Unprojected Coordinate Systems Long Term

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Explore adding support for more functions to be used in unprojected coordinate systems.

raster::terrain (terrain.R, terrain.cpp) uses haversine distance and ArcPro Surface Parameters uses a 3D Earth Centered, Earth Fixed coordinate system.

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From Guth and Kane, 2021 - "MICRODEM uses the geodetic formulas from Vincenty (1975). GRASS uses the 1970 geodesic code from the U.S. Naval Oceanographic Office (GRASS, n.d.), and ArcGIS does not specify what formulas it uses. Alternative geodesic algorithms like those of Karney (2013) could also be used... Vincenty (1975) formulas allow calculation of the grid rotation, so that the aspects from the algorithm can be converted to true north relatively easily, and all aspects in the GIS software can be referenced to true north."

GRASS. (n.d.). GRASS GIS 7 programmer’s manual.

Karney, C.F.F., 2013. Algorithms for geodesics. J Geod 87, 43–55. https://doi.org/10.1007/s00190-012-0578-z

Guth, P., Kane, M., 2021. Slope, aspect, and hillshade algorithms for non-square digital elevation models. Transactions in GIS 25, 2309–2332. https://doi.org/10.1111/tgis.12852

Vincenty, T., 1975. Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations. Survey Review 23, 88–93. https://doi.org/10.1179/sre.1975.23.176.88

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As an intermediate step can also use a "Z-factor"

https://pro.arcgis.com/en/pro-app/latest/tool-reference/3d-analyst/applying-a-z-factor.htm

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Karney equations implemented in geosphere package

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Also see Florinsky (2016) section 4.3 on the "Calculation of Local Morphometric Variables on a Spheroidal Equal Angular Grid" and Florinsky (2017).

Florinsky, I.V., 2016. Digital terrain analysis in soil science and geology, 2nd ed. Elsevier/Academic Press, Amsterdam.

Florinsky, I.V., 2017. Spheroidal equal angular DEMs: The specificity of morphometric treatment. Transactions in GIS 21, 1115–1129. https://doi.org/10.1111/tgis.12269