Demo of Customizable Wagner ESP using d3-geo

Customize Projection

Modified Projection

Bounding Parallel (ψ₀ = 70)

0 90

Bounding Meridian* (λ₀ = 50)

0 180

Ratio (p = 200)

50 600

xfactor (a = 100)

10 400

*) The setting Bounding Meridian has no effect on projections with straight parallels!

Customize Map

scale (120)

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.geoWagnerEquallySpacedParallels().poleline(70).parallels(50).ratio(200).xfactor(100).parentProjection(9)
Böhm Notation of current configuration: 70-50-200-100 (Wagner IX)

Final values that get passed to Wagner’s formula (here, rounded to 6 decimals):
ca = cm = cn = cx = cy =

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

Notes:
– This demo works with half integer values only, but actually, fractional values are allowed for the four parameters
– Thus, the min value for ψ₁ and λ₁ is 1 here, while actually it just needs to be greater than zero, i.e. values like 0.001 work.
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. That’ll work.

Open this configuration in the Wagner Variations Generator (WVG-9) (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.
Render predefined projections:

• Wagner III (Approx.)
• Wagner VI (Approx.)
• Wagner IX
• Wagner IX.i
• van der Grinten IV
• American Polyconic
• Nicolosi “telophasic”
• Rectangular Polyconic
• Apianus II
• Francula I (Approximation, variant of Wagner III)
• Francula II (Approximation, variant of Wagner VI)
• Canters W06 (Approximation, variant of Wagner VI)
• Francula IV (Variant of Wagner IX)
• Francula XII (Variant of American Polyconic)
• Francula XIII (Variant of Wagner IX)
• Canters W09 (Approximation, variant of Wagner IX)

When Karlheinz Wagner presented the projection nowadays known as Wagner IX in 1949, he explicitly allowed for customization in regards of changing the pole line length, the curvature of the parallels, and the aspect ratio of the axis.

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 integer values only, but in fact, the formula allows fractional numbers, too. To use these, try the WVG-9.
Please note that you’ve got four parameters in the WVG-9, as opposed to three parameters here; I dropped one parameter because it’s actually not needed. For more information on that, refer to this blogpost (also available in German).

For general information about Wagner’s transformation method, read this blogpost or the notes at the WVG-9 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!