Multilevel Editing of B-Spline Curves with Robust Orientation of Details

Abstract

We facilitate the editing of hierarchical B-spline curves at multiple resolutions by expressing a displacement function at each level in rotation minimizing frames (RMFs) on the curve at the next lower level. When the curve is edited at a particular level, RMFs at all the higher levels are updated, and the control points of the displacement function at each higher level are obtained from these new RMFs. This transfers details created at the current level to higher levels. Our method presents a hundred-fold faster way to reflect editing results compared to the traditional approach using Frenet frames. We demonstrate the effectiveness of our technique by showing several examples of editing curves with fine details.