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.
Highlights
Thanks to useful properties of B-spline, it has been considered the de factor standard for modeling freeform curves and surfaces in computer-aided design and computer graphics [1,2]
Where {ûi } are the node parameters specially chosen from the knot vector U j of D j (u). Even though this is an approximation to F j−1 (u) D j (u), it could be a practical technique for presenting the orientation of the displacement function D j (u) in rotation minimizing frames (RMFs) on C j−1 (u)
We have presented a new technique for editing multilevel B-spline curves by using RMFs [5] as local reference frames
Summary
Thanks to useful properties of B-spline, it has been considered the de factor standard for modeling freeform curves and surfaces in computer-aided design and computer graphics [1,2]. If we expect to maintain the orientation of the details made at the higher level, the edited displacements should be represented in certain coordinate frames on the curve at the lower level. Finkelstein and Salesin [4] discussed the orientation of details in this type of editing They used the Frenet frames (i.e., tangent, normal and bi-normal to a curve) to define a local coordinate system. We extend the traditional method for multilevel editing of B-spline curves to have correct orientation of details at each editing level. A user can change the overall shape of a curve, while preserving the orientation of details edited at higher levels. We present a robust and effective method for preserving orientation of details in the multilevel editing of B-spline curves.
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