三角Bézier曲线曲面光滑融合的构造

doi:10.3969/j.issn.0255-8297.2016.02.005

应用科学学报 ›› 2016, Vol. 34 ›› Issue (2): 154-162.doi: 10.3969/j.issn.0255-8297.2016.02.005

三角Bézier曲线曲面光滑融合的构造

刘华勇, 谢新平, 李璐, 张大明

安徽建筑大学数理学院, 合肥 230022

收稿日期:2015-09-14 修回日期:2015-12-02 出版日期:2016-03-30 发布日期:2016-03-30
作者简介:刘华勇,副教授,研究方向:计算机辅助几何设计和图形学,E-mail:aiaiwj@126.com
基金资助:
国家自然科学基金(No.61402010, No.61471003);安徽省高等学校自然科学研究项目基金(No.KJ2015A328, No.KJ2015JD16, No.KJ2014A041, No.KJ2016A151)资助

Smooth Blending of Trigonometric Bézier Curves and Surfaces

LIU Hua-yong, XIE Xin-ping, LI Lu, ZHANG Da-ming

School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230022, China

Received:2015-09-14 Revised:2015-12-02 Online:2016-03-30 Published:2016-03-30

摘要/Abstract

摘要： 为了使设计的曲线曲面能在相对简单的条件下满足较高的光滑融合,并且在不改变控制顶点的情况下可任意修改曲线曲面形状,构造了带形状参数的三角Bézier基函数.基于该组基函数定义了λC-Bézier曲线曲面,即分别有4个控制顶点定义的三角曲线和16个控制网格定义的三角曲面.讨论了曲线、曲面光滑融合需满足的条件,根据融合条件可构造分段光滑的组合曲线曲面.这样融合的曲线曲面能在一定条件下保证组合曲线、曲面的连续性.数值实例显示了该方法的有效性.

关键词: 三角样条, 融合, 连续性, 封闭曲线曲面

Abstract: Trigonometric polynomial functions with shape parameters are proposed. The λC-Bézier curve and surface basis can achieve higher order smoothness by joining in relatively simple conditions. Meanwhile, their shape can be adjusted freely without changing control points. Based on the trigonometric Bézier polynomial functions, we define a new λC-Bézier curve determined by four control points and a new λC-Bézier surface determined by sixteen control net.The smooth blending conditions of the new curve and surface are discussed. Under the blending conditions, we define a piecewise combination curve and surface consisting of the λC-Bézier curve and surface. The method automatically ensures continuity of the curve and surface. Experimental results show effectiveness of the method.

Key words: trigonometric spline, blending, continuity, closed curve and surface

中图分类号:

TP391.411

刘华勇, 谢新平, 李璐, 张大明. 三角Bézier曲线曲面光滑融合的构造[J]. 应用科学学报, 2016, 34(2): 154-162.

LIU Hua-yong, XIE Xin-ping, LI Lu, ZHANG Da-ming. Smooth Blending of Trigonometric Bézier Curves and Surfaces[J]. Journal of Applied Sciences, 2016, 34(2): 154-162.

参考文献

[1] 李军成. 一种构造任意类三次三角曲线的方法[J]. 小型微型计算机系统,2011, 32(7):1442-1445. Li J C. A method for constructing arbitrary quasi-cubic trigonometric curves[J]. Journal of Chinese Computer Systems, 2011, 32(7):1442-1445. (in Chinese)

[2] 严兰兰,韩旭里. 形状及光滑度可调的自动连续组合曲线曲面[J]. 计算机辅助设计与图形学学报,2014, 26(10):1654-1662. Yan L L, Han X L. Automatic continuous composite curve and surface with adjustable shape and smoothness[J]. Journal of Computer-Aided Design &Computer Graphics, 2014, 26(10):1654-1662. (in Chinese)

[3] Sarra S A, Sturgill D. A random variable shape parameter strategy for radial basis function approximation methods[J]. Engineering Analysis with Boundary Elements, 2009, 33(5):1239-1245.

[4] Yang L Q, Zeng X M. Bézier curves and surfaces with shape parameters[J]. International Journal of Computer Mathematics, 2009, 86(7):1253-1263.

[5] Liu Z, Tan J, Chen X, Zhang L. An approximation method to circular arcs[J]. Applied Mathematics and Computation, 2012, 219(4):13061311.

[6] Han X. Quadratic trigonometric polynomial curves with a shape parameter[J]. Computer Aided Geometric Design, 2002, 19(7):503512.

[7] Chen Q Y, Wang G Z. A class of Bezier-like curve[J]. Computer Aided Geometric Design, 2003, 20(1):29-39.

[8] 刘华勇,李璐,张大明. 任意阶参数连续的三角多项式样条曲线曲面调配[J]. 浙江大学学报:理学版,2014, 41(4):413-418. Liu H Y, Li L, Zhang D M. Blending of the trigonometric polynomial spline curve and surface with arbitrary continuous order[J]. Journal of Zhejiang University:Science Edition, 2014, 41(4):413-418. (in Chinese)

[9] 徐迎博,喻德生. 带形状参数的二次三角多项式Bézier曲线形状分析[J]. 浙江大学学报:理学报,2013,38(1):35-41. Xu Y B, Yu D S. Shape analysis of quadratic trigonometric polynomial Bézier curves with a shape parameter[J]. Journal of Zhejiang University:Science Edition, 2013, 40(1):35-41. (in Chinese)

[10] 王文涛,汪国昭. 带形状参数的三角多项式均匀B样条[J]. 计算机学报,2005, 28(7):1192-1198. Wang W T, Wang G Z. Trigonometric polynomial uniform B-spline with shape parameter[J]. Chinese Journal of Computers, 2005, 28(7):1192-1198. (in Chinese)

[11] 李军成,赵东标,杨炼. 拟三次三角样条插值曲线与曲面[J]. 小型微型计算机系统,2013, 34(3):680-684. Li J C, Zhao D B, Yang L. Quasi-cubic trigonometric spline interpolation curves and surfaces[J]. Journal of Chinese Computer Systems, 2013, 34(3):680-684. (in Chinese)

[12] 吴晓勤.带形状参数的Bézier曲线[J]. 中国图象图形学报,2006, 10(2):269-275. Wu X Q. Bézier curve with shape parameter[J]. Journal of Image and Graphics, 2006, 10(2):269-275. (in Chinese)

[13] Zhang J W, Kraus F L. Extending cubic uniform B-splines by unified trigonometric and hyperbolic basis[J]. Graphical Models, 2005, 67(2):100-119.

[14] 彭丰富,田良. 带形状控制的自由曲线曲面参数样条[J]. 中国图象图形学报,2015, 20(11):1511-1516. Peng F F, Tian L. Parameter spline for free-form curve and surface[J]. Journal of Image and Graphics, 2015, 20(11):1511-1516. (in Chinese)

[15] 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. Yan L L, Han X L. Trigonometric polynomial curve and surface with many advantages[J]. Journal of Computer-Aided Design & Computer Graphics, 2015, 27(10):1971-1979. (in Chinese)

[16] Hu G, Qin X Q. The construction of λμ-B-spline curves and its application to rotational surfaces[J]. Applied Mathematics and Computation, 2015, 266(2):194-211.

[17] Lai L M, Yuen M M F. Blending of mesh objects to parametric surface[J]. Computers & Graphics, 2015, 46(2):283-293.

[18] Zhu Y P, Han X L. New cubic rational basis with tension shape parameters[J]. Applied Mathematics-A Journal Chinese Universities, 2015, 30(3):273-298.

三角Bézier曲线曲面光滑融合的构造

Smooth Blending of Trigonometric Bézier Curves and Surfaces

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