过指定顶点的四次B样条曲线及其应用

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

摘要: 本文构造了插值给定型值点序列P_i(i=0,1,2,3,4)指定点且与始末两边相切的四次B样条曲线，并以此四次B样条曲线为轴线的管道光滑拼接了轴线异面圆管道。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、插值于始末端点两段连续的三次均匀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，具有容易构造等特点。具有理论意义和应用价值。

Abstract: In this paper, we construct a quartic B-spline curve that is interpolated to the appointed vertexes of the fixed value point sequence P_i(i=0,1,2,3,4) and tangent to the start and end points of the control polygon. Circular tubes whose axes are in non-coplanar are smoothly blended by tube take a quartic B-spline curve as its axis. The results show that the method is better than that in which tubes are smoothly blended between smoothly connected three-segment continuous tubes with cubic uniform B-spline curves as its axis, and tubes are smoothly blended by two-segment continuous tubes whose axis is a cubic uniform B-spline curve interpolated at both the start and end vertexes, 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, which has theoretical significance and application value.