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It would provide a fast, grid-like interpolation for any 2D data: think geospatial, GIS, etc. If I understand correctly, could also be used recursively to provide a lazy (but inefficient) way to calculate locations to an arbitrary precision.

Reminds me of topojson[0], a GeoJSON extension, that encodes features as topologies, instead of geometries.

[0]: https://github.com/topojson

Meshes are used in various kinds of simulation calculations: https://en.wikipedia.org/wiki/Finite_element_method ; there's also discrete exterior calculus: http://brickisland.net/cs177fa12/?cat=5

"various" is a crazy simplification: the propogation of radiation (think modeling wifi antenna output, on-chip photonic components, etc.), thermal properties of various electrical objects (think like exact temerature distribution across a resistor, heat distribution around a CPU, jet engines), modelling various materials for mechanical sturdiness and springiness, fluid modelling (the weather, aerodynamicity, etc.).

The list is huge!

mapping and path planning in robotics comes to mind