We propose a combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework. Our approach yields very eÆcient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom, where the known general roadmap techniques would give exponential complexity. It is based on a novel class of one-degree-of-freedom mechanisms induced...

Can humans recover metric structure from motion sequences or, as has been claimed by Todd and Bressan [(1990) Perception & Psychophysics, 48, 419-430], are they limited to recovering only relief structure? Two experiments were carried out to investigate this question. In a metric-structure task, the angular thresholds for discriminating two rotating bi-planar structures were approximately 91 de...