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

We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, surfaces of algebraic degree 2. This is a major step towards the computation of the full 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 kind of inputs including all degenerate ones where intersection curves have singularities or pairs of curves intersect with high multiplicity. It is exact in that it always computes the mathematical correct result. It is efficient measured in running times, i.e. we compare it with a previous implementation based on planar arrangements of the projected intersection curves