CIRCULAR VISIBILITY FROM A POINT IN A SIMPLE POLYGON

Abstract

In this paper we define the notion of circular visibility, and present an O (n log n) time algorithm to compute the portion of a given simple polygon [Formula: see text] circularly visible from a fixed point lying inside [Formula: see text]. The second problem that we study is the circle shooting from a fixed-point, which can be formulated as follows: Given a simple polygon [Formula: see text] and a point s inside [Formula: see text], preprocess [Formula: see text] so that given a circle π passing through s, one can quickly compute the first point of [Formula: see text] intersected by π as we follow π from s in a clockwise direction. We show that [Formula: see text] can be preprocessed, in time O (n log n), into a data structure of linear size, so that a query can be answered in logarithmic time.