Computing the intersection curve of two quadric surfaces is an important problem in geometric computation, ranging from shape modeling in computer graphics and CAD/CAM, collision detection in robotics and computational physics, to arrangement computation in computational geometry. We present the solution to the fundamental problem of complete classification of morphologies of the intersection c...

The paper reviews new approaches to computing the intersection curve of two surfaces of special types. We consider algorithms for intersecting a torus with a natural quadric or another torus. After that, we review a topological technique that computes the intersection curve of a sphere and a sugace of revolution. Finally, we consider the intersection of two ruled sueaces.

This paper describes a new technique for global shape improvement based upon features’ positions and geometrical constraints. It suggests a general incremental, framework whereby constraints can be added and integrated in the model reconstruction process, resulting in an optimal trade-off between minimization of the shape fitting error and the constraints’ tolerances. The objects treated are in...

This paper focuses on the blending of a plane with surfaces of revolution relying on Dupin cyclides, which are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century. A general algorithm is presented for the construction of two kinds of blends: pillar and recipient. This algorithm uses Rational Quadric Bézier Curves (RQBCs) to model ...