Ebook: Handbook of geometric constraint systems principles

Overview and preliminaries / Meera Sitharam and Troy Baker -- I. Geometric Reasoning, Factorization and Decomposition. Computer-assisted theorem proving in synthetic geometry / Julien Narboux, Predrag Janičić, and Jacques Fleuriot -- Coordinate-free theorem proving in incidence geometry / Jürgen Richter-Gebert and Hongbo Li -- Special positions of frameworks and Grassmann-Cayley algebra / Jessica Sidman and William Traves -- From molecular distance geometry to conformal geometric algebra / Timothy F. Havel and Hongbo Li -- Tree-decomposable and underconstrained geometric constraint problems / Ioannis Fudos, Christoph M. Hoffmann, and Robert Joan-Arinyo -- Geometric constraint decomposition: the general case / Troy Baker, Meera Sitharam, and Rahul Prabha -- II. Distance Geometry, Real Algebraic Geometry, and Configuration Spaces. Dimensional and universal rigidities of bar frameworks / A.Y. Alfakih -- Computations of metric/cut polyhedra and their relatives / Mathieu Dutoru Sikirić, Michel-Marie Deza, and Elena I. Deza -- Cayley configuration spaces / Meera Sitharam, Menghan Wang, Joel Willoughby, and Rahul Prabhu -- Constraint varieties in mechanism science / Hans-Peter Schröcker, Martin Pfurner, and Josef Schadlbauer -- Real algebraic geometry for geometric constraints / Frank Sottile -- III. Geometric Rigidity. Polyhedra in 3-space / Brigitte Servatius -- Tensegrity / Robert Connelly and Anthony Nixon -- Geometric conditions of rigidity in nongeneric settings / Oleg Karpenkov -- Generic global rigidity in general dimension / Steven J. Gortler -- Change of metrics in rigidity theory / Anthony Nixon and Walter Whiteley -- IV. Combinatorial Rigidity. Planar rigidity / Brigitte Servatius and Herman Servatius -- Inductive constructions for combinatorial local and global rigidity / Anthony Nixon and Elissa Ross -- Rigidity of body-bar-hinge frameworks / Csaba Király and Shin-Ichi Tanigawa -- Global rigidity of two-dimensional frameworks / Bill Jackson, Tibor Jordán, and Shin-Ichi Tanigawa -- Point-line frameworks / Bill Jackson and J.C. Owen -- Generic rigidity of body-and-cad frameworks / Audrey St. John -- Rigidity with polyhedral norms / Derek Kitson -- Combinatorial rigidity of symmetric and periodic frameworks / Bernd Schulze.