Extreme Fisheye Projections
and Stereographic Projections (Little Planet)

Fisheye images are generally created with a 180 degree field of view, that is, the view with a hemisphere as the projection surface. However, the mathematics that describes a fisheye can extend the angles to 360 (actually even further than that but it results in a space replication). The images below are the result of creating a fisheye projection with the camera looking straight down and the fisheye angle is 360 degrees. The result is strangely compelling, they can appear to be a planet on which extreme structures have been built.

Corresponding raw spherical panoramic image

The images here are captured using a 185 degree fisheye lens on a SLR camera. Three images are captured each with the camera/lens rotated 120 degrees horizontally with respect to the other images. These three fisheye images are stitched together to form a 360 degree by 180 degree spherical projection. This image (also linked to for each example) is then resampled to a 360 degree fisheye using locally developed software, namely sphere2fish.

Corresponding raw spherical panoramic image

There are some extreme distortions occurring, for example, the entire rim of the image is in fact a single point corresponding to the north pole.

Corresponding raw spherical panoramic image

The images here are all from the University of Western Australia. The first is the South side of Hackett hall, the second the North side, the last is the Reid Library.

Another technique that gives similar results, but perhaps more striking, uses stereographic projections. Corresponding stereographic projections given below.

The utility that creates these converts spherical projections into stereographic projections. The main variable is the size of the projection radius (-t).

Usage: sphere2stereo [options] sphereimage
Options
   -w n       width and height of the stereographic image, default = 512
   -t n       stereographic radius, default = 4
   -a n       antialiasing level, default = 2
   -o s       output file name, name derived from input filename

A stereographic projection can be visualiased as a sphere, a line is drawn from the north pole to each point on the sphere surface, for example P₁ and P₂. Where that line intersects a plane that touches the south pole, is the position of the point on the stereographic projection plane, for example P'₁ and P'₂.

Rotomahana, New Zealand