Add Quadrilateralized Spherical Cube (QSC) projection (patch attached).

[marlam]

The attached patch (which applies to SVN revision 2226, current as of 2012-07-13) adds support for the Quadrilateralized Spherical Cube (QSC) projection.

This projection is designed to be used with a cube model that subdivides the ellipsoid into six areas. The projection then maps each area to a square map (the corresponding cube side).

Such a cube model is very well suited for planetary-scale terrain rendering, as it allows quadtree-based data management.

A cube model can also use Gnomonic projection, but this introduces strong angle and area distortions. In contrast, QSC projection is an equal-area projection and at the same time introduces only limited angle distortions.

[marlam]

Software that uses this patch is now available at < http://ecm-planet.sourceforge.net/>.

[marlam]

To clarify: there seem to be two different projections under the name of "Quadrilateralized Spherical Cube".

The first one was proposed in (1) and is also known as the COBE QSC since it was used by the NASA Cosmic Background Explorer (COBE) project. It is an approximately equal-area projection.

The second one was proposed in (2), building on the work of (1). Unlike the COBE QSC, it is an exactly equal-area projection with a closed form expression.

This patch implements (2), as indicated by the source code comment at the top of the file.

See also (3) Sec. 5.6.2 and 5.6.3 for a description of both and some analysis.

(1) Chan F., O’Neill E.: Feasibility Study of a Quadrilateralized Spherical Cube Earth Data Base. Tech. Rep. EPRF 2-75 (CSC), Environmental Prediction Research Facility, Apr. 1975.

(2) O’Neill E., Laubscher R.: Extended Studies of a Quadrilateralized Spherical Cube Earth Data Base. Tech. Rep. NEPRF 3-76 (CSC), Naval Environmental Prediction Research Facility, May 1976.

(3) Calabretta, M. and Greisen, E.: Representations of celestial coordinates in FITS. Astronomy & Astrophysics 395, 3, 1077–1122, 2002.