Recursive subdivision and iteration in intersections and related problems

Abstract The intersection algorithms discussed here use recursive subdivision to decide the number of solutions, while iterative techniques are used to calculate the geometry of the solutions within a user specified tolerance. The framework developed supports a wide class of problems covering all intersection variants of curves and surfaces, closest point calculations and extremal point calculations. The algorithms aim to meet the requirements for correct topology and high accuracy originating from integrated sculptured surfaces and volume modellers.