A framework for synchronized editing of multiple curve representations

Editing curves and surfaces is difficult in part because their mathematical representations rarely correspond to most people's idea of a curve or surf ace. The implementation land hence, behavior) of most manipulation tools is intertwined with a particular curve or surface representation; this can ma ke reimplementing the tool with a different representation problematic. A s ystem using a single representation must therefore either limit the types o f tools available or convert existing tools to work on the system's represe ntation. In this paper we present a framework for editing curves or surfaces which s upports multiple representations and ensures that they stay synchronized. A s a proof of concept, we have created a curve editor which contains several tools each of which manipulate one of three different curve representation s: polylines, NURBs, and multiresolution B-splines.