Demo of Customizable Wagner ESP using d3-geo

Projections with equally spaced parallels (along the central meridian)


Rendered with:
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):

– 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:

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!


Source code of this page released under the GNU General Public License, version 3.

SVG files: All generated SVG images that are generated on this page are in the public domain. You may use the images in any manner, including modifying the content and design, electronic dissemination, and offset printing. The author of this site, Tobias Jung, renounces all financial claim to the data and invites you to use it for personal, educational, and commercial purposes.
No permission is needed to use the SVG files. Crediting the author is unnecessary. However, if you wish to cite the data source, simply use: Tobias Jung, Home · Legal Disclosure · Privacy Policy