Are there ways to improve processing time for TIN interpolation?

I'm using TIN interpolation as a step in a larger process. The interpolation step is taking a very long time (10+ hours to a few days), and I often end up with missing areas (see example below).
I'm only using ~2000 input points. My output raster is a 1m elevation raster grid covering about 25km x 5km so ~125 million cells. Output raster needs to match the resolution of another layer, so I can't just reduce the resolution.

The input values are essentially coming from elevation contours along a valley slope, but the valleys I'm working with are fairly steep, with frequent gradient changes - there is some room to use sparser input data, but I suspect not enough to cut processing time down to a few hours.

I've tried dividing the data into smaller blocks, but this doesn't seem to save any real time over processing it as a block. It does help with the missing data issues, however.

I've tried saving the output as both memory layers and on disk as a TIF, this doesn't seem to affect the processing time.

I'm using QGIS 3.8.3, have also tried on the LTR (3.4.12). I'm also open to a solution in R, as I use it for other steps in the process, but haven't found a TIN interpolation algorithm in R. I prefer the TIN algorithm to IDW or kriging because of how it respects the input contours and goes through known points.

Image with output raster missing an area. I assume that the missing area is the result of my computer running out of resources during the processing.
enter image description here

  • Ah, yes but the resulting triangular facets smooth the spatial structure of the data. TIN's should be used when the spatial process is unknown. I have found that objective spines work best for this type of interpolation. That said, for Delaunay triangulation try the deldir function in the deldir R package. There is also delaunay in spacestat and triangulate in RTriangle. – Jeffrey Evans Oct 25 '19 at 18:33
  • @JeffreyEvans can you explain what you mean by smoothing out the spatial structure? Doesn't any interpolation smooth out the data to some extent? And my understanding is that splines (at least the thin plate splines I've used) creates a smoother surface than TIN/Delaunay triangulation. – Brian Fisher Oct 25 '19 at 18:46
  • Yes, any interpolator can smooth the data but, the term "smooth" is subjective and can be addressed by choosing an appropriate statistic. I have found that TIN's produce less than ideal surfaces in representing elevation, specifically for geomorphometric applications. Objective is the operative term when using splines. A adaptation of TPS has been proven to be effective with high density point data by Evans & Hudak (2007) and Mitasova et al., (2005) as well as demonstrating TIN's tendency of eroding hillslopes while returning exact values of the point data, akin to overfit. – Jeffrey Evans Oct 25 '19 at 19:20

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