Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
Computing the optimal bridge between two convex polygons
Information Processing Letters
On optimal bridges between two convex regions
Information Processing Letters
An optimal algorithm for constructing an optimal bridge between two simple rectilinear polygons
Information Processing Letters
Efficient Algorithms for the Minimum Diameter Bridge Problem
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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Let π(a, b) denote the shortest path between two points a, b inside a simple polygon P, which totally lies in P. The geodesic distance between a and bin P is defined as the length of π (a, b), denoted by gd(a, b), in contrast with the Euclidean distance between a and b, denoted by d(a, b). Given two disjoint polygons Pand Q in the plane, the bridge problem asks for a line segment (optimal bridge)that connects a point p on the boundary of P and a point q on the boundary of Q such that the sum of three distances gd(p′, p), d(p, q)and gd(q, q′), with any p′ ∈ P and any q′ ∈ Q, is minimized. We present an O(nlog3n) time algorithm for finding an optimal bridge between two simple polygons. This significantly improves upon the previous O(n2)time bound.