Demo of Customizable Wagner VII/VIII using d3-geo

Customize Projection

Bounding Parallel (ψ₁ = 65)

0.5 90

Bounding Meridian (λ₁ = 60)

0.5 180

Areal Inflation at 60° N/S (S₆₀ = 0)

0 99

Axial Ratio (p = 200)

50 500

Customize Map

scale (140)

0 400

rotate (λ) (0)

-180 180

rotate (φ) (0)

-180 180

rotate (γ) (0)

-180 180

graticule spacing (10)

0 45

Customize Map Position

center (lon) (0)

-180 180

center (lat) (0)

-90 90

translate (x) (480)

0 960

translate (y) (250)

0 500

Rendered with:
d3.geoWagner().poleline(65).parallels(60).inflation(0).ratio(200)
Böhm Notation of current configuration: 65-60-60-0-200(Wagner VII)

Share the current configuration:

Only the projection parameters and the scale will be shared, no other values from the Customize Map or Position sections. There’s no technical reason for this, I’m just lazy. Sorry!

Final values that get passed to Wagner’s formula and can be applied in Geocart (here, rounded to 6 decimals):
a = b = m1 = m2 = n =

Final values as a single string (more convenient for sharing):

(In the nomenclature of the d3 script: a = cx,   b = cy)

Note:
With ψ₁ = 0 or λ₁ = 0 there was a bug in converting to Geocart parameters. So for the moment, I’ve simply set to minimum to 0.5. I guess usually you will not want the 0’s anyway – however, if you do want them, open the current configuration in the WVG (see link below), set the parameters to 0 there and copy the resulting parameters to Geocart. That’ll work.

Open this configuration in the Wagner Variations Generator (WVG-7) (which will give you a few more options, but doesn’t update the map on-the-fly).

Return to default configuration by reloading this page.

When Karlheinz Wagner presented the equal-area projection nowadays known as Wagner VII in 1941, he explicitly allowed for customization in regards of changing the pole line length, the curvature of the parallels, and the aspect ration of the axis. And when added the compromise projection known as Wagner VIII in 1949, he introduced an additional parameter to control the amount of areal inflation.

Use the sliders in the section Customize Projection to play with Wagner’s configuration parameters and see what the results look like.
The sections Customize Map and Customize Map Position have been added for convenience and might be helpful or simply interesting to modify; they are not part of Wagner’s transformation method.
Note: This demo works with half integer values only, but in fact, the formula allows all fractional numbers. To use these, try the WVG-7.

For more information about Wagner’s transformation method, read this blogpost or the notes at the WVG-7 or the article Das Umbeziffern – The Wagner Transformation Method.
For the d3 script source code used to render this projection, see the static examples.

This page utilizes code taken from d3indepth’s Projection explorer, thanks for sharing!