Panotools projections

19 February, 2024

The most common Panotools projections are Equirectangular to make interactive 360°x180° panoramas and Rectilinear to fix distortions of photos. But what about the others? With a small Field of View (FoV) the difference isn't that obvious, but with a large Field of View things change quite a bit.

Imagine yourself standing in front of a large object and try to take a photo. Using a wide angle lens will get you visible distortions once you go above 100° FoV because of the Rectilinear projection. Here is where the other projections come into place to map large Field of View objects to a print.

This is an example of an extreme Field of View, standing right in front of a Ferris Wheel

and taking several pictures using a 24mm lens:

There is no perfect print projection for this, but depending on the purpose, one of the Panotools projections supported by PTGui might do the trick. On the other hand, using an interactive panoramic viewer working off an Equirectangular projection will render a Rectilinear output in the viewer window. Close to perfect as possible, but not printable as one complete unit.

Here is a list of the projections and their appearance for extreme FoV.

Stereographic

Projection of a sphere to a plane. Angles are preserved, but distances and figures are distorted.

Rectilinear

The projection of a standard camera lens and has progressive visible distortion for increasing Field of View. Vertical and horizontal lines are preserved.

Cylindrical

The vertical projection is rectilinear and therefore has the same limitations as the Rectilinear projection for the vertical field of view. The horizontal projection is linear and perfectly suited for a 360° view. Nothing is distorted from left to right (horizontally), but from bottom to top (vertically). Vertical lines and the center horizontal line are preserved.

Equirectangular

Similar to the Cylindric projection, but the vertical projection maps the 180° FoV and is used for 360°x180° (full sphere) panoramic images. Vertical lines and the center horizontal line are preserved.