Surface/surface Intersections: a Three States Classification

Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. In this paper, we introduce a new strategy to classify surfaces against their intersection status. We replace exact geometric entities by fuzzy geometric ones. Intersecting surfaces are then replaced by fuzzy intersecting faces and their fuzzy intersection algorithm provides a three state classiication of surfaces: certainly intersecting, certainly non intersecting and potentially intersecting. In the cases of certainly intersecting surfaces the fuzzy intersection algorithms provide also starting points to march along the intersection curves.