Alternate projections: images derived from 360° panoramas. Below each 360°x180° equirectangular master image (click for an interactive version) are thumbnails of various projections showing all or part of the original in a variety of projection schemes.
See Panoramas and Projections at the foot of this page for notes on some of these alternate projections.
Palazzo Abatellis, Palermo | Room II
Triptych |
Hammer |
Magnipolar |
İsa Bey Mosque | Selçuk, Turkey
Circular fisheye |
Mirror ball |
Reuleaux 8 |
Hilandar monastery | Naos of the katholikon
Cylindrical |
Orthographic |
Pierce Quincunx |
Gus Fisher Gallery | El-Jay exhibition
Polar |
Panini |
Lagrange plus |
Outside the Church of Santa Maria dei Greci, Agrigento, Sicily
Hyperbolic |
Lagrange |
Mollweide |
Side-aisle of the duomo, Syracuse, Sicily
Horizontal cross |
Stereographic |
Balloon |
Panoramas can also be projected onto three-dimensional geometry, such as the five polyhedra known as the Platonic solids. Click the thumbnails below for stills and interactive 3D versions using a panorama of the interior of the Pantheon, Rome.
Interior of the Pantheon, Rome
Tetrahedron |
Cube |
Octahedron |
Dodecahedron |
Icosahedron |
The interactive panoramas in the 360° panoramas section present their scenes in 'normal' rectilinear perspective (where all straight lines are preserved: any line that is straight in the world, appears straight in the panorama). The original panoramic images from which these views are derived encompass 360° horizontally, and - where the zenith and nadir of a scene are included - 180° vertically.
To present such images in their entirety, rectilinear perspective fails - once the angle of view exceeds about 120° other solutions are needed and (as cartographers discovered long before the invention of photography) all such projections involve compromises producing varying amounts of distortion. (Indeed, even rectilinear perspective produces distortion, most evident when using wide-angle lenses.)
Below are examples of a few selected projections (based on a panorama at the Temple of Poseidon, Paestum).
Equirectangular (sometimes termed plate carrée) projection: the basis for spherical panoramas such as some of the interactive examples in the panoramas section as well as for the various derived images below; 360° horizontally x 180° vertically; as with cylindrical and mercator projections (roughly similar, but with limited vertical fields-of-view) only vertical lines and the horizon line are projected as straight lines in this projection, with all other lines curved. Distortion is minimal near the 'equator' but increases dramatically toward the 'poles' (top and bottom).
Rectilinear projection: a wide-angle 24mm lens (35mm equivalent/full-frame DSLR sensor). Horizontal angle of view: 74°
Rectilinear: a 14mm lens; about as far as rectilinear perspective can be pushed before the already heavy distortion at the periphery of an image becomes just too grotesque.
Circular or Fisheye projection: an 8mm fisheye lens; circular field of 180°
Mirror ball: the scene as if reflected from a mirror-surfaced sphere. Reflective spheres (such as Christmas tree baubles for instance) have the interesting property of reflecting very nearly the entire 360-degree scene around them (a much greater coverage than a fisheye lens). Those parts of the scene near the periphery are highly compressed, but can be seen more clearly by digitally 'unwrapping' or re-projecting the image. See the 360° Objects section for an interactive (rotating) version of a mirror ball image.
Panini projection: a recently 're-discovered' projection assumed to have been used by 18th century Veduta painters to portray extremely wide fields-of-view; diagonal straight lines through the centre of the image remain straight in this projection (as do vertical lines). This example has a HAoV of about 147° (far wider than possible with say the 14mm lens example above) with a not-too-objectionable bending of non-vanishing-point/non-vertical straight lines. For more on this see this New Scientist article.
Cylindrical projection with the scene's zenith at centre (rotated and cropped).
Mollweide projection: this shows the entire 360° x 180° scene as a 2:1 wide ellipse with parallel lines of latitude. Often used to display all-sky astronomical maps or other such imagery.
Horizontal Cross projection: a cube unfolded to reveal its six interior faces. Each face is a 90° x 90° rectilinear projection. A viewer at the centre of such a cube would see a 360° x 180° panoramic image in the same way as the interactive versions in the panoramas section are displayed.
'Little Planet' projection: a stereographic projection with the scene's nadir at centre. Lots of fun.