基于动态参数化的二次B样条插值曲线

参数化为构造B样条插值曲线提供了自由度，但在以往的研究中，这些自由度并未得到充分利用．该文给出的二次B样条曲线插值方法充分利用了参数化的自由度，直接利用插值曲线直观的几何约束条件如曲线在数据点处的切向、曲线段的相对高度等进行参数化，使得构造出的插值曲线不仅在两端，而且在中间各段具有预期的几何性质．该文的方法比起以往的参数化方法来，能更直观有效地控制插值曲线的形状．而且，所构造的插值曲线具有局部性质或近似局部性质，即当改变某个数据点的位置时，插值曲线的形状只作局部改变或除局部范围外，曲线形状改变很小或完全不变．不同于以往的插值方法，该文的方法在构造插值曲线的过程中根据曲线的几何约束条件动态地递推确定参数值、节点向量和控制顶点，整个过程不必解方程组，计算简便．该文还给出了相应的算法和应用例子．实验结果表明，该文的方法十分有效．

Quadratic B-Spline Interpolation Curves Based on Dynamic Parametrization

Parametrization provides degree of freedom for B-spline interpolation curves. B ut this degree of freedom has not been fully utilized in the past researches. In this paper, a interpolation method for quadratic B-spline curves is given whic h fully utilizes the degree of freedom of parametrization. With this method, the intuitive geometric constrained conditions of the interpolation curve such as t he tangents of the curve on data points and the relative heights of cur ve segments are directly used in parametrization and the resulted interpolation curve possesses the expectant geometric properties. Hence the shapes of the inte rpolation curves can be controlled more intuitively and effectively by this meth od than by the existing B-spline interpolation methods. In addition, the result ed interpolation curves have localness or nearly localness properties for the da ta points. Differing from the other interpolation methods which need solve equat ion sets, the method proposed in this paper simply recursively calculates parame ters, knots and control points dynamically according to the given geometric cons trained conditions of the interpolation curve in the process of constructing int erpolation curve. Two algorithms and some examples for this method are also give n and the results show that this method is very effective.