过特征多边形始末端点的四次均匀B样条曲线及其应用

Quadratic Uniform B-Spline Curve of Passing Start Point and End Point of the Characteristic Polygon and Its Application

摘要: 本文构造了过控制多边形始点和终点的四次均匀B样条曲线，并以此四次均匀B样条曲线为轴线的管道光滑拼接了轴线异面管道。该方法相较于过始末端点的三次均匀B样条曲线为轴线的管道光滑拼接轴线异面管道，通过给定位于曲线上的一些点，反算出B样条曲线的特征多边形的顶点构造的B样条曲线为轴线的管道光滑拼接轴线异面的管道有其不同的特性。具有一定的应用价值。

Abstract: In this paper, we construct a quartic uniform B-spline curve of passing start point and end point of the control polygon. Tubes whose axes are in non-coplaner are smoothly blended by tube taking a quartic uniform B-spline curve as its axis. Compared with the tube with cubic uniform B-spline curve as the axis passing through the start and end points, the tubes whose axes are in non-cop- laner are smoothly blended by the tube. By giving some points located on the curve, this method can calculate the vertices of the characteristic polygon of the B-spline curve. The constructed B- spline curve is used as the tube with axis, and tubes are smoothly blended by the tube whose axis is in non-coplaner which has different characteristics. It has certain application value.