Shortest Paths for Line Segments (Classic Reprint) - Softcover

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Excerpt from Shortest Paths for Line Segments

We study the problem of shortest paths for a line segment in the plane. As a measure of the distance traversed by a path, we take the average curve length of the orbits of prescribed points on the line segment. This problem is nontrivial even in free space in the absence of obstacles). We characterize all shortest paths of the line segment moving in free space under the measure (12, the average orbit length of the two endpoints.

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