Borbin the 🐱

The most common Panotools projections are Equirectangular to make interactive 360°×180° panoramas and Rectilinear to fix distortions of photos. But what about the others? With a small Field of View (FoV) the difference is not 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°×180° (full sphere) panoramic images. Vertical lines and the center horizontal line are preserved.

Equirectangular 360°×180° Example

Interactive Panorama Example

Circular

Fish eye projection.

Fullframe

Fish eye projection with limited Field of View.

Little Planet

Use this to complement a 360°×180° Equirectangular panorama!

Mercator

Similar to the Cylindric projection, but with less vertical stretching.

Vedutismo

Diagonal lines through the center are preserved.

All Transverse projections are rotated 90° and can map the vertical to a 360° Field of View.

Transverse Cylindrical

Cylindrical rotated 90°

Transverse Equirectangular

Equirectangular rotated 90°

Transverse Mercator

Mercator rotated 90°

Transverse Vedutismo

Vedutismo rotated 90°

See also The Balcony Panorama, Panotools projections example, Stereographic projection and Use Case for Transverse Mercator Projection ✅.

Westin Maui Resort, Ka'anapali, Strand und Pool.

Interactive Panorama Ka'anapali Beach

Interactive Panorama Ka'anapali Beach bei Sonnenuntergang

Interactive Panorama Westin Maui Resort Pool, Ka'anapali

Jeder kennt den Vollmond, aber gestern Nacht zeigte sich ein besonderes astronomisches Ereignis, als der zurückhaltende Halbmond aus seinem Versteck hinter den Bäumen hervortrat. Nach kurzer Zeit verschwand er wieder und es bleibt offen wann wir ihn wieder sehen werden.

Everyone knows the full moon, but last night a special astronomical event took place when the restrained crescent moon emerged from its hiding place behind the trees. After a short time he disappeared again and it remains open when we will see him again.

NIKON Z30, 18-140mm f/3,5-6,3 VR
1/30s f/6,3 ISO 2500 f=140mm/210mm

The TTArtisan 7.5mm f/2.0 is a manual focus full frame fisheye lens for APS-C cameras or a circular fisheye lens for full frame cameras. This lens has been used for all my Panoramas since Summer 2023.
The lens is remarkably sharp wide open and has an optimal Aperture of f/5.6 and much better compared to the 7Artisans 7.5mm f/2.8.

Best setting for 360°×180° Panoramas is at 0.5m(2ft) and f/5.6. This puts everything from near to infinity in focus:

A downside is the lens cap, which relies on friction from an inner fabric lining and can easily get lost.

Update

A set of 'Rubber Bands, Assorted Sizes' actually fixed the problem. Size #94 (3.15" × 0.75") works best, especially when glued in place with a contact cement adhesive.

1/640s f/5.6 ISO 100
See matching Panorama

1:1 (not sharpened)

enlarged (from the panorama picture)

See also
Laowa 4mm f/2.8 Fisheye Lens
AstrHori 6.5mm f/2.0 Fisheye Lens