Computing Rigid Components of Pseudo-Triangulation Mechanisms in Linear Time

Jack Snoeyink, The University of North Carolina at Chapel Hill
Ileana Streinu, Smith College

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We investigate the problem of detecting rigid components (maximal Laman subgraphs) in a pseudotriangulation mechanism and in arbitrary pointed planar frameworks.F or general Laman graphs with some missing edges, it is known that rigid components can be computed in O(n2) time.Here we make substantial use of the special geometry of pointed pseudo-triangulation mechanisms to achieve linear time. The main application is a more robust implementation and a substantial reduction in numerical computations for the solution to the Carpenter's Rule problem given by the second author.