A Fast Algorithm for Incremental Distance ... - Semantic Scholar
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A Fast Algorithm for Incremental Distance ... - Semantic Scholar
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A Fast Algorithm for Incremental Distance Calculation Ming C. Lin and John F. Canny University of California, Berkeley Berkeley, CA 94720
Abstract
tures fail the test, we step to a neighboring feature of one or both candidates, and try again. With some simple preprocessing, we can guarantee that every feature has a boundary and coboundary of constant size. This is how we can verify the closest feature pair in constant time. When a pair of features fail the test, the new pair we choose is guaranteed to be closer than the old one. So when the objects move and one of the closest features changes, we usually nd it after a single iteration. Even if the closest features are changing rapidly, say once per step along the path, our algorithm will take only slightly longer. Its also clear that the algorithm must terminate, in a number of steps at most equal to the number of feature pairs. This algorithm is a key part of our general planning algorithm, described in [1]. That algorithm creates a one-dimensional roadmap of the free space of a robot by tracing out curves of maximal clearance from obstacles. We use the algorithm in this paper to compute distances and closest points. From there we can easily compute gradients of the distance function in con guration space, and thereby nd the direction of the maximal clearance curves.
A simple and ecient algorithm for nding the closest points between two convex polyhedra is described here. Data from numerous experiments tested on a broad set of convex polyhedra on
