任意三角域上的C^2插值

本文提出了任意三角域上的一种Ｃ~２插值方法，该方法构造容易，计算简单、有效，它的逼近阶是Ｏ（ｈ９），代数精度集为｛ｘｉｙｊ，ｉ＋Ｊ≤８｝。

局部构造C^2连续的三次B样条插值曲线和双三次插值曲面

为了避免一般的局部插值算法生成的B样条曲线和曲面在段点处达不到理想的连续性以及出现多重内节点的问题,一种局部构造C2连续的三次B样条插值曲线和双三次插值曲面的方法被介绍。该方法借助节点插入算法逐步地迭代出样条控制顶点,其思想简单、几何直观、算法速度快,在曲线中夹直线段、尖点以及在曲面中夹棱边和平面都能比较容易实现。生成的曲线光滑度高、无重节点。文章最后还利用这种构造方法给出了一种在指定范围内按规定变形曲线的方法。

弧长反函数C^2保单调插值公式

Hetmite插值弧长函数的反函数 ,为参数曲线引入弧长参变量 .插值公式是保单调和C2 连续的 ,从而在实现弧长参数化时 ,节点处单位切矢 ,并保持参数曲线几何形状和C2 连续性 .

C^1 C^2INTERPOLATION OF SCATTERED DATA POINTS

In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.

C^2连续近似弧长参数化曲线

This paper presents a method for nearly arc-length parameterization based on the rational cubic function. The arc-length function of parametric curve is monotonic increasing, the monotonity preserving rational cubic approximation for the arc-length function is derived. The resulting nearly arc-length parametrized curve is C2-continuous and interpolates a set of points of original curve. At each of the points, nearly arc-length parametrized curve is accurate. Finally, an example illustrate that the method is very efficient.