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A Geometric Approach for Multi-Degree Spline

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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 C 1 and that between two adjacent segments of same degrees d is C d−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.

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Authors and Affiliations

  1. School of Mathematical Science, University of Science and Technology of China, Hefei, 230026, China

    Xin Li & Zhao Liu

  2. School of Computer Science, University of Science and Technology of China, Hefei, 230026, China

    Zhang-Jin Huang

Authors
  1. Xin Li
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  2. Zhang-Jin Huang
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  3. Zhao Liu
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Corresponding author

Correspondence to Xin Li.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos.11031007, 60903148, 60803066, the Chinese Universities Scientific Fund, the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry of China, and the Startup Scientific Research Foundation of Chinese Academy of Sciences.

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Li, X., Huang, ZJ. & Liu, Z. A Geometric Approach for Multi-Degree Spline. J. Comput. Sci. Technol. 27, 841–850 (2012). https://doi.org/10.1007/s11390-012-1268-2

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  • DOI: https://doi.org/10.1007/s11390-012-1268-2

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