34 Junction between two curves
76
35 Rational curves
85
Spline Surfaces
95
42 Particular case of Bézier surfaces
99
43 Interpolation and approximation
104
44 Bernstein polynomials
107
53 Delaunay triangulations
157
54 Construction Algorithm
165
55 Remarks about complexity
171
Notions of real algebraic geometry
175
62 Resultants and discriminants
180
63 Notions of semialgebraic sets
184
Plates
187
Bibliography
193
Index
195
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