ABSTRACT

Terrain derivative calculations from triangulated irregular network (TIN)-based digital elevation models (DEMs) have been extensively explored in geomorphometry. However, most calculation methods focus on the triangulation facets of TIN-based DEMs and ignore the vertices. In fact, these vertices are the original sampling points from the terrain surface and serve as the basis for triangulation. In this study, we argue that terrain derivative calculations using TIN-based DEMs should focus on the vertices. Employing examples with slope and aspect, we applied the TIN vertex-based method to a mathematical surface and a real topography using TIN-based DEMs with a range of sampling point densities. We performed a comparative analysis of the TIN vertex-based, TIN facet-based, and grid-based methods. Assessments on the mathematical surface showed that the TIN vertex-based method achieved the highest accuracy among the three methods. Error analysis for the real landform case indicated that the TIN vertex-based method performed slightly better than the grid-based method for slope calculation and slightly worse than the grid-based method for aspect calculation. Among the three methods, the TIN facet-based method was most sensitive to error. The TIN vertex-based method can provide a reference for the slope and aspect calculation based on point clouds.

摘要

基于不规则三角网 (TIN) 的数字高程模型 (DEM) 的地形导数计算已在地貌测量学中得到广泛探索。然而，大多数计算方法侧重于基于 TIN 的 DEM 的三角剖分面，而忽略了顶点。实际上，这些顶点是地形表面的原始采样点，是三角测量的基础。在本研究中，我们认为使用基于 TIN 的 DEM 的地形导数计算应侧重于顶点。通过使用坡度和坡向示例，我们将基于 TIN 顶点的方法应用于数学表面和使用具有一系列采样点密度的基于 TIN 的 DEM 的真实地形。我们对基于 TIN 顶点、基于 TIN 面和基于网格的方法进行了比较分析。对数学表面的评估表明，基于 TIN 顶点的方法在三种方法中实现了最高的准确度。实际地形案例的误差分析表明，基于 TIN 顶点的方法在坡度计算中的表现略好于基于网格的方法，而在坡向计算中则略逊于基于网格的方法。在这三种方法中，基于 TIN 分面的方法对错误最为敏感。基于TIN顶点的方法可以为基于点云的坡度和坡向计算提供参考。实际地形案例的误差分析表明，基于 TIN 顶点的方法在坡度计算中的表现略好于基于网格的方法，而在坡向计算中则略逊于基于网格的方法。在这三种方法中，基于 TIN 分面的方法对错误最为敏感。基于TIN顶点的方法可以为基于点云的坡度和坡向计算提供参考。实际地形案例的误差分析表明，基于 TIN 顶点的方法在坡度计算中的表现略好于基于网格的方法，而在坡向计算中则略逊于基于网格的方法。在这三种方法中，基于 TIN 分面的方法对错误最为敏感。基于TIN顶点的方法可以为基于点云的坡度和坡向计算提供参考。