三维空间离散点数据场的插值方法

Interpolation algorithm for data field of 3D spatial scattered points

给出了一种根据三维离散点生成六面体单元并构造六面体9节点形函数进行插值的算法，该算法不受被插值模型单元形态限制，绕每一待插值点都能搜索到惟一的六面体插值单元，每一个数据的插出应用了被插值点周围8～16个已知节点的数据．给出了一种有限元逆变换算法，该算法收敛稳定、可较好地适应含有扭面等较不规则六面体单元局部坐标求解．实例表明，该方法精度较高，较好地实现了三维空间离散点数据场的插值．

An interpolation algorithm for generating the hexahedron element according to three-dimensional scattered data field is put forward. The shape function for the element of hexahedron with 9 nodes is utilized in the interpolation. Without the restriction of the meshes form of the interpolated model, this algorithm can find an only hexahedron around every interpolated point for interpolation by using 8-16 surrounding points＇ data when each point is interpolated. An FEM inverse transform algorithm is put forward as well. This inverse transform algorithm has stable convergence and the adaptability for irregular hexahedrons which contain twisted face when that the two algorithms mentioned above have hi figuring out the local coordinates. The example shows gh accuracy, effectively realizing the interpolation for three-dimensional spatial scattered data field.