Title
A geometric approach for multi-degree spline
Document Type
Conference Proceeding
Publication Date
7-1-2012
Abstract
Multi-degree spline (MD-spline for short) is a generalization of B-spline which comprises of polynomial segments of various degrees. The present paper provides a new definition for MD-spline curves in a geometric intuitive way based on an efficient and simple evaluation algorithm. MD-spline curves maintain various desirable properties of B-spline curves, such as convex hull, local support and variation diminishing properties. They can also be refined exactly with knot insertion. The continuity between two adjacent segments with different degrees is at least C1 and that between two adjacent segments of same degrees d is Cd?1. Benefited by the exact refinement algorithm, we also provide several operators for MD-spline curves, such as converting each curve segment into Bézier form, an efficient merging algorithm and a new curve subdivision scheme which allows different degrees for each segment. © 2012 Springer Science+Business Media, LLC & Science Press. China.
Publication Source (Journal or Book title)
Journal of Computer Science and Technology
First Page
841
Last Page
850
Recommended Citation
Li, X., Huang, Z., & Liu, Z. (2012). A geometric approach for multi-degree spline. Journal of Computer Science and Technology, 27 (4), 841-850. https://doi.org/10.1007/s11390-012-1268-2