Geodesic Fréchet distance inside a simple polygon

Speed-constrained geodesic fréchet distance inside a simple polygon

Given two polygonal curves inside a simple polygon, we study the problem of finding the Fréchet distance between the two curves under the following two conditions (i) the distance between two points on the curves is measured as the length of the shortest path between them lying inside the simple polygon, and (ii) the traversal along each segment of the polygonal curves is restricted to be betwe...

Geodesic Fréchet and Hausdorff Distance inside a Simple Polygon 3

Constrained Geodesic Centers of a Simple Polygon

For any two points in a simple polygon P , the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regi...

Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set of point sites S in a static simple polygon P . Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P . All distances are measured using the geodesic distance, that is, the length of the shortest path...

Computing the Fréchet distance between simple polygons

We present the first polynomial-time algorithm for computing the Fréchet distance for a non-trivial class of surfaces: simple polygons. For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths in the other polygon.