Abstract: This paper constructs three order cubic equidistant-knot polynomial B-spline parameter curve，and relationship function of de Boor control point and segment cubic Bézier control point.This curve has the property similar to quadratic B-spline curve：C¹-continuous with respect to parametric variable，curves at each spline intervals represented by linear combinations of three de Boor control points，with invariability under affine transformation，including quadratic uniform B-spline curve，etc；And property of shape adjustability：blending function including shape parameter，and with explicit geometric significance，be able applying to control the shape or transform of the curve.And provide the properties and conditions of convex hull property，conformal property of de Boor control polygon，discuss the impact of shape parameter to curve shape.

Key words: spline curve, blending function, shape parameter, affine invariant

摘要： 构造了三阶三次等距结点的多项式B样条参数曲线，给出了de Boor控制顶点与分段三次Bézier控制顶点的关系式。该曲线具有一些类似于二次B样条曲线的性质：关于参变量为C¹连续，每个样条区间上的曲线由三个de Boor控制顶点的线性组合表示，具有仿射变换下的不变性，包含了二次均匀B样条曲线等。还具有形状可调性质：调配函数中含有形状参数，具有明显的几何意义，可用于调控曲线的形状或变形。给出了其具有凸包性、对de Boor控制多边形保形性等性质及其条件，讨论了形状参数对曲线形状的影响。

关键词: 样条曲线, 调配函数, 形状参数, 仿射不变性