This is the first in a subseries of Maths in Art where I will look at some fantastic warped panoramas and make reference to the mathematics behind it.
The image above may look like an eclipse with a strange planet, but it started out as a 360° panorama and has been wrapped around into a circle.
In maths we call this a polar transformation, it takes something in Cartesian coordinates ( ‘up & down ‘ and ‘left & right’ ) to polar coordinates. In these new coordinates a horizontal line, such as the horizon, is mapped to a circle but vertical lines remain straight, such as trees and the sides of buildings.
A computer program such as Photoshop can change an image by taking a pixel in Cartesian coordinates to a new location in polar coordinates. There are other types of coordinates which would map the image differently and we will see them in later posts.
Stitching the images is a lot harder than one would imagine, the continuity in clouds is particularly impressive. On his site Jerome talks viewers through the process.
In addition to swinging 360° around the landscape the details further from the horizon such as sky and the grass beneath the photographers feet need to be captured to.
This image is particularly interesting as a planet seems to grow out of the palm leaves. In the same way perspective makes closer things apear bigger normally the closer an object is to the camera the taller it becomes.
I’m not normally a fan of extreme texturing (like you see on Instagram filters) but for these fantasy planets it seems fitting and works well and enhances the space-esque feel.
You can view Jerome’s website panoplanets.com to get a more detailed explanation to make your own. You can view all his planets here. You can follow me here on WordPress or Facebook to get updates about future posts.