Finding shortest paths in the presence of orthogonal obstacles using a combined L1 and link metric
SWAT '90 Proceedings of the second Scandinavian workshop on Algorithm theory
Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Finding an Optimal Bridge between Two Polygons
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Building bridges between convex regions
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
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Let P and Q be two disjoint rectilinear polygons in the plane. We say P and Q are in Case 1 if there exists a rectinlinear line segment to connect them; otherwise, we say they are in Case 2. In this paper, we present optimal algorithms for solving the following problem. Given two disjoint rectinlinear polygons P and Q in the plane, we want to add a rectilinear line segment to connect then when they are in Case 1, or add two rectilinear line segments, one is vertical and the other is horizontal, to connect P and Q when they are in Case 2. Our objective is to minimize the maximum of the L1-distances between points in one polygon and points in the other polygon through one or two line segments. Let V (P) and V(Q) be the vertex sets of P and Q, respectively, and let |V(P)| = m and |V (Q)| = n. In this paper, we present O(m + n) time algorithms for the above two cases.