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<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="index.html">Projections</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="adams_hemi.html">Adams Hemisphere in a Square</a></li>
<li class="toctree-l3"><a class="reference internal" href="adams_ws1.html">Adams World in a Square I</a></li>
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<li class="toctree-l3"><a class="reference internal" href="aea.html">Albers Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="aeqd.html">Azimuthal Equidistant</a></li>
<li class="toctree-l3"><a class="reference internal" href="airy.html">Airy</a></li>
<li class="toctree-l3"><a class="reference internal" href="aitoff.html">Aitoff</a></li>
<li class="toctree-l3"><a class="reference internal" href="alsk.html">Modified Stereographic of Alaska</a></li>
<li class="toctree-l3"><a class="reference internal" href="apian.html">Apian Globular I</a></li>
<li class="toctree-l3"><a class="reference internal" href="august.html">August Epicycloidal</a></li>
<li class="toctree-l3"><a class="reference internal" href="bacon.html">Bacon Globular</a></li>
<li class="toctree-l3"><a class="reference internal" href="bertin1953.html">Bertin 1953</a></li>
<li class="toctree-l3"><a class="reference internal" href="bipc.html">Bipolar conic of western hemisphere</a></li>
<li class="toctree-l3"><a class="reference internal" href="boggs.html">Boggs Eumorphic</a></li>
<li class="toctree-l3"><a class="reference internal" href="bonne.html">Bonne (Werner lat_1=90)</a></li>
<li class="toctree-l3"><a class="reference internal" href="calcofi.html">Cal Coop Ocean Fish Invest Lines/Stations</a></li>
<li class="toctree-l3"><a class="reference internal" href="cass.html">Cassini (Cassini-Soldner)</a></li>
<li class="toctree-l3"><a class="reference internal" href="cc.html">Central Cylindrical</a></li>
<li class="toctree-l3"><a class="reference internal" href="ccon.html">Central Conic</a></li>
<li class="toctree-l3"><a class="reference internal" href="cea.html">Equal Area Cylindrical</a></li>
<li class="toctree-l3"><a class="reference internal" href="chamb.html">Chamberlin Trimetric</a></li>
<li class="toctree-l3"><a class="reference internal" href="collg.html">Collignon</a></li>
<li class="toctree-l3"><a class="reference internal" href="col_urban.html">Colombia Urban</a></li>
<li class="toctree-l3"><a class="reference internal" href="comill.html">Compact Miller</a></li>
<li class="toctree-l3"><a class="reference internal" href="crast.html">Craster Parabolic (Putnins P4)</a></li>
<li class="toctree-l3"><a class="reference internal" href="denoy.html">Denoyer Semi-Elliptical</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck1.html">Eckert I</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck2.html">Eckert II</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck3.html">Eckert III</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck4.html">Eckert IV</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck5.html">Eckert V</a></li>
<li class="toctree-l3"><a class="reference internal" href="eck6.html">Eckert VI</a></li>
<li class="toctree-l3"><a class="reference internal" href="eqc.html">Equidistant Cylindrical (Plate Carrée)</a></li>
<li class="toctree-l3"><a class="reference internal" href="eqdc.html">Equidistant Conic</a></li>
<li class="toctree-l3"><a class="reference internal" href="eqearth.html">Equal Earth</a></li>
<li class="toctree-l3"><a class="reference internal" href="euler.html">Euler</a></li>
<li class="toctree-l3"><a class="reference internal" href="fahey.html">Fahey</a></li>
<li class="toctree-l3"><a class="reference internal" href="fouc.html">Foucaut</a></li>
<li class="toctree-l3"><a class="reference internal" href="fouc_s.html">Foucaut Sinusoidal</a></li>
<li class="toctree-l3"><a class="reference internal" href="gall.html">Gall (Gall Stereographic)</a></li>
<li class="toctree-l3"><a class="reference internal" href="geos.html">Geostationary Satellite View</a></li>
<li class="toctree-l3"><a class="reference internal" href="gins8.html">Ginsburg VIII (TsNIIGAiK)</a></li>
<li class="toctree-l3"><a class="reference internal" href="gn_sinu.html">General Sinusoidal Series</a></li>
<li class="toctree-l3"><a class="reference internal" href="gnom.html">Gnomonic</a></li>
<li class="toctree-l3"><a class="reference internal" href="goode.html">Goode Homolosine</a></li>
<li class="toctree-l3"><a class="reference internal" href="gs48.html">Modified Stereographic of 48 U.S.</a></li>
<li class="toctree-l3"><a class="reference internal" href="gs50.html">Modified Stereographic of 50 U.S.</a></li>
<li class="toctree-l3"><a class="reference internal" href="guyou.html">Guyou</a></li>
<li class="toctree-l3"><a class="reference internal" href="hammer.html">Hammer & Eckert-Greifendorff</a></li>
<li class="toctree-l3"><a class="reference internal" href="hatano.html">Hatano Asymmetrical Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="healpix.html">HEALPix</a></li>
<li class="toctree-l3"><a class="reference internal" href="rhealpix.html">rHEALPix</a></li>
<li class="toctree-l3"><a class="reference internal" href="igh.html">Interrupted Goode Homolosine</a></li>
<li class="toctree-l3"><a class="reference internal" href="igh_o.html">Interrupted Goode Homolosine (Oceanic View)</a></li>
<li class="toctree-l3"><a class="reference internal" href="imw_p.html">International Map of the World Polyconic</a></li>
<li class="toctree-l3"><a class="reference internal" href="isea.html">Icosahedral Snyder Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="kav5.html">Kavrayskiy V</a></li>
<li class="toctree-l3"><a class="reference internal" href="kav7.html">Kavrayskiy VII</a></li>
<li class="toctree-l3"><a class="reference internal" href="krovak.html">Krovak</a></li>
<li class="toctree-l3"><a class="reference internal" href="labrd.html">Laborde</a></li>
<li class="toctree-l3"><a class="reference internal" href="laea.html">Lambert Azimuthal Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="lagrng.html">Lagrange</a></li>
<li class="toctree-l3"><a class="reference internal" href="larr.html">Larrivee</a></li>
<li class="toctree-l3"><a class="reference internal" href="lask.html">Laskowski</a></li>
<li class="toctree-l3"><a class="reference internal" href="lcc.html">Lambert Conformal Conic</a></li>
<li class="toctree-l3"><a class="reference internal" href="lcca.html">Lambert Conformal Conic Alternative</a></li>
<li class="toctree-l3"><a class="reference internal" href="leac.html">Lambert Equal Area Conic</a></li>
<li class="toctree-l3"><a class="reference internal" href="lee_os.html">Lee Oblated Stereographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="loxim.html">Loximuthal</a></li>
<li class="toctree-l3"><a class="reference internal" href="lsat.html">Space oblique for LANDSAT</a></li>
<li class="toctree-l3"><a class="reference internal" href="mbt_s.html">McBryde-Thomas Flat-Polar Sine (No. 1)</a></li>
<li class="toctree-l3"><a class="reference internal" href="mbt_fps.html">McBryde-Thomas Flat-Pole Sine (No. 2)</a></li>
<li class="toctree-l3"><a class="reference internal" href="mbtfpp.html">McBride-Thomas Flat-Polar Parabolic</a></li>
<li class="toctree-l3"><a class="reference internal" href="mbtfpq.html">McBryde-Thomas Flat-Polar Quartic</a></li>
<li class="toctree-l3"><a class="reference internal" href="mbtfps.html">McBryde-Thomas Flat-Polar Sinusoidal</a></li>
<li class="toctree-l3"><a class="reference internal" href="merc.html">Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="mil_os.html">Miller Oblated Stereographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="mill.html">Miller Cylindrical</a></li>
<li class="toctree-l3"><a class="reference internal" href="misrsom.html">Space oblique for MISR</a></li>
<li class="toctree-l3"><a class="reference internal" href="moll.html">Mollweide</a></li>
<li class="toctree-l3"><a class="reference internal" href="murd1.html">Murdoch I</a></li>
<li class="toctree-l3"><a class="reference internal" href="murd2.html">Murdoch II</a></li>
<li class="toctree-l3"><a class="reference internal" href="murd3.html">Murdoch III</a></li>
<li class="toctree-l3"><a class="reference internal" href="natearth.html">Natural Earth</a></li>
<li class="toctree-l3"><a class="reference internal" href="natearth2.html">Natural Earth II</a></li>
<li class="toctree-l3"><a class="reference internal" href="nell.html">Nell</a></li>
<li class="toctree-l3"><a class="reference internal" href="nell_h.html">Nell-Hammer</a></li>
<li class="toctree-l3"><a class="reference internal" href="nicol.html">Nicolosi Globular</a></li>
<li class="toctree-l3"><a class="reference internal" href="nsper.html">Near-sided perspective</a></li>
<li class="toctree-l3"><a class="reference internal" href="nzmg.html">New Zealand Map Grid</a></li>
<li class="toctree-l3"><a class="reference internal" href="ob_tran.html">General Oblique Transformation</a></li>
<li class="toctree-l3"><a class="reference internal" href="ocea.html">Oblique Cylindrical Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="oea.html">Oblated Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="omerc.html">Oblique Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="ortel.html">Ortelius Oval</a></li>
<li class="toctree-l3"><a class="reference internal" href="ortho.html">Orthographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="patterson.html">Patterson</a></li>
<li class="toctree-l3"><a class="reference internal" href="pconic.html">Perspective Conic</a></li>
<li class="toctree-l3"><a class="reference internal" href="peirce_q.html">Peirce Quincuncial</a></li>
<li class="toctree-l3"><a class="reference internal" href="poly.html">Polyconic (American)</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp1.html">Putnins P1</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp2.html">Putnins P2</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp3.html">Putnins P3</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp3p.html">Putnins P3’</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp4p.html">Putnins P4’</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp5.html">Putnins P5</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp5p.html">Putnins P5’</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp6.html">Putnins P6</a></li>
<li class="toctree-l3"><a class="reference internal" href="putp6p.html">Putnins P6’</a></li>
<li class="toctree-l3"><a class="reference internal" href="qua_aut.html">Quartic Authalic</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="#">Quadrilateralized Spherical Cube</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#usage">Usage</a></li>
<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li>
<li class="toctree-l4"><a class="reference internal" href="#further-reading">Further reading</a></li>
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<li class="toctree-l3"><a class="reference internal" href="robin.html">Robinson</a></li>
<li class="toctree-l3"><a class="reference internal" href="rouss.html">Roussilhe Stereographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="rpoly.html">Rectangular Polyconic</a></li>
<li class="toctree-l3"><a class="reference internal" href="s2.html">S2</a></li>
<li class="toctree-l3"><a class="reference internal" href="sch.html">Spherical Cross-track Height</a></li>
<li class="toctree-l3"><a class="reference internal" href="sinu.html">Sinusoidal (Sanson-Flamsteed)</a></li>
<li class="toctree-l3"><a class="reference internal" href="somerc.html">Swiss Oblique Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="stere.html">Stereographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="sterea.html">Oblique Stereographic Alternative</a></li>
<li class="toctree-l3"><a class="reference internal" href="gstmerc.html">Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)</a></li>
<li class="toctree-l3"><a class="reference internal" href="tcc.html">Transverse Central Cylindrical</a></li>
<li class="toctree-l3"><a class="reference internal" href="tcea.html">Transverse Cylindrical Equal Area</a></li>
<li class="toctree-l3"><a class="reference internal" href="times.html">Times</a></li>
<li class="toctree-l3"><a class="reference internal" href="tissot.html">Tissot</a></li>
<li class="toctree-l3"><a class="reference internal" href="tmerc.html">Transverse Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="tobmerc.html">Tobler-Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="tpeqd.html">Two Point Equidistant</a></li>
<li class="toctree-l3"><a class="reference internal" href="tpers.html">Tilted perspective</a></li>
<li class="toctree-l3"><a class="reference internal" href="ups.html">Universal Polar Stereographic</a></li>
<li class="toctree-l3"><a class="reference internal" href="urm5.html">Urmaev V</a></li>
<li class="toctree-l3"><a class="reference internal" href="urmfps.html">Urmaev Flat-Polar Sinusoidal</a></li>
<li class="toctree-l3"><a class="reference internal" href="utm.html">Universal Transverse Mercator (UTM)</a></li>
<li class="toctree-l3"><a class="reference internal" href="vandg.html">van der Grinten (I)</a></li>
<li class="toctree-l3"><a class="reference internal" href="vandg2.html">van der Grinten II</a></li>
<li class="toctree-l3"><a class="reference internal" href="vandg3.html">van der Grinten III</a></li>
<li class="toctree-l3"><a class="reference internal" href="vandg4.html">van der Grinten IV</a></li>
<li class="toctree-l3"><a class="reference internal" href="vitk1.html">Vitkovsky I</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag1.html">Wagner I (Kavrayskiy VI)</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag2.html">Wagner II</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag3.html">Wagner III</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag4.html">Wagner IV</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag5.html">Wagner V</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag6.html">Wagner VI</a></li>
<li class="toctree-l3"><a class="reference internal" href="wag7.html">Wagner VII</a></li>
<li class="toctree-l3"><a class="reference internal" href="webmerc.html">Web Mercator / Pseudo Mercator</a></li>
<li class="toctree-l3"><a class="reference internal" href="weren.html">Werenskiold I</a></li>
<li class="toctree-l3"><a class="reference internal" href="wink1.html">Winkel I</a></li>
<li class="toctree-l3"><a class="reference internal" href="wink2.html">Winkel II</a></li>
<li class="toctree-l3"><a class="reference internal" href="wintri.html">Winkel Tripel</a></li>
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<li>Quadrilateralized Spherical Cube</li>
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<section id="quadrilateralized-spherical-cube">
<span id="qsc"></span><h1>Quadrilateralized Spherical Cube<a class="headerlink" href="#quadrilateralized-spherical-cube" title="Permalink to this headline">¶</a></h1>
<table class="docutils align-default">
<colgroup>
<col style="width: 27%" />
<col style="width: 73%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Classification</strong></p></td>
<td><p>Azimuthal</p></td>
</tr>
<tr class="row-even"><td><p><strong>Available forms</strong></p></td>
<td><p>Forward and inverse, ellipsoidal</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Defined area</strong></p></td>
<td><p>Global</p></td>
</tr>
<tr class="row-even"><td><p><strong>Alias</strong></p></td>
<td><p>qsc</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Domain</strong></p></td>
<td><p>2D</p></td>
</tr>
<tr class="row-even"><td><p><strong>Input type</strong></p></td>
<td><p>Geodetic coordinates</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Output type</strong></p></td>
<td><p>Projected coordinates</p></td>
</tr>
</tbody>
</table>
<p>The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project
a sphere surface onto the six sides of a cube:</p>
<a class="reference internal image-reference" href="../../_images/qsc_concept.jpg"><img alt="Quadrilateralized Spherical Cube" class="align-center" src="../../_images/qsc_concept.jpg" style="width: 500px;" /></a>
<p>For this purpose, other alternatives can be used, notably <a class="reference internal" href="gnom.html#gnom"><span class="std std-ref">Gnomonic</span></a> or
<a class="reference internal" href="healpix.html#healpix"><span class="std std-ref">HEALPix</span></a>. However, QSC projection has the following favorable properties:</p>
<p>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 <span id="id1">[<a class="reference internal" href="../../zreferences.html#id25" title="Lambers, M. and Kolb, A. Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data. In Bregler, C., Sander, P., and Wimmer, M., editors, Pacific Graphics Short Papers. The Eurographics Association, 2012. doi:10.2312/PE/PG/PG2012short/005-010.">LambersKolb2012</a>]</span> for an example.</p>
<p>The QSC projection was introduced by <span id="id2">[<a class="reference internal" href="../../zreferences.html#id27" title="O'Neill, E. M. and Laubscher, R. E. Extended studies of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 3-76 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1976. URL: https://archive.org/details/DTIC_ADA026294.">ONeilLaubscher1976</a>]</span>,
building on previous work by <span id="id3">[<a class="reference internal" href="../../zreferences.html#id6" title="Chan, F. K. and O'Neill, E. M. Feasibility study of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 2-75 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1975. URL: https://archive.org/details/ADA010232.">ChanONeil1975</a>]</span>. For clarity: The
earlier QSC variant described in <span id="id4">[<a class="reference internal" href="../../zreferences.html#id6" title="Chan, F. K. and O'Neill, E. M. Feasibility study of a quadrilateralized spherical cube earth data base. Tech. Rep. EPRF 2-75 (CSC), Computer Sciences Corporation, System Sciences Division, Silver Spring, Md, 1975. URL: https://archive.org/details/ADA010232.">ChanONeil1975</a>]</span> 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.</p>
<p>See also <span id="id5">[<a class="reference internal" href="../../zreferences.html#id5" title="Calabretta, M. R. and Greisen, E. W. Representations of celestial coordinates in FITS. Astronomy & Astrophysics, 395(3):1077–1122, 2002. doi:10.1051/0004-6361:20021327.">CalabrettaGreisen2002</a>]</span> Sec. 5.6.2 and 5.6.3 for a description of both and
some analysis.</p>
<p>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:</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 56%" />
<col style="width: 44%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=0</span></code></p></td>
<td><p>front cube side</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=90</span></code></p></td>
<td><p>right cube side</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=180</span></code></p></td>
<td><p>back cube side</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=0</span> <span class="pre">+lon_0=-90</span></code></p></td>
<td><p>left cube side</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=90</span></code></p></td>
<td><p>top cube side</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+lat_0=-90</span></code></p></td>
<td><p>bottom cube side</p></td>
</tr>
</tbody>
</table>
<p>Furthermore, this implementation allows the projection to be applied to ellipsoids.
A preceding shift to a sphere is performed automatically; see <span id="id6">[<a class="reference internal" href="../../zreferences.html#id25" title="Lambers, M. and Kolb, A. Ellipsoidal cube maps for accurate rendering of planetary-scale terrain data. In Bregler, C., Sander, P., and Wimmer, M., editors, Pacific Graphics Short Papers. The Eurographics Association, 2012. doi:10.2312/PE/PG/PG2012short/005-010.">LambersKolb2012</a>]</span> for details.</p>
<section id="usage">
<h2>Usage<a class="headerlink" href="#usage" title="Permalink to this headline">¶</a></h2>
<p>The following example uses QSC projection via GDAL to create the six cube side
maps from a world map for the WGS84 ellipsoid:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>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
</pre></div>
</div>
<p>Explanation:</p>
<ul class="simple">
<li><p>QSC projection is selected with <code class="docutils literal notranslate"><span class="pre">+wktext</span> <span class="pre">+proj=qsc</span></code>.</p></li>
<li><p>The WGS84 ellipsoid is specified with <code class="docutils literal notranslate"><span class="pre">+ellps=WGS84</span></code>.</p></li>
<li><p>The cube side is selected with <code class="docutils literal notranslate"><span class="pre">+lat_0=...</span> <span class="pre">+lon_0=...</span></code>.</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">-wo</span></code> options are necessary for GDAL to avoid holes in the output maps.</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">-te</span></code> option limits the extends of the output map to the major axis diameter
(from -radius to +radius in both x and y direction). These are the dimensions of one side
of the circumscribing cube.</p></li>
</ul>
<p>The resulting images can be laid out in a grid like below.</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 24%" />
<col style="width: 27%" />
<col style="width: 25%" />
<col style="width: 24%" />
</colgroup>
<tbody>
<tr class="row-odd"><td></td>
<td><p><a class="reference internal" href="../../_images/qsc_topside.jpg"><img alt="Top side" class="align-middle" src="../../_images/qsc_topside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="../../_images/qsc_leftside.jpg"><img alt="Left side" class="align-middle" src="../../_images/qsc_leftside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
<td><p><a class="reference internal" href="../../_images/qsc_frontside.jpg"><img alt="Front side" class="align-middle" src="../../_images/qsc_frontside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
<td><p><a class="reference internal" href="../../_images/qsc_rightside.jpg"><img alt="Right side" class="align-middle" src="../../_images/qsc_rightside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
<td><p><a class="reference internal" href="../../_images/qsc_backside.jpg"><img alt="Back side" class="align-middle" src="../../_images/qsc_backside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p><a class="reference internal" href="../../_images/qsc_bottomside.jpg"><img alt="Bottom side" class="align-middle" src="../../_images/qsc_bottomside.jpg" style="width: 128.0px; height: 128.0px;" /></a></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</section>
<section id="parameters">
<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>All parameters for the projection are optional.</p>
</div>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-lon_0">
<span id="cmdoption-arg-lon-0"></span><span class="sig-name descname"><span class="pre">+lon_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lon_0" title="Permalink to this definition">¶</a></dt>
<dd><p>Longitude of projection center.</p>
<p><em>Defaults to 0.0.</em></p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-lat_0">
<span id="cmdoption-arg-lat-0"></span><span class="sig-name descname"><span class="pre">+lat_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-lat_0" title="Permalink to this definition">¶</a></dt>
<dd><p>Latitude of projection center.</p>
<p><em>Defaults to 0.0.</em></p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-ellps">
<span class="sig-name descname"><span class="pre">+ellps</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-ellps" title="Permalink to this definition">¶</a></dt>
<dd><p>The name of a built-in ellipsoid definition.</p>
<p>See <a class="reference internal" href="../../usage/ellipsoids.html#ellipsoids"><span class="std std-ref">Ellipsoids</span></a> for more information, or execute
<a class="reference internal" href="../../apps/proj.html#cmdoption-proj-le"><code class="xref std std-option docutils literal notranslate"><span class="pre">proj</span> <span class="pre">-le</span></code></a> for a list of built-in ellipsoid names.</p>
<p><em>Defaults to “GRS80”.</em></p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-x_0">
<span id="cmdoption-arg-x-0"></span><span class="sig-name descname"><span class="pre">+x_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-x_0" title="Permalink to this definition">¶</a></dt>
<dd><p>False easting.</p>
<p><em>Defaults to 0.0.</em></p>
</dd></dl>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-y_0">
<span id="cmdoption-arg-y-0"></span><span class="sig-name descname"><span class="pre">+y_0</span></span><span class="sig-prename descclassname"><span class="pre">=<value></span></span><a class="headerlink" href="#cmdoption-arg-y_0" title="Permalink to this definition">¶</a></dt>
<dd><p>False northing.</p>
<p><em>Defaults to 0.0.</em></p>
</dd></dl>
</section>
<section id="further-reading">
<h2>Further reading<a class="headerlink" href="#further-reading" title="Permalink to this headline">¶</a></h2>
<ol class="arabic simple">
<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Quadrilateralized_spherical_cube">Wikipedia</a></p></li>
<li><p><a class="reference external" href="https://lambda.gsfc.nasa.gov/product/cobe/skymap_info_new.cfm">NASA</a></p></li>
</ol>
</section>
</section>
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