Panoramas are an exciting creative application of photography and recently, of computing. Panoramas offer a unique, immersive perspective to the viewer. To the photographer, panoramas present an interesting artistic and technical challenge.
Panoramas come in different shapes and flavours, so let's set a definition. A dictionary tells us a panorama is "a picture (or series of pictures) representing a continuous scene". This continuous scene can come straight from a (special) camera or it can be assembled from multiple images using the panorama tools.
Technically three different types of panoramas are distinguished
A partial Panorama is an image created from assembling together 2 or more images to create a single wide angle image. Partial panoramas are created in exactly the same was as full spherical panoramas, but cover only a fraction of the view sphere (less than 360 degrees in longitude around the horizon, and/or less than 180 degrees in latitude). Example partial panos include Max Lyon's GigaPixel image, created with 196 source images! Partial panoramas are often printed, whereas full spherical panoramas are more often viewed online with special panorama viewers.
Immersive panoramas are panoramas that allow you to look everywhere around you, including straight up and straight down. Immersive panoramas come in two subflavors, spherical and cubic ones. (this needs text, guys)
Representing a spherical view of the world on a flat computer monitor or print requires some manner of mapping from the 3D sphere in which the camera and viewer are embedded to 2D. The techniques used for mapping are of exactly the same type long used by map makers to project the entire globe, or portions of it, onto two dimensional maps. There is no single, unique projection for representing sections of the sphere on the globe. Instead, all projections have various attributes and limitations. There are many classes of projections used for various purposes (e.g. Mathword's Project Page), but only a few are traditionally used for panoramic imaging.
Some of the most common projections when working with Panoramic imaging are:
Spherical/ Equirectangular projection
Also called the "non projection", this is a representation of the sphere which maps longitude is mapped directly to the horizontal coordinate, and longitude is mapped to the vertical. This projection is often used for source images in panoramic viewers like PTViewer. See definition for Equirectangular Projection for more.
This is the projection most commonly used for printed panoramas with large ranges of longitude. It can be envisioned by imagining wrapping a flat piece of paper around the sphere tangent to the equator, and projecting a light out from the center of the sphere. A full range of longitude, up to 360 degrees, can be represented with a cylindrical projection, but near the poles, the images become very distorted. See Cylindrical Projection for more.
This is a fundamental projection which can be envisioned by imagining placing a flat piece of paper tangent to a sphere and projecting a light out from its center. Obviously, only a maximum of 180 degrees of longitude can be represented with this projection, and practically far less. Most non-fisheye cameras produce a nearly rectilinear image over their field of view. The Rectilinear projection is often used for prints of panoramas which cover less than ~120 degrees of longitude, since straight lines are preserved. See Rectilinear Projection for more.