Quadrilateralized Spherical Cube

The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project a sphere surface onto the six sides of a cube:

Classification: Azimuthal

Available forms: Forward and inverse, ellipsoidal

Defined area: Global

Alias: qsc

Domain: 2D

Input type: Geodetic coordinates

Output type: Projected coordinates

Projection String

+proj=qsc
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For this purpose, other alternatives can be used, notably gnom or healpix. However, QSC projection has the following favorable properties:

It is an equal-area projection, and at the same time introduces only limited angular distortions. It treats all cube sides equally, i.e. it does not use different projections for polar areas and equatorial areas. These properties make QSC projection a good choice for planetary-scale terrain rendering. Map data can be organized in quadtree structures for each cube side. See LambersKolb2012 for an example.

The QSC projection was introduced by ONeilLaubscher1976, building on previous work by ChanONeil1975. For clarity: The earlier QSC variant described in ChanONeil1975 became known as the COBE QSC since it was used by the NASA Cosmic Background Explorer (COBE) project; it is an approximately equal-area projection and is not the same as the QSC projection. See also CalabrettaGreisen2002 Sec. 5.6.2 and 5.6.3 for a description of both and some analysis.

In this implementation, the QSC projection projects onto one side of a circumscribed cube. The cube side is selected by choosing one of the following six projection centers:

+lat_0=0 +lon_0=0 | front cube side |

+lat_0=0 +lon_0=90 | right cube side |

+lat_0=0 +lon_0=180 | back cube side |

+lat_0=0 +lon_0=-90 | left cube side |

+lat_0=90 | top cube side |

+lat_0=-90 | bottom cube side |

Required Parameters

• +lat_0=<value>: Latitude of the projection center.
• +lon_0=<value>: Longitude of the projection center.

Optional Parameters

• +ellps=<value>: Ellipsoid parameters (default: WGS84).
• +x_0=<value>: False easting.
• +y_0=<value>: False northing.

Usage Example

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84  +lat_0=0 +lon_0=0"        \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff frontside.tiff

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=90"        \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff rightside.tiff

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=180"       \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff backside.tiff

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=-90"       \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff leftside.tiff

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=90 +lon_0=0"        \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff topside.tiff

gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=-90 +lon_0=0"       \
    -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137  \
    worldmap.tiff bottomside.tiff
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Further Reading

• Wikipedia
• NASA