一类带形状参数的混合Coons曲面及其性质
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摘要
为拓宽Coons曲面的应用范围,文章在三角混合函数空间给出一组带形状参数λ的混合函数,并分析该混合基函数的性质.基于此混合基函数,构造一种带形状参数的混合Coons曲面片,该曲面片的优点在于不仅具有传统Coons曲面的良好性质,而且具有形状可调性.给出数值实例,说明其形状可调.
In order to widen the application of Coons patch,in this paper we provide a class of blending basis functions called HC-blending basis function,and analyse the properties of HC-blending basis function.Based on the HC-blending basis functions,we construct HC-Coons patch with shape parameters.The HCCoons patch not only has the same superiority to bi-cubic Coons patch,but also can adjust its shape by parameters.So we can achieve the goal of adjusting its shape.
In order to widen the application of Coons patch,in this paper we provide a class of blending basis functions called HC-blending basis function,and analyse the properties of HC-blending basis function.Based on the HC-blending basis functions,we construct HC-Coons patch with shape parameters.The HCCoons patch not only has the same superiority to bi-cubic Coons patch,but also can adjust its shape by parameters.So we can achieve the goal of adjusting its shape.
引文
[1]HAN Xuli.A class of general quartic spline curves with shape parameter[J]. Computer Aided Geometric Design,2011,28(3):151-163.
[2]严兰兰,韩旭里.高阶连续的形状可调的三角多项式曲线曲面[J].中国图象图形学报,2015,20(3):427-436.
[3]严兰兰,韩旭里.具有多种优点的三角多项式曲线曲面[J].计算机辅助设计与图形学学报,2015,27(10):1971-1979.
[4]HAN Xuli.Shape-preserving piecewise rational interpolation with higher order continuity[J]. Applied Mathematics and Computation,2018,337:1-13.
[5]HAN Xuli.Shape-preserving piecewise rational interpolation with quartic numerator and quadratic denominator[J].Applied Mathematidcs and Computation,2015,251:258-274.
[6]ZHU Yuanpeng,HAN Xuli.Shape preserving C2rational quartic interpolation spline with two parameters[J]. International Journal of Computer Mathematics,2015,92(10):2160-2177.
[7]HUSSAIN M,SALEEM S. C2rational quadratic trigonometric spline[J]. Egyptian Informatics Journal,2013,14:211-220.
[8]HAN Xuli.Piecewise quartic polynomial curves with a local shape parameter[J]. Journal of Computational and Applied Mathematics,2006,195(1/2):34-45.
[9]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.
[10]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.
[11]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.
[12]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2002.
[13]LI Yang,TANG Wencheng,LIU Haichen.C-Coons patch and its proterty[J]. Journal of Computer-Aided Design&Computer Graphics,2003,15(9):1177-1180.
[14]李岩,韩旭里.带形状参数的混合Coons类曲面[J].计算机工程与应用,2009,45(28):72-74.
[15]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.
[16]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社,2001.
[2]严兰兰,韩旭里.高阶连续的形状可调的三角多项式曲线曲面[J].中国图象图形学报,2015,20(3):427-436.
[3]严兰兰,韩旭里.具有多种优点的三角多项式曲线曲面[J].计算机辅助设计与图形学学报,2015,27(10):1971-1979.
[4]HAN Xuli.Shape-preserving piecewise rational interpolation with higher order continuity[J]. Applied Mathematics and Computation,2018,337:1-13.
[5]HAN Xuli.Shape-preserving piecewise rational interpolation with quartic numerator and quadratic denominator[J].Applied Mathematidcs and Computation,2015,251:258-274.
[6]ZHU Yuanpeng,HAN Xuli.Shape preserving C2rational quartic interpolation spline with two parameters[J]. International Journal of Computer Mathematics,2015,92(10):2160-2177.
[7]HUSSAIN M,SALEEM S. C2rational quadratic trigonometric spline[J]. Egyptian Informatics Journal,2013,14:211-220.
[8]HAN Xuli.Piecewise quartic polynomial curves with a local shape parameter[J]. Journal of Computational and Applied Mathematics,2006,195(1/2):34-45.
[9]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.
[10]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.
[11]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.
[12]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2002.
[13]LI Yang,TANG Wencheng,LIU Haichen.C-Coons patch and its proterty[J]. Journal of Computer-Aided Design&Computer Graphics,2003,15(9):1177-1180.
[14]李岩,韩旭里.带形状参数的混合Coons类曲面[J].计算机工程与应用,2009,45(28):72-74.
[15]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.
[16]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社,2001.