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COMPGEOM
2004
ACM

An energy-driven approach to linkage unfolding

13 years 9 months ago
An energy-driven approach to linkage unfolding
We present a new algorithm for unfolding planar polygonal linkages without self-intersection based on following the gradient flow of a “repulsive” energy function. This algorithm has several advantages over previous methods. (1) The output motion is represented explicitly and exactly as a piecewise-linear curve in angle space. As a consequence, an exact snapshot of the linkage at any time can be extracted from the output in strongly polynomial time (on a real RAM supporting arithmetic, sin, and arcsin). (2) Each linear step of the motion can be computed exactly in O(n2 ) time on a real RAM where n is the number of vertices. (3) We explicitly bound the number of linear steps (and hence the running time) as a polynomial in n and the ratio between the maximum edge length and the initial minimum distance between a vertex and an edge. (4) Our method is practical and easy to implement. We provide a publicly accessible Java applet [1] that implements the algorithm.
Jason H. Cantarella, Erik D. Demaine, Hayley N. Ib
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where COMPGEOM
Authors Jason H. Cantarella, Erik D. Demaine, Hayley N. Iben, James F. O'Brien
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