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We show that the region lit by a point light source inside a simple n-gon after at most k reeections oo the boundary has combinatorial complexity O(n 2k), for any k 1. A lower bound of ((n=k ? (1)) 2k) is also established which matches the upper bound for any xed k. A simple near-optimal algorithm for computing the illuminated region is presented, which… (More)

We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and dzffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray… (More)

Let s be a point source of light inside a polygon P of n vertices. A polygonal path from s to some point t inside P is called a diffuse reflection path if the turning points of the path lie on edges of P. A diffuse reflection path is said to be optimal if it has the minimum number of reflections on the path. The problem of computing a diffuse reflection… (More)

We consider direct visibility in simple orthogonal polygons and derive tight lower and upper bounds on the number of strictly internal and external visibility edges. We also show a lower bound of ⌈ n 2 ⌉ − 1 on the number of diffuse reflections required for completely illuminating an orthogonal polygon from an arbitrary point inside it. Further, we derive… (More)

We develop protocols for preparing a GHZ state and, in general, a pure multi-partite maximally entangled state in a distributed network with apriori quantum entanglement between agents using classical communication and local operations. We investigate and characterize the minimal combinatorics of the sharing of EPR pairs required amongst agents in a network… (More)