HP Labs Technical Reports

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Multiresolution Control for Non-Uniform B-Spline Curve Editing

Elber, Gershon; Gotsman, Craig



Abstract: The piecewise polynomial B-spline representation is widely used throughout the CAGD community as the representation of choice. However, the locality of B-spline curves, while important in many respects, disables global control of the curve, preventing efficient and easy manipulation. Multiresolution representations for uniform B-spline curves have been recently proposed to alleviate this problem. Herein, we extend the use of multiresolution representations to non-uniform B-spline (NUBS) curves, including periodic curves. Our method supports local non-uniform refinement and (dis)continuity preservation. The multiresolution decomposition of the freeform NUBS curve is computed using least-squares approximation, based on existing data reduction techniques. The least-squares decomposition allows us to support NUBS curves, but it also imposes some preprocessing penalties in both time and space compared to techniques for multiresolution uniform B-spline curves. Nonetheless, the entire process is fast enough to enable interactive editing of complex NUBS curves, as is demonstrated by an interactive editor implemented to test our methods.

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