Title: Envelopes of nonlinear geometry Abstract: Simplification of nonlinear geometry such as polynomial curves or surfaces is an important problem in CAGD. Algorithms for rendering curves or surfaces or for computing intersections of surfaces usually require the conversion of the curved geometry into piecewise linear segments. This talk describes a new method for simplifying nonlinear geometry that improves on the popular methods of min-max bounding boxes and the convex hull.