• Corpus ID: 15424584

An Algorithm for Computing Constrained Reflection Paths in Simple Polygon

  title={An Algorithm for Computing Constrained Reflection Paths in Simple Polygon},
  author={Arijit Bishnu and Subir Kumar Ghosh and Partha P. Goswami and Sudebkumar Prasant Pal and Swami Sarvattomananda},
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple and piecewise-convex. However, computing optimal paths in the context of diffuse or specular reflections does not seem to be an easy task. A path from a light source $s$ to $t$ inside $P$ is called a diffuse reflection path if the turning points of the path lie… 

Diffuse Reflection Radius in a Simple Polygon

It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source after at most at least four diffuse reflections, and this bound is the best possible.

On the Complexity of Minimum-Link Path Problems

It is proved that computing the minimum-link diffuse reflection path, motivated by ray tracing in computer graphics, is NP-hard, even for two-dimensional polygonal domains with holes.

On the complexity of minimum-link path problems

The minimum-link diffuse reflection path is proved to be NP-hard, even for two-dimensional polygonal domains with holes, and the open problem from [Mitchell et al.'1992] mentioned in the handbook and The Open Problems Project is resolved.



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.

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.

NC-Algorithms for Minimum Link Path and Related Problems

Algorithms that require O (log n loglog n ) time and O ( n ) space using O (n ) processors for both the minimum link path and minimum nested polygon problems are presented.

Visibility with One Reflection

A Θ(n2) worst-case bound on the combinatorial complexity of both Vs(S) and Vd( S) is presented and simple O( n2 log2 n) time algorithms for constructing the sets are described.

Computing the Visibility Polygon from a Convex Set and Related Problems

  • S. Ghosh
  • Computer Science, Mathematics
    J. Algorithms
  • 1991

Visibility with reflection in triangulated surfaces

This work analysis of the previously unstudied situation where the light is allowed to reflect off the walls of the container according to laws of geometric optics, and at most a fixed number of consecutive reflections is permitted.

A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections

Abstract.It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(s) of a

The Complexity of Diffuse Reflections in a Simple Polygon

The complexity of the visibility region formed by a point light source after k diffuse reflections in a simple n-sided polygon is O(n9), which is the first result polynomial in n, with no dependence

Visibility Algorithms in the Plane

Basic algorithms for point visibility, weak visibility, shortest paths, visibility graphs, link paths, and visibility queries are all discussed and several geometric properties are established through lemmas and theorems.