The Problem of Bypassing an Obstacle

Vladimir I. Arnold
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Vladimir I. Arnold: Steklov Mathematical Institute

Chapter 13 in Catastrophe Theory, 1992, pp 75-78 from Springer

Abstract: Abstract Let us consider an obstacle in three-dimensional Euclidean space, bounded by a smooth surface. It is clear that the shortest path from x to y avoiding the obstacle consists of straight-line segments and segments of geodesics (curves of minimal length) on the surface of the obstacle. The geometry of the shortest paths is greatly affected by the various bendings of the obstacle surface.

Date: 1992
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DOI: 10.1007/978-3-642-58124-3_13

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