基于C^1自然邻近插值的曲面拟合

Surface Fitting Based on C^1 Natural Neighbor Interpolation

以C^0连续non-Sibsonian插值作为三次单纯形Bernstein-Bézier多项式的基坐标,构造C1连续自然邻近插值函数。介绍了高阶连续函数的构建原理和性质。将C1连续自然邻近插值函数应用于曲面拟合场合,由于Voronoi图能够自动调整数据点分布不规则和密度不均匀在空间上的差异,即使对于散乱数据点,也能获得较好的拟合结果。

C1 natural neighbor interpolation can be realized when C0 non-Sibsonian interpolation is introduced in the Bernstein-Bézier surface representation of a cubic simplex. The principle and properties of C1 natural neighbor interpolation are described and the surface fitting is given. The Voronoi diagram can adjust the spatial discrepancy caused by irregular data and data of varying density, so even for the scattered data, C1 natural neighbor interpolation can get accurate fitting results.