If I wanted to interpolate points along a Great Circle Arc, it makes sense that either endpoint of the Great Circle is a satisfactory starting place. Next, I suppose I'll need a projection to preserve distances along the Great Circle. Unless someone corrects me, I think an Azimuthal Equidistant projection centered on either endpoint of the Great Circle would work.
From Wikipedia, with respect to an Azimuthal Equidistant projection "all points on the map are at proportionately correct distances from the center point", and additionally, it's "useful for showing airline distances from [the] center point of projection".
I suspect I can implement the Azimuthal Equidistant in Proj4js, but I've never really customized a projection before, so basically I'm just curious whether I'm doing it properly..
Now if I go to SpatialReference.org and search for Azimuthal Equidistant, I see both north and south pole-centered customizations of the projection. Respectively, they're implemented in Proj4js like so:
North Pole Azimuthal Equidistant:
Proj4js.defs["ESRI:102016"] = "+proj=aeqd +lat_0=90 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs";
South Pole Azimuthal Equidistant:
Proj4js.defs["ESRI:102019"] = "+proj=aeqd +lat_0=-90 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs";
It follows that the only value changing in either projection is the latitude, itself, +lat_0=, which changes from 90 to -90. So I'm pretty sure I just need to set these +lat_0 and +lon_0 appropriately, and bingo–the Azimuthal Equidistant is properly defined.
So with all of this said..
Is this a valid way to define an Azimuthal Equidistant projection relative to a specific place, like Columbia, South Carolina? (Lon: -81.020742, Lat: 34.008654)
Proj4js.defs["CUSTOM:10001"] = "+proj=aeqd +lat_0=34.008654 +lon_0=-81.020742 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs";
I hate to ask such a Yes or No question, so please note the additional opportunity to remark on whether this is a wise choice of projection considering the scenario (interpolating points at fixed distances along a Great Circle Arc).
Best Answer
This looks ok. If you run into reprojecting problems, try the spherical version, as I explained here:
Manipulating Azimuthal Equidistant Projections in QGIS