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Beskrivning
Covering algebriac and differential geometry, the concept of Lie groups, and the relation of Lie groups to planar kinematics, line geometry and representation theory, this work deals with the application of these geometrical methods to robotics, in the areas of statics, dynamics, gripping solid objects, posture and screw systems.
"This marvelous book will occupy an important place in the scientific literature." --Prof. Heinz-Otto Peitgen, author of The Beauty of Fractals "...will perform a valuable service by popularizing this enlightening and bewitching form of mathematics." --Steven Levy "...full of delights and an excellent introduction to L-systems" --Alvy Ray Smith, IEEE Graphics and its Applications
Innehållsförteckning
1 Graphical modeling using L-systems.- 1.1 Rewriting systems.- 1.2 DOL-systems.- 1.3 Turtle interpretation of strings.- 1.4 Synthesis of DOL-systems.- 1.5 Modeling in three dimensions.- 1.6 Branching structures.- 1.7 Stochastic L-systems.- 1.8 Context-sensitive L-systems.- 1.9 Growth functions.- 2 Modeling of trees.- 3 Developmental models of herbaceous plants.- 3.1 Levels of model specification.- 3.2 Branching patterns.- 3.3 Models of inflorescences.- 4 Phyllotaxis.- 4.1 The planar model.- 4.2 The cylindrical model.- 5 Models of plant organs.- 5.1 Predefined surfaces.- 5.2 Developmental surface models.- 5.3 Models of compound leaves.- 6 Animation of plant development.- 6.1 Timed DOL-systems.- 6.2 Selection of growth functions.- 7 Modeling of cellular layers.- 7.1 Map L-systems.- 7.2 Graphical interpretation of maps.- 7.3 Microsorium linguaeforme.- 7.4 Dryopteris thelypteris.- 7.5 Modeling spherical cell layers.- 7.6 Modeling 3D cellular structures.- 8 Fractal properties of plants.- 8.1 Symmetry and self-similarity.- 8.2 Plant models and iterated function systems.- Epilogue.- Appendix A Software environment for plant modeling.- A.1 A virtual laboratory in botany.- A.2 List of laboratory programs.- Appendix B About the figures.- Turtle interpretation of symbols.