Generation of an optimal triangulated irregular network for topographic surface via optimal transport theory

A digital elevation model (DEM) is widely recognized as the most effective digital representation of the Earth’s surface and serves as the fundamental platform for simulating various Earth systems. Extensive efforts have been devoted to exploring methods for generating high-fidelity DEM datasets that are computationally efficient for diverse applications. However, the existing methods do not guarantee the optimal digital representation of the Earth’s surface. This study proposed a novel curvature-based geodesic centroidal Voronoi tessellation method for generating a topographic triangulated irregular network (TIN) DEM based on optimal transport theory. This study is the first to present a globally optimized digital representation of the Earth’s surface with a predetermined number of vertices, which is crucial for computational feasibility. This study achieves the optimal TIN by measuring mean curvature and introducing geodesic distances on the topographic surface. Representative vertices that best adapt to the topography are identified through an optimal surface approximation process. Experimental results confirm that the proposed method effectively generates the optimal digital representation of the topographic surface with the lowest elevation errors and minimal deviations from the original topographic features. By generating optimal TIN DEM with any desired number of vertices, the proposed method not only balances high-precision representation and computational efficiency but also offers a novel approach to deepening the understanding of topographic structures. Furthermore, it provides an effective solution for compressing extensive topographic data and facilitating multiscale representation of the Earth’s surface.

数字高程模型（Digital Elevation Model, DEM）是目前公认的最具效力的地球表面数字化表征方式，亦是支撑各类地球系统模拟的基础平台。学界已投入大量精力探索可兼顾计算效率与多场景应用需求的高保真DEM数据集生成方法。然而，现有方法无法保证实现地球表面的最优数字化表征。本研究提出了一种基于曲率的测地质心Voronoi剖分方法，可基于最优传输理论生成地形不规则三角网（triangulated irregular network, TIN）型DEM。本研究首次实现了基于固定顶点数量的全局优化地球表面数字化表征，这对保障计算可行性至关重要。本研究通过测算地形表面的平均曲率并引入测地距离，依托最优地表近似流程筛选出最适配地形特征的代表性顶点，以此构建最优不规则三角网。实验结果表明，所提方法可有效生成地形表面的最优数字化表征，其高程误差最低且与原始地形特征的偏差最小。通过自定义顶点数量生成最优TIN型DEM，本方法既兼顾了高精度表征与计算效率，也为深化地形结构认知提供了全新路径。此外，该方法可为海量地形数据压缩及实现地球表面多尺度表征提供有效解决方案。