Computing shortest paths among curved obstacles in the plane

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
University of Notre Dame, Notre Dame, IN, USA;Utah State University, Logan, UT, USA
Venue:
Proceedings of the twenty-ninth annual symposium on Computational geometry
Year:
2013

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Abstract

In this paper, we study the problem of finding Euclidean shortest paths among curved obstacles in the plane. We model curved obstacles as splinegons. A splinegon can be viewed as replacing each edge of a polygon by a convex curved edge, and each curved edge is assumed to be of O(1) complexity. Given in the plane two points s and t and a set of h pairwise disjoint splinegons with a total of n vertices, we present an algorithm that can compute a shortest path from s to t avoiding the splinegons in O(n+hlogεh+k) time for any ε0, where k is a parameter sensitive to the input splinegons and k=O(h2). If all splinegons are convex, a common tangent of two splinegons is "free" if it does not intersect the interior of any splingegon; our techniques yield an output sensitive algorithm for computing all free common tangents of the h splinegons in O(n+hlogh+k) time and O(n) working space, where k is the number of all free common tangents.