Shortest Paths with Single-Point Visibility Constraint

Abstract

In this paper, the problem of finding the shortest path between two points in the presence of single-point visibility constraints is studied. In these types of constraint, there should be at least one point on the output path from which a fixed viewpoint is visible. The problem is studied in various domains, including simple polygons, polygonal domains and polyhedral surfaces. The method is based on partitioning the boundary of the visibility region of the viewpoint into a number of intervals. This is done from the combinatorial structure of the shortest paths from the source and destination to the points on the boundary. The result for the case of simple polygons is optimal with O(n) time bound. The running time for the cases of polygonal domains and convex and non-convex polyhedral surfaces are O(n^2), O(n^2) and O(n^3), respectively.