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Volume 27 Issue 4
July  2012
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Xin Li, Zhang-Jin Huang, Zhao Liu. A Geometric Approach for Multi-Degree Spline[J]. Journal of Computer Science and Technology, 2012, 27(4): 841-850. DOI: 10.1007/s11390-012-1268-2
Citation: Xin Li, Zhang-Jin Huang, Zhao Liu. A Geometric Approach for Multi-Degree Spline[J]. Journal of Computer Science and Technology, 2012, 27(4): 841-850. DOI: 10.1007/s11390-012-1268-2
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A Geometric Approach for Multi-Degree Spline

  • 1. School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China;
    2. School of Computer Science, University of Science and Technology of China, Hefei 230026, China

Funds: 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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  • Received Date: January 16, 2011
  • Revised Date: May 01, 2012
  • Published Date: July 04, 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.
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    • References (10)
  • [1]
    Sederberg T W, Zheng J M, Sewell D, Sabin M. Non-uniformrecursive subdivision surfaces. In Proc. the 25th SIGGRAPH,Orlando, USA, July 1998, pp.387-394.
    [2]
    Peters J. Patching Catmull-Clark meshes. In Proc. the27th SIGGRAPH, New Orleans, Louisiana, USA, July 2000,pp.255-258.
    [3]
    Kaklis P D, Pandelis D G. Convexity-preserving polynomialsplines of non-uniform degree. IMA Journal of NumericalAnalysis, 1990, 10(2): 223-234.
    [4]
    Costantini P. Variable degree polynomial splines. In Curvesand Surfaces with Applications in CAGD, Rabut C, LeMehaute A, Schumaker L L (Eds.), Nashville: Vanderbilt UniversityPress, 1997, pp.85-94.
    [5]
    Costantini P. Curve and surface construction using variabledegree polynomial splines. Computer Aided Geometric Design,2000, 17(5): 419-446.
    [6]
    Wang G Z, Deng C Y. On the degree elevation of B-splinecurves and corner cutting. Computer Aided Geometric Design,2007, 24(2): 90-98.
    [7]
    Shen W Q, Wang G Z. A basis of multi-degree splines. ComputerAided Geometric Design. 2010, 27(1): 23-35.
    [8]
    Shen W Q, Wang G Z. Changeable degree spline basis functions.Journal of Computational and Applied Mathematics,2010, 234(8): 2516-2529.
    [9]
    Sederberg T W, Zheng J M, Song X W. Knot intervals andmulti-degree splines. Computer Aided Geometric Design,2003, 20(7): 455-468.
    [10]
    Lyche T, Morken K. Knot removal for parametric B-splinecurves and surfaces. Computer Aided Geometric Design,1987, 4(3): 217-230.
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