Constraining plane configurations in computer-aided design : Combinatorics of directions and lengths

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 double...

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Bibliographic Details
Published in:SIAM journal on discrete mathematics 1999, Vol.12 (1), p.136-153
Main Authors: SERVATIUS, B, WHITELEY, W
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied mathematics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Convex and discrete geometry
Design
Designs and configurations
Exact sciences and technology
Geometry
Mathematics
Sciences and techniques of general use
Theoretical computing
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Summary: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.
ISSN:0895-4801
1095-7146
DOI:10.1137/S0895480196307342