三次有理B样条曲线及其应用

Cubic Rational B-Spline Curve and Its Application

本文构造了通过给定控制多边形的始末端点且与始末控制多边形相切的一段三次有理B样条曲线,并以三次有理B样条曲线为轴线的管道光滑拼接了轴线异面管道。该方法相较于三段连续的三次均匀B样条曲线为轴线的三段光滑拼接的管道光滑拼接轴线异面管道和两段连续的二次均匀B样条曲线为轴线的两段光滑拼接的管道光滑拼接轴线异面管道其构造简单,易于应用。

In this paper, we construct a section of cubic rational B-spline curve which is tangent to the start and end points of the control polygon. Tubes whose axes are in non-coplaner are smoothly blended by tube take cubic rational B-spline curve as its axis. Compared with the three-segment smooth blending tubes with three-segment continuous cubic uniform B-spline curves as the axis between tubes whose axes are non-coplana, and the two-segment smooth blending tubes with quadratic uniform B-spline curves as the axis between tubes whose axes are non-coplana, the proposed method has the advantages of simple structure and easy application.