Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation. Key words: Arrangement, intersection of surfaces, quadrics, pencils of quadrics, curve parameterization. Preprint submitted to Journal of Symbolic Computation June 8, 2009 

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Laurent Dupont, Michael Hemmer, Sylvain Petitjean, Elmar Schömer
• Keywords: Adjacency Graph, Algorithms, ESA 2007, Exact, Intersection Points