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为了增强三维地质模型的准确性,突出复杂地质体局部相关性较高的特点,避免传统插值方法中存在的计算复杂度高、多依赖人工经验等缺点,在建模过程中引入了自然邻点插值(NNI)方法对三维离散数据进行插值。而现有的NNI方法无法直接应用于有限域的边界插值计算,成为该方法应用于三维地质建模的最大难点问题。依据Voronoi cells和Delaunay triangles的几何性质,采用non-Sibsonian(Laplace)插值方法构造形函数,详细证明了NNI方法在边界处的连续性,实现了边界插值且降低了其计算复杂度,解决了此难点问题。通过构建城市地质模型实例,验证了该方法的正确性和有效性。
In order to enhance the accuracy of three-dimensional geological model, highlighting the local correlation of complex geological bodies and avoiding the disadvantages of traditional interpolation methods, such as high computational complexity and dependence on artificial experience, the natural neighbors Interpolation (NNI) method interpolates three-dimensional discrete data. However, the existing NNI method can not be directly applied to the boundary interpolation calculation of finite fields, which becomes the most difficult problem when the method is applied to 3D geological modeling. According to the geometric properties of Voronoi cells and Delaunay triangles, the non-Sibsonian (Laplace) interpolation method is used to construct the shape function, which proves the continuity of the NNI method at the boundary and the boundary interpolation and reduces the computational complexity. Difficult problems. By constructing an example of urban geological model, the correctness and effectiveness of the method are verified.