Body-and-cad geometric constraint systems

Authors:
Kirk Haller;Audrey Lee-St. John;Meera Sitharam;Ileana Streinu;Neil White
Affiliations:
SolidWorks Corporation, Concord, MA;Mount Holyoke College, South Hadley, MA;University of Florida, Gainesville, FL;Smith College, Northampton, MA;University of Florida, Gainesville, FL
Venue:
Proceedings of the 2009 ACM symposium on Applied Computing
Year:
2009

Citing 9
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
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 rooted-forest partition with uniform vertex demand

Journal of Combinatorial Optimization
Designing and fabricating mechanical automata from mocap sequences

ACM Transactions on Graphics (TOG)

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, angle 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.