Abstract: Given a way of constructing a shape preserving and interpolatory spline with G²-continuity by using parametric cubic segments.The process consists of three step：（1）Computing the optimal tangent directions for interpolation spline so that the energy of curve is a minimum.（2）Using the formula of curvature which is given in this paper，computed the curvature of every interpolation data point，then the module of tangent vectors were obtained on the condition that the curve is G²-continuity and shape preserving.（3）Then each segment is determined by Hermite interpolation satisfying given endpoint（position and tangent） conditions.Numerical examples are given to show the efficiency of this method.

摘要： 给出了一种在能量优化意义下构造G²连续保形插值三次参数样条曲线的方法。具体步骤如下：（1）以曲线应变能最小为目标构造目标函数，通过解线性方程组，求出优化意义下的每个插值点处的最优切矢方向；（2）用文中给出的简易公式求出各插值点的曲率，进而计算出插值点处的切矢模长，使曲线满足G²连续、保形插值的条件；（3）用Hermite插值方法求出相邻两插值点间的曲线。实验结果显示了方法的有效性。