Write a computer program computing the Delaunay triangulation of afinite set of points in the plane using the method of lift ing to a paraboloid.   Q50: Let {p1,...,pn} be a finite set of points...

Write a computer program computing the Delaunay triangulation of afinite set of points in the plane using the method of lift ing to a

paraboloid.

Q50:

Let {p1,...,pn} be a finite set of points contained in a given square S. Consider the following path-planning problem. Given an initial positions and a final position t both on the boundary on the given square S, f in d aC2-continuous path from staying in side S with the property that at any given time, appoint moving on the path is as f ar as possible from then earest point pi. You may think of the points piasradar stations and the moving particle as a flying air plane. The air plane istrying to maximize the minimum distance from the radars. Solve the above problem as best as you can using Voronoi diagrams and B-splines.