Red-Blue Intersection Detection Algorithms, with Applications to Motion Planning and Collision Detection (Classic Reprint)

Excerpt from Red-Blue Intersection Detection Algorithms, With Applications to Motion Planning and Collision Detection
In this section, we give an efficient algorithm for the case when the red arcs in I. Are non-intersecting line segments which form the boundary of a simple polygon B (see figure 1) or, more generally, non intersecting Jordan arcs whose union is the boundary of a simply-connected region. Let a(i) denote the arrangement of I (i.e. The planar map induced by these arcs; its vertices are the intersection points of the arcs and their endpoints, its edges are maximal connected subsets of the arcs which do not contain any vertex, and its faces are maximal connected subsets of the plane which do not contain any vertex or edge). Let 2 denote any fixed point on 613. The following Lemma is a simple but a key observation which allows us to obtain an efficient algorithm.
Lemma Let 77 be the face of a(i) containing the point 2. Then 68 and I intersect if and only if and 68 intersect.
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