Cutting polygons and a problem on illumination of stages.

Abstract

This work presents the solution to two problems in Computational Geometry. First, we introduce an algorithm to calculate (provided an O( n log n) preprocessing or linear if the polygon is convex) the area of an n-gon "cut" by a query interior segment in O(n log n) time. As an application we also show how to find the line cutting 1r of the area of a convex polygon and parallel to a given line. Secondly, we show how to illuminate a stage represented by a line segment s , with floodlights placed at n points above s such that the sum of their angles is minimized. The algorithm runs in theta(n log n) time and we include a videotape presenting it.