EJMT Abstract

The study of envelopes requires a strong dialog between algebraic computations and graphic representations. Both are available using a Computer Algebra System, and sometimes accompanied by a Dynamic Geometry System. The two kinds of software have different affordances, whence different characteristics of the animations. Visualization raises specific problems. We illustrate this with examples of 1-parameter and 2-parameter families of surfaces in 3D space. In certain cases, the envelopes have non-isolated singularities; we study them switching between parametric and implicit presentations. Finally, networking between kinds of software and between visualization and symbolic computations is discussed.