COMPUTATIONAL LINE GEOMETRY

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Ouvrage 9783540420583 : COMPUTATIONAL LINE GEOMETRY

Pottmann, H., Technische Universit„t Wien, Austria; Wallner, J., Technische Universit„t Wien, Austria
Computational Line Geometry
2001. IX, 563 pp. 264 figs., 17 in color. Hardcover
The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applications in particular.
Keywords: line geometry, scientific computing, geometric design, visualization, kinematics
Table of Contents
Preface
Table of Contents
1
Fundamentals
1
1.1
Real Projective Geometry
1
1.2
Basic Projective Differential Geometry
68
1.3
Elementary Concepts of Algebraic Geometry
86
1.4
Rational Curves and Surfaces in Geometric Design
105
2
Models of Line Space
133
2.1
The Klein Model
133
2.2
The Grassmann Algebra
144
2.3
The Study Sphere
154
3
Linear Complexes
159
3.1
The Structure of a Linear Complex
159
3.2
Linear Manifolds of Complexes
171
3.3
Reguli and Bundles of Linear Complexes
181
3.4
Applications
185
4
Approximation in Line Space
195
4.1
Fitting Linear Complexes
195
4.2
Kinematic Surfaces
202
4.3
Approximation via Local Mappings into Euclidean 4-Space
211
4.4
Approximation in the Set of Line Segments
221
5
Ruled Surfaces
223
5.1
Projective Differential Geometry of Ruled Surfaces
223
5.2
Algebraic Ruled Surfaces
238
5.3
Euclidean Geometry of Ruled Surfaces
261
5.4
Numerical Geometry of Ruled Surfaces
282
Color Plates
311
6
Developable Surfaces
327
6.1
Differential Geometry of Developable Surfaces
327
6.2
Dual Representation
334
6.3
Developable Surfaces of Constant Slope and Applications
358
6.4
Connecting Developables and Applications
396
6.5
Developable Surfaces with Creases
416
7
Line Congruences and Line Complexes
423
7.1
Line Congruences
423
7.2
Line Complexes
474
8
Linear Line Mappings - Computational Kinematics
497
8.1
Linear Line Mappings and Visualization of the Klein Model
497
8.2
Kinematic Mappings
522
8.3
Motion Design
538
References
547
List of Symbols
556
Index
557

Auteur : POTTMANN
Editeur : SPRINGER VERLAG
Nombre de pages : 563
Date de publication : 08 2001

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