## 72 Citations

### Incremental Algorithms to Update Visibility Polygons

- Computer Science, MathematicsCALDAM
- 2017

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…

### Characterizing and Recognizing Weak Visibility Polygons

- Mathematics, Computer ScienceComput. Geom.
- 1993

### Algorithms for computing diffuse reflection paths in polygons

- Computer ScienceThe Visual Computer
- 2011

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

- Computer Science, MathematicsCALDAM
- 2019

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

- Computer ScienceInt. J. Comput. Geom. Appl.
- 1997

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)

- Computer Science, MathematicsSCG '90
- 1990

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

- Computer ScienceSWAT
- 1992

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

- Computer ScienceFundam. Informaticae
- 2021

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

- Computer Science, MathematicsArXiv
- 2017

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

- Computer ScienceISAAC
- 2022

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.

## References

SHOWING 1-10 OF 22 REFERENCES

### Worst-case optimal algorithms for constructing visibility polygons with holes

- Computer Science, MathematicsSCG '86
- 1986

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.

### Computing the visibility polygon from an edge

- Computer ScienceComput. Vis. Graph. Image Process.
- 1986

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

- Mathematics, Computer ScienceIEEE Transactions on Computers
- 1981

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

- Mathematics, Computer ScienceNetworks
- 1984

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

- Computer Science, MathematicsPattern Recognit. Lett.
- 1986

### An Optimal Algorithm for Finding the Kernel of a Polygon

- Computer ScienceJACM
- 1979

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

- Mathematics, Computer SciencePattern Recognit. Lett.
- 1982

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

- MathematicsFSTTCS
- 1984

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

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 1989

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.