三角Bézier曲线曲面光滑融合的构造

doi:10.3969/j.issn.0255-8297.2016.02.005

Abstract

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

CLC Number:

TP391.411

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.

References

[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.

Smooth Blending of Trigonometric Bézier Curves and Surfaces

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