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Front. Inform. Technol. Electron. Eng.  2011, Vol. 12 Issue (10): 800-808    DOI: 10.1631/jzus.C1000381
    
Non-uniform B-spline curves with multiple shape parameters
Juan Cao1, Guo-zhao Wang2
1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China 2 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence. These curves not only have the many valued properties of the usual non-uniform B-spline curves, but also are shape adjustable under fixed control polygons. Our method is based on the degree elevation of B-spline curves, where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline. We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms, which are indispensable from the user’s perspective.

Key wordsNon-uniform B-spline      Shape parameter      Degree elevation     
Received: 01 November 2010      Published: 08 October 2011
CLC:  TP391.72  
Cite this article:

Juan Cao, Guo-zhao Wang. Non-uniform B-spline curves with multiple shape parameters. Front. Inform. Technol. Electron. Eng., 2011, 12(10): 800-808.

URL:

http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1000381     OR     http://www.zjujournals.com/xueshu/fitee/Y2011/V12/I10/800


Non-uniform B-spline curves with multiple shape parameters

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence. These curves not only have the many valued properties of the usual non-uniform B-spline curves, but also are shape adjustable under fixed control polygons. Our method is based on the degree elevation of B-spline curves, where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline. We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms, which are indispensable from the user’s perspective.

关键词: Non-uniform B-spline,  Shape parameter,  Degree elevation 
[1] Xiao-juan Duan, Guo-zhao Wang. Degree elevation of unified and extended spline curves[J]. Front. Inform. Technol. Electron. Eng., 2014, 15(12): 1098-1105.