Difference between revisions of "Rectilinear Projection"
(Link to cubic projection and main projection pages.) 
(Link to cubic projection and main projection pages.) 
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Revision as of 18:58, 6 April 2005
This is a type of projection for mapping a portion of the surface of a sphere to a flat image. It is also called the "gnomic", "gnomonic", or "tangentplane" projection, and can be envisioned by imagining placing a flat piece of paper tangent to a sphere at a single point, and illuminating the surface from the sphere's center. Mathworld's page has an example and describes the mathematics underlying this projection.
The is a fundamental projection in panoramic imaging, because most ordinary (nonfisheye) camera lenses produce an image very close to being rectilinear over their entire field of view. Pinhole cameras, in fact, provide exactly a tangentplane mapping of the sphere onto their detector planes, and most simple imaging systems (consumer cameras with nonfisheye lenses among them) approximate this quite well. Thus it is the most common source image projection for partial panoramas.
The rectilinear projection also has the fundamental property that straight lines in real 3D space are mapped to straight lines in the projected image. This property makes the rectilinear image very useful for printed panoramas which do not cover an excessively large range of longitude or latitude (e.g. <120 degrees). Many Panoramic Viewers which show only a portion of a scene at a time do so using the rectilinear projection (regardless of what projection the full sphere source image was in).
The Cubic Projection is a special subcase of the rectilinear projection, in which 90 by 90 degree rectilinear subprojections are made onto 6 faces of a cube.