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Quadratic Polynomial Interpolation onTriangular Domain

机译：三角域上的二次多项式插值

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In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
机译：在自然地形的模拟中，采样点的连续性并不总是相互协调的，传统的插值方法往往不能如实地反映出数据点中的形状信息。因此，提出了一种在三角域上构造多项式插值曲面的新方法。首先，将空间分散的数据点投影到平面上，然后进行三角剖分;其次，在每个顶点上构造一个C连续的分段二次多项式面片，要求所有面片都尽可能靠近线插值。最后，通过最小化目标函数获得未知量，并对边界点进行特殊处理。结果表面在满足一定精度和连续性要求的条件下，尽可能地保留数据点的尽可能多的属性，而不是同时凸出。新方法计算简单，具有良好的局部性，适用于矿井，探井的形体拟合等。实验中给出了新表面的结果。

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