  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.
