Smooth digital terrain modelling in irregular domain using adaptive finite element thin plate spline smoother

Digital terrain models of geological information occasionally require smooth data in domains with complex irregular boundaries due to its data distribution. Traditional thin plate splines produce visually pleasing surfaces, but they are too computationally expensive for data of large sizes. Finite element thin plate spline smoother (TPSFEM) is an alternative that uses first-order finite elements to efficiently interpolate and smooth large data sets. Previous studies focused on regular square domains, which are insufficient for real-world applications. This article builds on prior work and investigates the performance of the TPSFEM and adaptive mesh refinement for real-world data sets in irregular domains. The Dirichlet boundaries are approximated using the thin plate spline and data-dependent weights are applied to prevent over-refinement near boundaries. Three geological surveys (aerial, terrestrial and bathymetric) with distinct data distribution patterns were tested in the numerical experiments. We found that irregular domains with adaptive mesh refinement significantly improve the efficiency of the interpolation. While the inconsistency in approximated boundary conditions, we may prevent it using additional constraints like weights. This finding is also applicable to other finite element-based smoothers.