Inverse Icosahedral Snyder Equal Area (ISEA) Projection

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Inverse Icosahedral Snyder Equal Area (ISEA) Projection

Sirdeshmukh, Neeraj



I am trying to implement the inverse ISEA projection documented in:


An Equal-Area Map Projection For Polyhedral Globes, John Snyder, October 1992

Cartographica The International Journal for Geographic Information and Geovisualization 29(1):10-21


For the purposes of my current project, I extended the code for the forward Snyder ISEA projection found at to work with a rhombus-based Discrete Global Grid System (DGGS). I converted this from C to Python.

Now, I am trying to implement the inverse projection according to the description provided on page 14 of the above paper.

However, the problem is that the value for the spherical distance, z, is not getting properly calculated (it is about 0.5-2 units “off” from the value that results after using the forward ISEA formula for the same lat,long point). The azimuth Az, however, is getting properly calculated, and the only problem it seems is with the value of z. Therefore, the latitude and longitude of a point gets incorrectly calculated from the inverse, and is off by 50-100 kms from the true location.  I am attaching the main part of the Python code to this email, and it uses the same constants defined in the forward projection code.

If anyone can provide some guidance as to where I am going wrong, or what the problem could be, I would greatly appreciate it.  If any additional information is needed, please let me know.


Neeraj Sirdeshmukh

Student, Delft University Of Technology




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