Surfaces Intersection for Solids Algebra: a Classiication Algorithm

Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. This paper introduces a new strategy to classify surfaces against their intersection status, where exact geometric entities are replaced by fuzzy geometric ones. Intersecting surfaces are thus replaced by fuzzy intersecting faces and a fuzzy intersection algorithm provides a three-state classiication of surfaces couples: certainly intersecting, certainly non intersecting and potentially intersecting. In case of certainly intersecting surface couples the fuzzy intersection algorithm provides also starting points to march along the intersection curve, which turns most of the potentially intersecting couples in certainly intersecting ones. The remaining potential intersections are then subdivided to reene their status. Statistic shows the eeciency of this global strategy.