基于空间网格表面距离的插值曲面

Interpolation Surface Based on Space-Mesh-Surface Distance

主要讨论基于空间网格表面距离的插值曲面 .定义了一种空间网格表面距离 ,基于空间网格表面距离 ,给出了两种定义在空间网格上的插值曲面 :基于网格表面距离的径向基函数插值曲面和基于网格表面距离的Kriging插值曲面 ,讨论了曲面的无穷阶光滑性 ,给出了一种计算网格表面距离的折线跟踪算法 .作为整体曲面 ,此类插值曲面与网格表面形状较为相符 ,比较适合于局部插值与参数估计 ,如梯度。

In this paper, the concept of space-mesh-surface distance is introduced. Base d on the space-mesh-surface distance, two kinds of interpolation surfaces defi ned on space-mesh-surface of triangulation are constructed. They are space-me sh-surface distance based radial basis function interpolation surface and Krigi ng interpolation surface. The infinite smoothness of the surface is discussed fo r those points that have unique distance path on space-mesh-surface. An algori thm for computing space-mesh-surface distance, named broken line tracing metho d, is given. As a whole interpolation surface, they are well in consistence with the space-mesh-surface in shapes and are suitable to be applied in local shap e estimation, such as gradient and direction estimations.