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 surface. The implementation (and hence, behavior) of most manipulation tools is intertwined with a particular curve or surface representation; this can make reimplementing the tool with a different representation problematic. A system using a single representation must therefore either limit the types of tools available or convert existing tools to work on the system's representation.
In this paper we present a framework for editing curves or surfaces which supports multiple representations and ensures that they stay synchronized. As a proof of concept, we have created a curve editor which contains several tools each of which manipulate one of three different curve representations: polylines, NURBs, and multi-resolution B-splines.