散乱数据点分片二次多项式加权平均插值

Weighted Combination Interpolation by Piecewise Quadric Polynomial to Scatter Data Points

将空间散乱数据点划分为三角形网格 ,在每个给定数据点处构造C1连续的分片二次多项式曲面片 ,每个三角形上的曲面片由各个顶点处的C1连续的分片二次曲面片加权平均确定 ,整体的C1曲面由各三角形上的曲面片拼合而成 该方法所构造的曲面函数结构简单、易于计算 ,具有数据点建议的形状

The new method triangulates the given data points into triangle network, and at the adjacent region of each point a C 1 piecewise quadric interpolation patch is constructed The surface patch on each triangle is constructed by the weighted combination of the three quadric patches at the vertices of the triangle All the triangle patches are combined together to form the whole surface with C 1 continuities The surface constructed by the new method has the shape suggested by the given data points, and the method is simple in construction and efficient in calculation Finally, an example is given to make comparison with other methods