What Are Little Planet Projections?
We’ve seen these wonderful forms of photographic manipulation many times before on APOD, but how are they done?
Little planets are created by applying a stereographic projection to a spherical panorama. It is possible to seamlessly move from a birds-eye view in the sky to that of a bug on the ground!
To generate these images we start with a spherical (equirectangular) panorama. This is an image where the x-axis corresponds to the longitude around a sphere (0-360 degrees) and the y-axis is the latitude (-90 to 90 degrees).
For any longitude or latitude position on a sphere we can retrieve the colour directly from the corresponding x,y coordinates on the panorama image. A proper equirectangular panorama should be twice as wide as tall, e.g. 1024x512 pixels.
Stereographic projection is a mapping that projects a sphere onto a plane, as illustrated with the world map below. It is conformal, which means that it preserves angles locally (note the grid lines still cross each other at right angles) although it doesn’t preserve areas or distances.
As we already have the colour of each longitude and latitude point on a sphere from the equirectangular panorama the inverse stereographic projection formulas are used, as described by Mathworld.
Want to give it a try? A few folks have already written tutorials on this emerging art form. You can check out a couple of these tutorials over at flickr here and here, but I’m sure there are many more on the web. Now go on and make a couple of little planets of your own!
Want to submit sky or astro photography to CWL? Head over to the submissions section. If you’ve got some of your own or generally favorite awesome photos you’d like to share with us.. Don’t be shy! If it’s awesome, best believe it will be posted.