The convex hull of ellipsoids

The treatment of curved algebraic surfaces becomes more and more the focus of attention in Computational Geometry. We present a video that illustrates the computation of the convex hull of a set of ellipsoids. The underlying algorithm is an application of our work on determining a cell in a 3-dimensional arrangement of quadrics, see [3]. In the video, the main emphasis is on a simple and comprehensible visualization of the geometric aspects of the algorithm. In addition, we give some insights into the underlying mathematical problems. The Algorithm There are well known efficient and robust algorithms for the calculation of the convex hull of a set of points or a set of spheres ([1], [2]). In our video, we show how to compute the convex hull of a set of ellipsoids with exact arithmetic (Fig. 1, 2). The video consists of three different parts. First, we illustrate how the problem of computing the convex hull can be reduced to the problem of calculating a cell in a 3dimensional arrangeme...

• Type: Conference
• Year: 2001
• Where: COMPGEOM
• Authors: Nicola Geismann, Michael Hemmer, Elmar Schömer
• Keywords: Cell, COMPGEOM 2001, Convex Hull, Curved Algebraic Surfaces, Discrete Geometry