Description
The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts.
The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research.
Key Features:
- A comprehensive reference handbook authored by top researchers
- Includes fundamentals and techniques from multiple perspectives that span several research communities
- Provides recent results and a graded program of open problems and conjectures
- Can be used for senior undergraduate or graduate topics course introduction to the area
- Detailed list of figures and tables
About the Editors:
Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison.
Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst.
Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.
Table of Contents
Overview and preliminaries. Computer-assisted Theorem Proving in Synthetic Geometry. Coordinate-Free Theorem Proving in Incidence Geometry. Special positions of frameworks and the Grassmann-Cayley Algebra. From Molecular Distance Geometry to Conformal Geometric Algebra. Tree-decomposable and Underconstrained Geometric Constraint Problems. Geometric Constraint Decomposition: The General Case. Dimensional and Universal Rigidities of Bar Frameworks. Computations of metric/cut polyhedra and their relatives. Cayley Configuration Spaces. Constraint Varieties in Mechanism Science. Real Algebraic Geometry for Geometric Constraints. Polyhedra in 3-Space. Tensegrity. Geometric Conditions of Rigidity in Nongeneric settings. Generic Global Rigidity in General Dimension. Change of Metrics in Rigidity Theory. Planar Rigidity. Inductive constructions for combinatorial local and global rigidity. Rigidity of Body-bar-hinge Frameworks. Global rigidity of two-dimensional frameworks. Point-line frameworks. Generic rigidity of body-and-cad frameworks. Rigidity with polyhedral norms. Combinatorial rigidity of symmetric and periodic frameworks.
