讨论了构造C2连续的四次样条插值曲面问题。把四次样条函数降为C2连续可提供额外的自由度，用于提高曲面的插值精度和控制曲面的形状。给出了一个确定自由度的方法和C2连续的四次样条曲线需满足的连续性方程，提出了构造C2连续的四次样条插值曲面的新方法。新方法的特点是曲面需满足的连续性方程是三对角占优势的，曲面的不连续点在给定的数据点处。所构造的曲面具有四次多项式插值精度。最后以实例对新方法和现有三、四次样条函数方法的插值精度做了比较。

The construction of a GC1 cubicinterpolatiing curve that lies on the same side of a given straight line as the data points is studied. The main task is to choose appropriate approaches to modify tangent vectors at the data points for the desired curve. Three types of approches for changing the magnitudes of the tangent vectors are presented.The first-type approach modifies the tanggent vectors by applying a constraint to the curve segment. The second one does thework by optimization techniques. The thired one is a modification of the existing method. Three critera are prsented to compare the three types of approaches with the existing method. the experiments that test the effectiveess of the approaches are included.

The current cubic spline curve interpolation scheme is derived based on the implicit assumption that the magnitude of the first derivative of the curve is close to a constant. However, the assumption is not realized by the interpolation scheme. A knot choosing technique for parametric cubic spline interpolating curve construction that accommodates this assumption is presented. A comparison of the new method with several existing methods is performed and test results are included.

将扰动约束技应用于Bézier曲线的隆阶给出了理想的结果。讨论了将这类方法应用于B样曲线降价时结果不理想的原因，提出了采用最佳平方带近技术对B样条曲线做隆价运逄的方法；并用实例对该方法和基于扰动约束的隆价方法进了比较。