Computational Line Geometry

From the reviews:

MATHEMATICAL REVIEWS

"In this book, the authors have combined results from the classical parts of geometry with computational methods, This results in a unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in. The book will help to bring the concepts and techniques of line geometryto the attention of a wider audience."

This book for the first time studies line geometry from the viewpoint of scientific computation and shows the interplay between theory and numerous applications Includes supplementary material: sn.pub/extras

Autorentext

Alexander Bobenko is a professor at the Technische Universität Berlin. He is an author with Yuri Suris of the book "Discrete Differential Geometry", and editor of several books in geometry and mathematical physics. He is the Coordinator of the DFG Collaboration Research Center "Discretization in Geometry and Dynamics". Carl Lutz is a doctoral student at Technische Universität Berlin. He wrote his master thesis under the supervision of Alexander Bobenko on the topic "Laguerre Geometry in Space Forms". Helmut Pottmann is a professor at King Abdullah University of Science and Technology in Saudi Arabia and at Technische Universität Wien. He has co-authored two books ("Computational Line Geometry" and "Architectural Geometry") and has been founding director of the Visual Computing Center at KAUST and the Center for Geometry and Computational Design at TU Wien. Jan Techter is a postdoc at Technische Universität Berlin. He wrote his doctoral thesis under the supervision of Alexander Bobenko on the topic "Discrete Confocal Quadrics and Checkerboard Incircular Nets".

Zusammenfassung

From the reviews:

MATHEMATICAL REVIEWS

"In this book, the authors have combined results from the classical parts of geometry with computational methods, This results in a unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in. The book will help to bring the concepts and techniques of line geometryto the attention of a wider audience."

Inhalt
Fundamentals.- Models of Line Space.- Linear Complexes.- Approximation in Line Space.- Ruled Surfaces.- Developable Surfaces.- Line Congruences and Line Complexes.- Linear Line Mappings #x2014; Computational Kinematics.