Robust interval algorithm for curve intersections

In this paper, we develop and study a robust algorithm for computing intersections of two planar interval polynomial curves. The intersection problems include well-conditioned transveral intersections as well as ill-conditioned cases such as tangential and overlapping intersections. Key components of our methods are the reduction of the intersection problems into solving systems of nonlinear interval polynomial equations which consist of m equations with n unknowns. An earlier interval nonlinear polynomial solver for balanced system based on Bernstein subdivision method coupled with rounded interval arithmetic is extended to solve unbalanced systems. The solver provides results with numerical certainty and verifiability. Examples illustrate our techniques.