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arXiv · 1105.3234

Rigid components in fixed-lattice and cone frameworks

Matthew Berardi·Brent Heeringa·Justin Malestein·Louis Theran
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Abstract

We study the fundamental algorithmic rigidity problems for generic frameworks periodic with respect to a fixed lattice or a finite-order rotation in the plane. For fixed-lattice frameworks we give an $O(n^2)$ algorithm for deciding generic rigidity and an O(n^3) algorithm for computing rigid components. If the order of rotation is part of the input, we give an O(n^4) algorithm for deciding rigidity; in the case where the rotation's order is 3, a more specialized algorithm solves all the fundamental algorithmic rigidity problems in O(n^2) time.

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Matthew Berardi, Brent Heeringa, Justin Malestein, Louis Theran. 2011-05-16. Rigid components in fixed-lattice and cone frameworks. https://arxiv.org/abs/1105.3234

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