Body-and-cad geometric constraint systems

Authors:
Kirk Haller;Audrey Lee-St.John;Meera Sitharam;Ileana Streinu;Neil White
Affiliations:
SolidWorks Corporation, Concord, MA 01742, United States;Mount Holyoke College, South Hadley, MA 01075, United States;University of Florida, Gainesville, FL 32611, United States;Smith College, Northampton, MA 01063, United States;University of Florida, Gainesville, FL 32611, United States
Venue:
Computational Geometry: Theory and Applications
Year:
2012

Citing 15
Cited 2

The algebraic geometry of motions of bar-and-body frameworks

SIAM Journal on Algebraic and Discrete Methods
Geometric applications of the Grassmann-Cayley algebra

Handbook of discrete and computational geometry
Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths

SIAM Journal on Discrete Mathematics
Decomposition plans for geometric constraint systems, part I: performance measures for CAD

Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms

Journal of Symbolic Computation
Geometrical Methods in Robotics

Geometrical Methods in Robotics
Automated short proof generation for projective geometric theorems with Cayley and bracket algebras: I. incidence geometry

Journal of Symbolic Computation
Constraining Plane Configurations in CAD: Circles, Lines, and Angles in the Plane

SIAM Journal on Discrete Mathematics
Combinatorial decomposition, generic independence and algebraic complexity of geometric constraints systems: applications in biology and engineering

Combinatorial decomposition, generic independence and algebraic complexity of geometric constraints systems: applications in biology and engineering
Geometric constraint systems with applications in cad and biology

Geometric constraint systems with applications in cad and biology
Sparse hypergraphs and pebble game algorithms

European Journal of Combinatorics
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving

Computer-Aided Design
Algebraic Algorithms for Matching and Matroid Problems

SIAM Journal on Computing
Optimized parametrization of systems of incidences between rigid bodies

Journal of Symbolic Computation
Generalized Stewart-Gough platforms and their direct kinematics

IEEE Transactions on Robotics

Combinatorics and the rigidity of CAD systems

Computer-Aided Design
Defining tools to address over-constrained geometric problems in Computer Aided Design

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance constraints. We identify 21 relevant geometric constraints and develop the corresponding infinitesimal rigidity theory for these structures. The classical body-and-bar rigidity model can be viewed as a body-and-cad structure that uses only one constraint from this new class. As a consequence, we identify a new, necessary, but not sufficient, counting condition for minimal rigidity of body-and-cad structures: nested sparsity. This is a slight generalization of the well-known sparsity condition of Maxwell.