Urrutia, Jorge,Contreras, Felipe.2009-03-192009-03-1919981998Source: Masters Abstracts International, Volume: 42-06, page: 2227.9780612900493http://hdl.handle.net/10393/4324http://dx.doi.org/10.20381/ruor-10203This 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.98 p.Theater.Thesis