二次B样条曲线及其应用  

Quadratic B-spline Curve and Its Application

作　　者：王芳[1] 白根柱 WANG Fang;BAI Genzhu(Department of Basic Courses,Zhejiang Changzheng Vocational&Technical College,Hangzhou 310023,China;College of Mathematics,Inner Mongolia University for the Nationalities,Tongliao 028043,China)

机构地区：[1]浙江长征职业技术学院基础部,杭州310023 [2]内蒙古民族大学数学学院,内蒙古通辽28043

出　　处：《湖北民族大学学报（自然科学版）》2020年第2期209-213,共5页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(11561052);浙江省教育厅一般项目(Y201636628).

摘　　要：基于二次均匀B样条曲线以其特征多边形的中点为两个端点、特征多边形的两边为其端点切矢量的这一特性,利用两段光滑连接的二次均匀B样条曲线光滑拼接两个轴线异面管道轴线的基础上,完成了三种管道的光滑拼接,即两个粗细相同的轴线异面圆管道的光滑拼接、两个粗细不同的轴线异面圆管道的光滑拼接、两个轴线异面椭圆管道的光滑拼接.这种以二次均匀B样条曲线为轴线而构造出的光滑拼接管道其表达式简洁,拼接效果非常好,更易于应用.In this paper,based on the characteristics that the midpoints of the characteristic polygon are two endpoints and the two sides of the the characteristic polygon are tangent vectors of the endpoints of the quadratic uniform B-spline curve,two segments of quadratic uniform B-spline curve are used to connect the axes of two tubes with non-coplanar axes,and the smooth blending of three kinds of tubes is completed.The three kinds of tubes are the smooth blending tube between two non-coplanar circular tubes with same radius,two non-coplanar circular tubes with different radius,and two non-coplanar elliptical tubes.The smooth blending tube constructed with the quadratic uniform B-spline curve as the axis has a concise expression,the blending effect shows good results,and the obtained results are more applicable.

关 键 词：B样条曲线 轴线 管道 光滑拼接 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]