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annex-b: Corrected mention that ISEA preserves angles and distance
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(it does not)
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jerstlouis committed Sep 20, 2024
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Expand Up @@ -38,7 +38,7 @@ The following example JSON DGGRS definitions conform to this schema.
The following DGGRS is for an axis-aligned and equal-area DGGH based on the https://doi.org/10.3138/27H7-8K88-4882-1752[Icosahedral Snyder Equal-Area (ISEA)] planar projection (see https://proj.org/en/9.4/operations/projections/isea.html[PROJ] and https://github.com/mocnik-science/geogrid/blob/master/src/main/java/org/giscience/utils/geogrid/projections/ISEAProjection.java[geogrid] for open-source implementations) using rhombuses with a refinement ratio of 9.
When the ISEA projection is rotated 60 degrees, sheared horizontally by 30 degrees and units are mapped to a 5x6 space, the zones become square and their edges are aligned with the CRS axes, while remaining equal area.
A https://docs.ogc.org/is/17-083r4/17-083r4.html[2D Tile Matrix Set] can also be defined in this transformed CRS, allowing for compatibility with https://docs.ogc.org/is/20-057/20-057.html[OGC API - Tiles], https://portal.ogc.org/files/?artifact_id=35326[WMTS] and traditional client and visualization software with no built-in DGGS functionality.
This transformed CRS no longer preserves angles and distances, although the topology, indexing, and surface geometry on the Earth model remains the same as in the original ISEA CRS where angles and distances are preserved.
This transformed CRS distorts angles and distances more than the planar ISEA projection, but the topology, indexing, and surface geometry on the Earth model remains the same as in that planar ISEA projection.

While the ISEA projection is defined for an authalic sphere, this DGGRS assumes that when importing or exporting data referenced to the WGS84 ellipsoid a conversion between geodetic and authalic latitude is performed.
This guarantees that all zones are exactly the same area on the surface of the ellipsoid.
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