Handbook of Geometric Constraint Systems Principles: 1st Edition (Hardback) book cover

Handbook of Geometric Constraint Systems Principles

1st Edition

Edited by Meera Sitharam, Audrey St. John, Jessica Sidman

Chapman and Hall/CRC

578 pages | 209 B/W Illus.

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Hardback: 9781498738910
pub: 2018-07-25
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pub: 2018-07-20
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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.

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. http://www.cise.ufl.edu/~sitharam

Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. http://minerva.cs.mtholyoke.edu/

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. http://www.mtholyoke.edu/~jsidman/

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT012000
MATHEMATICS / Geometry / General
MAT036000
MATHEMATICS / Combinatorics