Handbook of Geometric Constraint Systems Principles

ISBN-13: 9781498738910 / Angielski / Twarda / 2018 / 578 str.

Meera Sitharam; Audrey St John; Jessica Sidman

Opis

Finite configurations of geometric primitives under local metric and algebraic constraints arise in many situations in mathematics as well as in engineering and science applications. The former situations result in multiple perspectives, tools and techniques from algebraic geometry and topology; from combinatorics; from finite metric spaces, asymptotic geometry and convex analysis; and from complexity. The latter situations give rise to fresh new problems and directions.

Spis treści

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.