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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue ( 6): 4-    DOI: 10.1631/jzus.2005.A0497
    
B¨|zier curves with shape parameter
WANG Wen-tao, WANG Guo-zhao
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  In this paper, B¨|zier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the B¨|zier curves with shape parameter. The B¨|zier basis curves with shape parameter have most properties of Bernstein basis and the B¨|zier curves. Moreover the shape parameter can adjust the curves?ˉ shape with the same control polygon. As the increase of the shape parameter, the B¨|zier curves with shape parameter approximate to the control polygon. In the last, the B¨|zier surface with shape parameter is also constructed and it has most properties of B¨|zier surface.

Key words： Mathematics Bézier curve      Bézier basis with shape parameter      Bernstein basis     
Received: 20 January 2004     
CLC:  TP391  
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WANG Wen-tao
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Cite this article:

WANG Wen-tao, WANG Guo-zhao. B¨|zier curves with shape parameter. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 6): 4-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A0497     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I 6/4

[1] ZHANG Xing-wang, WANG Guo-jin. A new algorithm for designing developable Bézier surfaces[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(12): 14-.
[2] SHEN Wan-qiang, WANG Guo-zhao. A class of quasi Bézier curves based on hyperbolic polynomials[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(Supplement 1): 116-123.