Transforming an under-constrained geometric constraint problem into a well-constrained one
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Morphing polyhedra with parallel faces: Counterexamples
Computational Geometry: Theory and Applications
Body-and-cad geometric constraint systems
Proceedings of the 2009 ACM symposium on Applied Computing
Globally rigid circuits of the direction--length rigidity matroid
Journal of Combinatorial Theory Series B
Geometric properties of Assur graphs
European Journal of Combinatorics
Body-and-cad geometric constraint systems
Computational Geometry: Theory and Applications
Scaling the size of a formation using relative position feedback
Automatica (Journal of IFAC)
Combinatorics and the rigidity of CAD systems
Computer-Aided Design
On frame and orientation localization for relative sensing networks
Automatica (Journal of IFAC)
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Configurations of points in the plane constrained by directions only or by lengths alone lead to equivalent theories known as parallel drawings and infinitesimal rigidity of plane frameworks. We combine these two theories by introducing a new matroid on the edge set of the complete graph with doubled edges to describe the combinatorial properties of direction-length designs.