Computing a cell in an arrangement of quadrics.

3-dimensional arrangement of quadrics. We solve the problem by
using rational arithmetic and reducing it to planar arrangements of
algebraic curves. Degenerate situations such as tangential intersections
and self-intersections of curves are intrinsic to the planar
arrangements we obtain. The coordinates of the intersection points
are given by the roots of univariate polynomials.
We succeed in locating all intersection points either by extended
local box hit counting arguments or by globally characterizing
them with simple square root expressions.
The latter is realized by a clever factorization of the univariate
polynomials. Only the combination of these two results
facilitates a practical and implementable algorithm.