Stereographic projections of panoramic views are becoming quite commonplace and can be impressive; despite this, they are not difficult to make. This illustrated tutorial shows how to do it.
You will need Photoshop and (usually) a 360x180° panoramic image.
Conventionally, Little Planet views use as their source a 360 x 180° panoramic view which is twice as wide as it is high. The reason for this is that the left edge of this type of image will always merge seamlessly with the right edge. If they didn't, the finished result would have an obvious seam.
For me the interesting thing was realising that the main requirement is not for a strictly panoramic image: any shape will do, as long as the left edge will merge with the right edge without leaving an obvious seam running radially from the center of the picture. Interesting and often unexpected results can be obtained using images of this type. I'll illustrate this by using examples of both types of image.
The first step is to make the picture square. In Photoshop, go to Image size (Command-I, PC ctrl-I). Make sure that "Constrain proportions" is DESELECTED, because the proportions are going to be altered.
Note the figure in the Height box: type this into the Width box and press Return.
Now both examples are square.
Now the picture must be rotated 180°: Image > Image rotation > 180°:
Apply Polar>Rectangular transformation: Filter > Distort > Polar coordinates... using Rectangular to polar. The zoom level has been adjusted so all of the 'planet' is visible:
Crop and/or rotate to taste, and there is the result!
If you use my technique please mention my name and include a reference to my web site: "http://www.brianwatsonphoto.co.uk".