Abstract
Let p and q be two points in a simple polygon P. This chapter provides the Chazelle algorithm for computing the ESP between p and q that is contained in P. It uses triangulation of simple polygons as presented in the previous chapter as a preprocessing step, and has a time complexity that is determined by that of the prior triangulation.
This chapter provides two rubberband algorithms for computing a shortest path between p and q that is contained in P. The two algorithms use previously known results on triangular or trapezoidal decompositions of simple polygons, and have \(\kappa(\varepsilon) {\mathcal{O}} (n\log n)\) time complexity (where the super-linear time complexity is only due to preprocessing, i.e., for the decomposition of the simple polygon P, \(\kappa(\varepsilon)= \frac{L_{0} - L}{\varepsilon}\), L is the length of an optimal path and L 0 the length of the initial path, as introduced in Sect. 3.5.
Obstacles are those frightful things you see when you take your eyes off your goal.
Henry Ford (1863–1947)
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© 2011 Springer-Verlag London Limited
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Li, F., Klette, R. (2011). ESPs in Simple Polygons. In: Euclidean Shortest Paths. Springer, London. https://doi.org/10.1007/978-1-4471-2256-2_6
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DOI: https://doi.org/10.1007/978-1-4471-2256-2_6
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