基于反求控制点的B样条曲面重建算法的实现
|
摘要
由于B样条曲面具有很好的局部修改性,因此在逆向工程中更广泛地应用B样条曲面来进行曲面重建。本文在散乱数据模型四边形网格划分优化处理的基础上,设计了基于反求控制点的B样条3次曲面重建算法,定义了基本概念,解决型值点的选取及参数化,追赶法求解控制点,曲面拟合等问题。在VC++编译环境下,进行算法的程序编写与调试,通过OPENGL函数显示了控制网格和拟合曲面。算法的运行结果说明了算法的可行性和可靠性。
Because of the good local modification of B-spline curve,it is widely used to reconstruct the B-spline surface in reverse engineering. Based on optimization quadrilateral meshes of the cloud data model by reverse control points,an algorithm for reconstructing quasi-uniform B-spline surface is designed. The basic concepts are defined,and a set of solutions are given,including selection and parameterization of model points,a selection method for solving control points equation,and fitting surfaces. The algorithm is implemented by VC++,and the control meshes and fitting surface are implemented by OPENGL functions. The results of the algorithm show its feasibility and reliability.
Because of the good local modification of B-spline curve,it is widely used to reconstruct the B-spline surface in reverse engineering. Based on optimization quadrilateral meshes of the cloud data model by reverse control points,an algorithm for reconstructing quasi-uniform B-spline surface is designed. The basic concepts are defined,and a set of solutions are given,including selection and parameterization of model points,a selection method for solving control points equation,and fitting surfaces. The algorithm is implemented by VC++,and the control meshes and fitting surface are implemented by OPENGL functions. The results of the algorithm show its feasibility and reliability.
引文
[1]PARK H.An error-bounded approximate method for representing planar curves in B-splines[J].Computer Aided Geometric Design,2004,21(5):479-497.
[2]张丽艳,周来水,蔡炜斌,等.基于截面测量数据的B样条曲面重建[J].应用科学学报,2002,20(2):173-177.
[3]周儒荣,张丽艳,苏旭,等.海量散乱点的曲面重建算法研究[J].软件学报,2001,12(2):249-255.
[4]王青,王融清,鲍虎军,等.散乱数据点的增量快速曲面重建算法[J].软件学报,2000,11(9):1221-1227.
[5]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,2013.
[6]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2000.
[7]程进三,高小山.构造两曲面的拼接曲面[J].工程图学学报,2005,26(1):40-44.
[8]RELVAS C,RAMOS A,COMPLETO A,et al.Accuracy control of complex surfaces in reverse engineering[J].International Journal of Precision Engineering and Manufac Turing,2011,12(6):1035-1042.
[9]CHEN Xiao-diao,MA Wei-yin,PAUL J.Multi-degree reduction of bezier curve using reparameterizaetion[J].ComputerAided Design,2011,43(2):161-169.
[10]BLAN K E.Topology recovery technique for complex freeform surface model after local geometry repair[J].Chinese Journal of Mechanical Engineering,2013,26(1):197-206.
[11]吴丽娟,刘丽,张彩明.非封闭曲面的海量空间数据点四边形网格生成算法[J].计算机辅助设与图形学学报,2007,19(2):151-156.
[12]魏海涛.计算机图形学[M].第2版,北京:电子工业出版社,2007.
[13]袁晶,杜娜,董文忠,等.散乱数据点B样条曲面重构算法的设计与实现[J].沈阳师范大学学报(自然科学版),2015,33(2):253-256.
[14]李梦娇,袁晶,杜娜,等.准均匀B样条曲面重建的误差分析与改进方法[J].沈阳师范大学学报(自然科学版),2016,34(2):217-221.
[15]古玉屏,唐月红.任意散乱点集的B样条曲面重建[J].计算机应用研究,2015,32(2):635-637.
[2]张丽艳,周来水,蔡炜斌,等.基于截面测量数据的B样条曲面重建[J].应用科学学报,2002,20(2):173-177.
[3]周儒荣,张丽艳,苏旭,等.海量散乱点的曲面重建算法研究[J].软件学报,2001,12(2):249-255.
[4]王青,王融清,鲍虎军,等.散乱数据点的增量快速曲面重建算法[J].软件学报,2000,11(9):1221-1227.
[5]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,2013.
[6]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2000.
[7]程进三,高小山.构造两曲面的拼接曲面[J].工程图学学报,2005,26(1):40-44.
[8]RELVAS C,RAMOS A,COMPLETO A,et al.Accuracy control of complex surfaces in reverse engineering[J].International Journal of Precision Engineering and Manufac Turing,2011,12(6):1035-1042.
[9]CHEN Xiao-diao,MA Wei-yin,PAUL J.Multi-degree reduction of bezier curve using reparameterizaetion[J].ComputerAided Design,2011,43(2):161-169.
[10]BLAN K E.Topology recovery technique for complex freeform surface model after local geometry repair[J].Chinese Journal of Mechanical Engineering,2013,26(1):197-206.
[11]吴丽娟,刘丽,张彩明.非封闭曲面的海量空间数据点四边形网格生成算法[J].计算机辅助设与图形学学报,2007,19(2):151-156.
[12]魏海涛.计算机图形学[M].第2版,北京:电子工业出版社,2007.
[13]袁晶,杜娜,董文忠,等.散乱数据点B样条曲面重构算法的设计与实现[J].沈阳师范大学学报(自然科学版),2015,33(2):253-256.
[14]李梦娇,袁晶,杜娜,等.准均匀B样条曲面重建的误差分析与改进方法[J].沈阳师范大学学报(自然科学版),2016,34(2):217-221.
[15]古玉屏,唐月红.任意散乱点集的B样条曲面重建[J].计算机应用研究,2015,32(2):635-637.