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Digital terrain models (DTMs) are created using elevation data collected ingeological surveys using varied sampling techniques like airborne lidar anddepth soundings. This often leads to large data sets with differentdistribution patterns, which may require smooth data approximations inirregular domains with complex boundaries. The thin plate spline (TPS)interpolates scattered data and produces visually pleasing surfaces, but it istoo computationally expensive for large data sizes. The finite element thinplate spline (TPSFEM) possesses smoothing properties similar to those of theTPS and interpolates large data sets efficiently. This article investigates theperformance of the TPSFEM and adaptive mesh refinement in irregular domains.Boundary conditions are critical for the accuracy of the solution in domainswith arbitrary-shaped boundaries and are approximated using the TPS with asubset of sampled points. Numerical experiments are conducted on aerial,terrestrial and bathymetric surveys. It is shown that the TPSFEM works well insquare and irregular domains for modelling terrain surfaces and adaptiverefinement significantly improves its efficiency. A comparison of the TPSFEM,TPS and compactly supported radial basis functions indicates itscompetitiveness in terms of accuracy and costs.

Smooth digital terrain modelling in irregular domain using finite element thin plate splines and adaptive refinement