Related papers: The geodesic edge center of a simple polygon

The geodesic between two points $a$ and $b$ in the interior of a simple polygon~$P$ is the shortest polygonal path inside $P$ that connects $a$ to $b$. It is thus the natural generalization of straight line segments on unconstrained point…

We consider the problem of finding a geodesic disc of smallest radius containing at least $k$ points from a set of $n$ points in a simple polygon that has $m$ vertices, $r$ of which are reflex vertices. We refer to such a disc as a SKEG…

In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…

A closed quasigeodesic is a closed curve on the surface of a polyhedron with at most $180^\circ$ of surface on both sides at all points; such curves can be locally unfolded straight. In 1949, Pogorelov proved that every convex polyhedron…

Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths…

A closed quasigeodesic on a convex polyhedron is a closed curve that is locally straight outside of the vertices, where it forms an angle at most $\pi$ on both sides. While the existence of a simple closed quasigeodesic on a convex…

A vertex in a graph is called central if it minimizes its maximum distance to the other vertices. The radius of a graph $G$ is the largest distance between a central vertex and the other vertices, and it is denoted by $rad(G)$. In the…

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We…

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d_G(u,v) is at least…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

A hotspot is an axis-aligned square of fixed side length $s$, the duration of the presence of an entity moving in the plane in which is maximised. An exact hotspot of a polygonal trajectory with $n$ edges can be found in $O(n^2)$. Defining…

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input…

We present an algorithm to find an {\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$. Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the…

In this paper, an efficient algorithm to find the center of the biggest circle inscribed in a given polygon is described. This work was inspired by the publication of Daniel Garcia-Castellanos & Umberto Lombardo and their algorithm used to…

Let $P$ be a polygon with $k$ vertices. Let $R$ and $B$ be two simple, interior disjoint curves on the boundary of $P$, with $n$ and $m$ vertices. We show how to compute the Fr\'echet distance between $R$ and $B$ using the geodesic…

A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…

Based on Welzl's algorithm for smallest circles and spheres we develop a simple linear time algorithm for finding the smallest circle enclosing a point cloud on a sphere. The algorithm yields correct results as long as the point cloud is…

We show that the geodesic diameter of a polygonal domain with n vertices can be computed in O(n^4 log n) time by considering O(n^3) candidate diameter endpoints; the endpoints are a subset of vertices of the overlay of shortest path maps…

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…