基于无网格法的坡度坡向提取

Extraction of slope and aspect based on Meshless method

无网格法是从有限元法发展而来的数值方法,它不依赖于网格,在计算力学领域受到广泛关注。文章将无网格法应用于坡度坡向地形因子的提取,构建数学模型,计算任意点的坡度坡向值。通过实验分析发现,曲面离散数据分布均匀,计算结果精度高。对根据等高线离散的实测数据进行分析表明,在三种情况下坡度误差超过14°,坡向误差超过119°,分别为:邻域内采样点与待求解点几乎呈直线分布时;采样点聚集于待求解点一侧时;待求解点与采样点几乎处于同一平面时。可见该方法对采样点数据分布要求高。

Meshless method is evolved from the Finite Element method, which does not depend on the grid and attracts widespread attention in the field of computational mechanics. It was applied in the extraction of slope and aspect in the paper. The mathematical models were constructed to calculate the slope and aspect of any point based on the sampling points in neighborhood. Experimental analysis demonstrated that the discrete points of surface distribute uniformly, so that results could be obtained with high precision. Moreover, when the slope and aspect were calculated with discrete points of contour lines, the slope error would be more than 14° and aspect error more than 119° in three cases： first, the sampling points and the point to be solved in neighborhood are almost linear distribution; second, the sampling points gather in one side of the point to be solved; third, the sampling points and the point to be solved are almost in the same plane. From above it could showed that the method required uniform distribution of sampling points.