arXiv:2611.12894v1 Announce Type: cross Abstract: Satellite altimetry samples ice sheets densely along tracks but sparsely across tracks, with frequent gaps in spatial coverage. We study the impact of this irregular support on surface reconstruction and introduce a new method, D-TIN, that applies Delaunay triangulation and barycentric interpolation directly to observed locations. A spatial holdout removes contiguous track intervals and nearby same-pass observations. We compare D-TIN with two common workflows, kriging and tile-based polynomial interpolation, to evaluate its accuracy and computational efficiency. Across seven ICESat-1 campaigns, D-TIN reduces RMSE by 12.1 m to 23.6 m relative to independent 5 km tile and polynomial based reconstruction. Its aggregate accuracy is close to the ordinary kriging workflow using a 1 km grid on the commonly used GStatSim platform while its median runtime is 252 times lower. A fixed-weight multiscale extension of D-TIN, called MS-D-TIN, gives the lowest aggregate RMSE, 67.5 m, while retaining the low computational cost of the D-TIN family.