基于C^∞基函数的自然邻点插值（NNI）方法在科学计算可视化上的应用

A C~∞ Basis Function-based NNI Method and Its Application to Visualization in Scientific Computing

插值方法及插值基函数的选择是可视化技术的一个关键问题。该文首先根据平面域上分布的数据点集，将平面域剖分为 Ｖｏｒｏｎｏｉ ｃｅｌｌｓ进而得到相应的 Ｄｅｌａｕｎａｒ三角化网格。然后基于 Ｖｏｒｏｎｏｉ ｃｅｌｌｓ的几何性质，应用自然邻点插值（ＮＮＩ）方法，介绍了一种具有无穷次连续可微的 Ｃ∞插值基函数及其数学性质。将基于 Ｃ”基函数的 ＮＮＩ方法用于把复杂数据场重构成一个具有规则网格的经验模型。最后再根据规则网格，生成三维立体图、等值线图、矢量分布图等。文章通过实例表明了基于Ｃ∞基函数的ＮＮＩ方法能够很好地应用于处理极不规则分布数据场的可视化。

The Natural Neighbour Interpolation (NNI ) method based on C∞ basis function is described in this paper. Defined by a finite set of distinct data points of any planar domain,we can divide the plane into Voronoi cells and get the corresponding Delaunay triangulation. Using our efficient method,a complex data field with irregularly distributed data points can be reconstructed as a model with regular grid. Based on the regular grid,the data field is visualized by contour map,perspective view, streamline and vector quiver etc.