EJMT Abstract

Envelopes of parametric families of curves and of surfaces is a classical topic suffering from a non-well developed theory. Previous works studied one-parameter families of plane curves, and showed how automated methods are efficient to revive the topic. In this paper, we analyse the transition from 2D to 3D, which is non-trivial, in particular because of visualization issues and of technological features available for 2D, but maybe not in a 3D setting. The study of envelopes enables also to make connections between different mathematical domains, such as between Differential Geometry and Abstract Algebra (polynomial rings and their ideals). This provides an access to new algorithms implemented in CAS, and enhances automated methods of exploration and proof.