| 三次均匀B样条曲线的新扩展及应用 |
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| 引用本文： | 胡钢,刘哲,徐华楠.三次均匀B样条曲线的新扩展及应用[J].计算机工程与应用,2008,44(32):161-164. |
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| 作者姓名： | 胡钢 刘哲 徐华楠 |
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| 作者单位： | 1.西北工业大学 理学院，西安 710072 2.西安理工大学 理学院，西安 710054 |
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| 摘 要： | 给出了一组含有2个形状参数λi，μi的三次多项式调配函数，它是三次均匀B样条基函数的扩展；分析了这组调配函数的性质，基于此组调配函数定义了一种带2个局部形状控制参数λi，μi的分段多项式样条曲线，它以三次均匀B样条曲线为特殊情形。新曲线不仅具有灵活的局部形状可调性和更强的描述能力，而且可以在不改变曲线G1连续性和不影响曲线其他各段形状的同时，通过改变局部形状参数对曲线每段的形状进行多种方式的局部调整。最后讨论了新曲线在曲线造型中的应用，并给出了一个扩展曲面的定义。实例表明，新扩展曲线为曲线/曲面的设计提供了一种有效的新方法。
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| 关 键 词： | 三次均匀B样条 调配函数 局部形状参数 扩展 曲线设计 |
| 收稿时间： | 2007-12-11 |
| 修稿时间： | 2008-2-29
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New extensions of cubic uniform B-spline curve and its applications |
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| HU Gang,LIU Zhe,XU Hua-nan.New extensions of cubic uniform B-spline curve and its applications[J].Computer Engineering and Applications,2008,44(32):161-164. |
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| Authors: | HU Gang LIU Zhe XU Hua-nan |
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| Affiliation: | 1.School of Science，Northwestern Polytechnical University，Xi’an 710072，China 2.School of Science，Xi’an University of Technology，Xi’an 710054，China |
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| Abstract: | In order to construct B-spline curves with local shape control parameters，a class of polynomial basis functions with two local shape parameters λi，μi is presented in this paper.It is extensions of classical cubic uniform B-spline basis functions.Properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve is constructed with two local shape control parameters λi，μi accordingly.The curve not only inherits the outstanding properties of the cubic uniform B-spline curves，but also has a good performance on adjusting their local shapes by changing the two local shape control parameters.In particular，the G1 continuuity and the shapes of other segments of the curve can remain unchangeably during the manipulation on the shape of each segment on the curve.Furthermore，its applications in curve design and interpolation are discussed and an extend application on surface design is also presented.Modeling examples show that the new curve is very valuable for the design of curves and surfaces. |
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| Keywords: | cubic uniform B-spline blending functions local shape parameter extension curve design |
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