过指定顶点的三次B样条曲线及其应用

Cubic B-Spline Curve of Passing Appointed Vertexes and Its Application

摘要: 本文构造了通过给定控制多边形指定顶点且与始末控制多边形的始末边相切的两段连续三次B样条曲线，并以此两段连续的三次B样条曲线为轴线的管道光滑拼接了轴线异面椭圆管道。该方法相较于三段连续的三次均匀B样条曲线为轴线的管道、插值于两端点并与控制多边形的始末边相切的三次有理B样条曲线为轴线的管道、两段连续二次B样条曲线为轴线的管道光滑拼接轴线异面管道，各有其优越性。具有理论意义和应用价值。

Abstract: In this paper, we construct continuous two-section of cubic B-spline curve which is tangent to the start and end points of the control polygon. And we construct a tube that smoothly blends two ellipse tubes whose axes non-coplanar with the two continuous cubic B-spline curves as its axes. The results show that the method is better than that in which tubes are smoothly blended between smoothly connected three-segment tubes with cubic uniform B-spline curves as its axis, and tubes are smoothly blended by tube whose axis is a cubic rational B-spline curve interpolated at both ends and tangent to the start and end edges of the control polygon, and tubes are smoothly blended between smoothly connected two-segment tubes and quadratic uniform B-spline curves as its axis, which has theoretical significance and application value.