带形状参数的R-Coons曲面
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摘要
为了解决传统Coons曲面不具备形状可调性,不能精确表示椭球面、椭圆锥面、椭圆柱面等二次曲面的问题,在有理函数空间上构造了一组有理混合基函数,称之为R-Hermite基。首先分析了R-Hermite基的性质;其次基于R-Hermite基,利用张量积方法,构造了一种新的带两个形状参数的有理Coons曲面,并称之为R-Coons曲面,R-Coons曲面不仅具有传统Coons曲面的良好性质,还具备形状可调性;最后给出了曲面精确表示椭球面、椭圆锥面、椭圆柱面的方法,并通过实例说明方法的有效性。
In order to solve the lack of shape adjustability of the traditional Coons surface and the inability to accurately represent ellipsoid, elliptical cone, and elliptical cylinder etc., a set of rational hybrid basis functions is constructed in rational space, which is named R-Hermite basis. Firstly, the properties of R-Hermite basis are illustrated. Secondly, based on the R-Hermite basis, a rational Coons surface with two shape parameters is constructed by using the tensor product method, and it is called R-Coons surface, which not only has the good properties of traditional Coons surface, but also has shape adjustability. Finally, the method that can accurately represent ellipsoid, elliptical cone and elliptical cylinder is given, and some examples are illustrated to prove the effectiveness of the method.
In order to solve the lack of shape adjustability of the traditional Coons surface and the inability to accurately represent ellipsoid, elliptical cone, and elliptical cylinder etc., a set of rational hybrid basis functions is constructed in rational space, which is named R-Hermite basis. Firstly, the properties of R-Hermite basis are illustrated. Secondly, based on the R-Hermite basis, a rational Coons surface with two shape parameters is constructed by using the tensor product method, and it is called R-Coons surface, which not only has the good properties of traditional Coons surface, but also has shape adjustability. Finally, the method that can accurately represent ellipsoid, elliptical cone and elliptical cylinder is given, and some examples are illustrated to prove the effectiveness of the method.
引文
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[13]李军成,赵东标,陆永华.带参数有理Coons曲面插值的图像缩放方法[J].计算机辅助设计与图形学学报,2011,23(11):1853-1859.
[14]LES P,TILLER W.非均匀有理B样条[M].赵罡,穆国旺,王拉柱,译.北京:清华大学出版社,2010:7-30.
[2]HUSSAIN M,SIDRA S.2C rational quadratic trigonometric spline[J].Egyptian Informatics Journal,2013,14:211-220.
[3]仇茹,杭后俊,潘俊超.带三参数的类四次Bezier曲线及其应用研究[J].计算机工程与应用,2014,50(20):158-162.
[4]严兰兰,韩旭里.基于全正基的三次均匀B样条曲线的扩展[J].图学学报,2016,37(3):329-336.
[5]尹池江,檀结庆.带多形状参数的三角多项式均匀B样条曲线曲面[J].计算机辅助设计与图形学学报,2011,23(7):1131-1138.
[6]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2002:57-65.
[7]WANG Y,TAN J,LI Z,et al.Bi-cubic C-Coons surface and its applications[J].Journal of Information and Computational Science,2012,9(7):1895-1903.
[8]裴芳,韩旭里,李岩.带形状参数的Coons类曲面的构造与拼接[J].计算机工程与应用,2013,49(10):163-166.
[9]王晶昕,董莹,倪静.带调节参数的双二阶三角多项式Coons曲面片[J].大连交通大学学报,2013,34(1):110-112.
[10]李杨,汤文成,刘海晨.C-Coons曲面及其性质[J].计算机辅助设计与图形学学报,2003,15(9):1177-1180.
[11]邹倩,韩旭里,包崇兵.两种带形状参数的有理Coons曲面[J].工程图学学报,2009,30(6):71-75.
[12]李军成,杨炼,李炳君.双三次Coons曲面片的两种扩展[J].计算机应用研究,2011,28(11):4389-4391.
[13]李军成,赵东标,陆永华.带参数有理Coons曲面插值的图像缩放方法[J].计算机辅助设计与图形学学报,2011,23(11):1853-1859.
[14]LES P,TILLER W.非均匀有理B样条[M].赵罡,穆国旺,王拉柱,译.北京:清华大学出版社,2010:7-30.