A New Optimal Algorithm for Computing the Visibility Area of a simple Polygon from a Viewpoint

Given a simple polygon mathcal P of n vertices in the Plane. We study the problem of computing the visibility area from a given viewpoint q inside mathcal P where only sub-linear variables are allowed for working space. Without any memory-constrained, this problem was previously solved in O(n) -time and O(n) -variables space. In a newer research, the visibility area of a point be computed in O(n) -time, using O(√n) variables for working space. In this paper, we present an optimal-time algorithm, using O(c/log n) variables space for computing visibility area, where c<n is the number of critical vertices. We keep the algorithm in the linear-time and reduce space as much as possible.