Ellipsoid With Non-ruled Quadric Surface Intersection Curve Parameters,

Quadric surfaces are the simplest curved surfaces and are widely used in CAD/CAM or solid modeling. Ellipsoid is the special and boundary quadric surface, whose speciality is highly utilized in the practical application. Computing quadric surface intersection curve is an important operation in computing the boundary representation of a three dimensional object in solid modeling system, and is applied in other geometric processing as well. If at least one of two quadric surfaces is ruled surface, computing their intersection is simpler. If none of two quadric surfaces is ruled surface, judge the type of intersection on the basis of the root distribution of characteristic equations of two quadric surfaces and then standardize two quadric surfaces according to the type of the intersection, which converts a quadric surface into ruled surface. This paper presents a parameterized algorithm of the ellipsoid and intersection of unruled quadric, and provides corresponding examples to the type of intersection.