Computing the Visibility Polygon from a Convex Set and Related Problems

  title={Computing the Visibility Polygon from a Convex Set and Related Problems},
  author={Subir Kumar Ghosh},
  journal={J. Algorithms},
  • S. Ghosh
  • Published 2 January 1991
  • Computer Science, Mathematics
  • J. Algorithms

Incremental Algorithms to Update Visibility Polygons

We consider the problem of updating the visibility polygon of a point located within the given simple polygon as that polygon is modified with the incremental addition of new vertices to it. In

Algorithms for computing diffuse reflection paths in polygons

Three different algorithms for constructing a diffuse reflection path from s to t inside a polygon P of n vertices are presented which produce suboptimal paths and the combinatorial approach used in the third algorithm gives a better bound on the number of reflections.

Maintaining the Visibility Graph of a Dynamic Simple Polygon

This algorithm preprocesses the initial simple polygon P to build few data structures, including the visibility graph of P, and is designed to compute the vertices of the current simplepolygon that are visible from a query point.

Optimal Shortest Path and Minimum-Link Path Queries Between Two Convex Polygons Inside a Simple Polygonal Obstacle

It is shown that shortest-path queries can be performed optimally in time O(logh + logn) (plus O(k) time for reporting the k edges of the path) using a data structure with O(n) space and preprocessing time, and that minimum-link- path queries can also be performed in optimal time.

Structured visibility profiles with applications to problems in simple polygons (extended abstract)

The structured visibility profile of a polygonal path is defined and how to compute it in linear time is shown and this result is applied to solve many problems inlinear time that previously required triangulation.

Parallel Algorithms for All Minimum Link Paths and Link Center Problems

This work shows that minimum link paths from a point to all vertices of P can be computed in O(log2n log log n) time using O(n) processors and proposes a parallel algorithm for computing the link center of P, which is the set of points x inside P such that the link distance from x to any other point in P is minimized.

Query-points visibility constraint minimum link paths in simple polygons

This work studies the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point, and proposes an algorithm with O(n) preprocessing time.

Dynamic algorithms for visibility polygons

We devise the following dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and/or deletions to the simple polygon. * A

Minimum Link Fencing

A variant of the geometric multicut problem, where a set P of colored and pairwise interior-disjoint polygons in the plane is given, it is shown that BMLF is NP -hard in general and that it is XP -time solvable when each fence contains at most two polygons and the number of segments per fence is the parameter.



Worst-case optimal algorithms for constructing visibility polygons with holes

A worst-ease lower bound of N(n 4) for explicitly computing the boundary of the visibility polygon from a line segment in the presence of other line segments is established, and an optimal algorithm to construct the boundary is designed.

Minimum Polygonal Separation

Computing the visibility polygon from an edge

An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge

An O(n), and thus optimal, algorithm is exhibited for determining edge visibility under any of the three definitions of a simple polygon from one of its edges.

Euclidean shortest paths in the presence of rectilinear barriers

The goal is to find interesting cases for which the solution can be obtained without the explicit construction of the entire visibility graph, which solve the problems by constructing the shortest-path tree from the source to all the vertices of the obstacles and to the destination.

Shortest path solves edge-to-edge visibility in a polygon

  • G. Toussaint
  • Computer Science, Mathematics
    Pattern Recognit. Lett.
  • 1986

An Optimal Algorithm for Finding the Kernel of a Polygon

It is shown that one can exploit the ordering of the half-planes corresponding to the sequence of the polygon's edges to obtain a kernel finding algorithm which runs m time O(n) and is therefore optimal.

Finding the convex hull of a simple polygon

  • J. Sklansky
  • Mathematics, Computer Science
    Pattern Recognit. Lett.
  • 1982

A Linear-Time Algorithm for Determining the Intersection Type of Two Star Polygons

The skeleton of a simple polygon is a combination of arcs that have the property that any interior point on an arc is equidistant from the closest two sides or two reflex corners, whichever combination is closer to the point.

Visibility and intersection problems in plane geometry

New data structures for solving various visibility and intersection problems about a simple polygonP onn vertices are developed and anO(logn)-time algorithm for determining which side ofP is first hit by a bullet fired from a point in a certain direction is developed.