This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used to model boundary values while the inner point data is used for modeling a load vector with the goal to generate a smooth surface. The construction of boundary data is an ill-posed problem, for which a special regularization approach is suggested. The method is designed for surface construction problems with a very limited amount of measured data. In the paper we apply the method by using empirical data of soil thickness and geological maps indicating exposed bedrock regions.

翻译：本文提出了一种基于经验数据的表面数学建模方法。该方法通过在给定内部点与内部曲线数据的区域上求解离散双调和方程实现。内部曲线数据用于构建边界值，而内部点数据则用于建模载荷向量，以生成光滑表面。边界数据的构建是一个不适定问题，为此我们提出了一种特殊的正则化方法。该方法专为测量数据极为有限的表面构建问题设计。在本文中，我们通过应用土壤厚度经验数据及指示基岩裸露区域的地质图来验证该方法。