How to translate MKT expression to D3 options on Albers projection?

Question

This is the standard MKT expression (here also translated to Proj.4 string) of Albers conicEqualArea for official Statistical Grid of Brazil:

PROJCS["Conica_Equivalente_de_Albers_Brasil",
    GEOGCS["GCS_SIRGAS2000",
        DATUM["D_SIRGAS2000",
            SPHEROID["Geodetic_Reference_System_of_1980",6378137,298.2572221009113]],
        PRIMEM["Greenwich",0],
        UNIT["Degree",0.017453292519943295]],
    PROJECTION["Albers"],
    PARAMETER["standard_parallel_1",-2],
    PARAMETER["standard_parallel_2",-22],
    PARAMETER["latitude_of_origin",-12],
    PARAMETER["central_meridian",-54],
    PARAMETER["false_easting",5000000],
    PARAMETER["false_northing",10000000],
    UNIT["Meter",1]]

The DATUM is the WGS 84 ("SIRGAS2000" is a alias for it).

How to translate all details to the D3.js v5 parametrization?

I try the obvious, as center and parallels, but it was not sufficient

var projection = d3.geoConicEqualArea()
  .parallels([-2,-22])  // IS IT?
  .scale(815)
  //.rotate([??,??]) // HERE THE PROBLEM... 
  .center([-54, -12])  // IS IT?

PS: where the D3 documentation for it? The D3 source-code of geoConicEqualArea() have no clues.

There is no official documentation that speaks specifically to creating a D3 projection from a projection definition. — Andrew Reid, Oct 28 '19 at 15:10

Andrew Reid · Accepted Answer · 2019-10-28T21:09:29.427

1

The parts that translate to a d3 Albers projection are as follows:

    PROJECTION["Albers"],
    PARAMETER["standard_parallel_1",-2],
    PARAMETER["standard_parallel_2",-22],
    PARAMETER["latitude_of_origin",-12],
    PARAMETER["central_meridian",-54],

You have the parallels, now you need to rotate. Also note, for any D3 projection, the rotation is applied to the centering coordinates. Generally, you'll want to rotate on the x and center on the y:

d3.geoAlbers()
 .parallels([-2,-22])
 .center([0,-12])
 .rotate([54,0])
 .translate([width/2,height/2])
 .scale(k)

I've rotated in the opposite direction along the x axis (rotated the earth under me so that I'm overtop of the central meridian, hence my rotation by -x). I've then centered on the y. Lastly I translate so that the intersection of the central longitude and meridian is centered in the map and apply a scale value that is appropriate.

If I want to center on a different area but keep the projection the same, I can modify projection.center(), but keep in mind that the coordinates provided here are relative to the rotation. I can also use projection.fitSize() or projection.fitExtent(), both of which set 'translate' and 'scale' values for the projection. None of center/scale/translate change the distortion in the D3 projection.

Of course this isn't a true replication of your projection as the coordinate space units are pixels, you will remain unable to measure distances in meters directly without some extra work.

See also

edited Oct 28 '19 at 21:09

answered Oct 28 '19 at 15:08

Andrew Reid

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Important to remember that [`d3.geoAlbers()`](https://github.com/d3/d3-geo/blob/master/src/projection/albers.js) is an alias for `geoConicEqualArea()`, is it? – Peter Krauss Oct 28 '19 at 17:01
I am [implementing an illustration here as open gist](https://bl.ocks.org/ppKrauss/raw/e6c12bf84e732ca4cbf0694808619cad/)... My aim is to compare maps in "Mercator vs Albers" and make sense to use your suggestion of `projection.fitExtent()`, but I not see how to fit both in the same scale, center and area... It is possible? – Peter Krauss Oct 28 '19 at 20:58
Not sure if I follow - you want to use fitSize/fitExtent to replicate the visual in the link? – Andrew Reid Oct 28 '19 at 21:21
Yes, use it as more precise and *automatic fit* to the box/grid, turning the figures more comparable... I can post another question if you prefere. – Peter Krauss Oct 28 '19 at 23:05
I could mock something up this evening (a bit busy for the immediate future) - though as long as projection type, rotation, and parallels (if applicable) are set, then fitSize/fitExtent on each projection will set projection translate and scale appropriately (center does not matter: center/translate are both shifts - one in degrees prior to projection, the other in pixels after projection). – Andrew Reid Oct 28 '19 at 23:44
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Something like [this](https://bl.ocks.org/Andrew-Reid/0ebddf4724a1658e43da01a5feff859b)? – Andrew Reid Oct 29 '19 at 02:52

How to translate MKT expression to D3 options on Albers projection?

1 Answers1