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.
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© 1992 Springer-Verlag Berlin Heidelberg
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Arnold, V.I. (1992). The Problem of Bypassing an Obstacle. In: Catastrophe Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58124-3_13
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DOI: https://doi.org/10.1007/978-3-642-58124-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54811-9
Online ISBN: 978-3-642-58124-3
eBook Packages: Springer Book Archive