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<h4><a name="uk.ac.starlink.ttools.func.Tilings">10.5.2 Tilings</a></h4>
<p>Pixel tiling functions for the celestial sphere.</p>
<p>The <code>k</code> parameter for the HEALPix functions is the
HEALPix order, which can be in the range 0<=k<=29.
This is the logarithm to base 2 of the HEALPix NSIDE parameter.
At order <code>k</code>, there are 12*4^k pixels on the sphere.
</p>
<p>
<dl>
<dt><strong><code>healpixNestIndex( k, lon, lat )</code></strong></dt>
<dd>Gives the pixel index for a given sky position in the HEALPix
NEST scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>lon</code> <em>(floating point)</em>: longitude in degrees
</li>
<li><code>lat</code> <em>(floating point)</em>: latitude in degrees
</li>
<li>return value <em>(long integer)</em>: pixel index
</li>
</ul>
</dd>
<dt><strong><code>healpixRingIndex( k, lon, lat )</code></strong></dt>
<dd>Gives the pixel index for a given sky position in the HEALPix
RING scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>lon</code> <em>(floating point)</em>: longitude in degrees
</li>
<li><code>lat</code> <em>(floating point)</em>: latitude in degrees
</li>
<li>return value <em>(long integer)</em>: pixel index
</li>
</ul>
</dd>
<dt><strong><code>healpixNestLon( k, index )</code></strong></dt>
<dd>Returns the longitude of the approximate center of the tile
with a given index in the HEALPix NEST scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>index</code> <em>(long integer)</em>: healpix index
</li>
<li>return value <em>(floating point)</em>: longitude in degrees
</li>
</ul>
</dd>
<dt><strong><code>healpixNestLat( k, index )</code></strong></dt>
<dd>Returns the latitude of the approximate center of the tile
with a given index in the HEALPix NEST scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>index</code> <em>(long integer)</em>: healpix index
</li>
<li>return value <em>(floating point)</em>: latitude in degrees
</li>
</ul>
</dd>
<dt><strong><code>healpixRingLon( k, index )</code></strong></dt>
<dd>Returns the longitude of the approximate center of the tile
with a given index in the HEALPix RING scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>index</code> <em>(long integer)</em>: healpix index
</li>
<li>return value <em>(floating point)</em>: longitude in degrees
</li>
</ul>
</dd>
<dt><strong><code>healpixRingLat( k, index )</code></strong></dt>
<dd>Returns the latitude of the approximate center of the tile
with a given index in the HEALPix NEST scheme.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>index</code> <em>(long integer)</em>: healpix index
</li>
<li>return value <em>(floating point)</em>: latitude in degrees
</li>
</ul>
</dd>
<dt><strong><code>healpixNestToRing( k, nestIndex )</code></strong></dt>
<dd>Converts a healpix ring index from the NEST to the RING scheme
at a given order.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>nestIndex</code> <em>(long integer)</em>: pixel index in NEST scheme
</li>
<li>return value <em>(long integer)</em>: pixel index in RING scheme
</li>
</ul>
</dd>
<dt><strong><code>healpixRingToNest( k, ringIndex )</code></strong></dt>
<dd>Converts a healpix ring index from the RING to the NEST scheme
at a given order.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li><code>ringIndex</code> <em>(long integer)</em>: pixel index in RING scheme
</li>
<li>return value <em>(long integer)</em>: pixel index in NEST scheme
</li>
</ul>
</dd>
<dt><strong><code>healpixK( pixelsize )</code></strong></dt>
<dd>Gives the HEALPix resolution parameter suitable for a given pixel size.
This <code>k</code> value is the logarithm to base 2 of the
Nside parameter.
<ul>
<li><code>pixelsize</code> <em>(floating point)</em>: pixel size in degrees
</li>
<li>return value <em>(integer)</em>: HEALPix order <code>k</code></li>
</ul>
</dd>
<dt><strong><code>healpixResolution( k )</code></strong></dt>
<dd>Gives the approximate resolution in degrees for a given HEALPix
resolution parameter <code>k</code>
This <code>k</code> value is the logarithm to base 2 of the
Nside parameter.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li>return value <em>(floating point)</em>: approximate angular resolution in degrees
</li>
</ul>
</dd>
<dt><strong><code>healpixSteradians( k )</code></strong></dt>
<dd>Returns the solid angle in steradians of each HEALPix pixel
at a given order.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li>return value <em>(floating point)</em>: pixel size in steradians
</li>
</ul>
</dd>
<dt><strong><code>healpixSqdeg( k )</code></strong></dt>
<dd>Returns the solid angle in square degrees of each HEALPix pixel
at a given order.
<ul>
<li><code>k</code> <em>(integer)</em>: HEALPix order (0..29)
</li>
<li>return value <em>(floating point)</em>: pixel size in steradians
</li>
</ul>
</dd>
<dt><strong><code>steradiansToSqdeg( sr )</code></strong></dt>
<dd>Converts a solid angle from steradians to square degrees.
<p>The unit sphere is 4*PI steradians = 360*360/PI square degrees.
<ul>
<li><code>sr</code> <em>(floating point)</em>: quantity in steradians
</li>
<li>return value <em>(floating point)</em>: quantity in sqare degrees
</li>
</ul>
</p>
</dd>
<dt><strong><code>sqdegToSteradians( sqdeg )</code></strong></dt>
<dd>Converts a solid angle from square degrees to steradians.
<p>The unit sphere is 4*PI steradians = 360*360/PI square degrees.
<ul>
<li><code>sqdeg</code> <em>(floating point)</em>: quantity in square degrees
</li>
<li>return value <em>(floating point)</em>: quantity in steradians
</li>
</ul>
</p>
</dd>
<dt><strong><code>htmLevel( pixelsize )</code></strong></dt>
<dd>Gives the HTM <code>level</code> parameter suitable for a given
pixel size.
<ul>
<li><code>pixelsize</code> <em>(floating point)</em>: required resolution in degrees
</li>
<li>return value <em>(integer)</em>: HTM level parameter
</li>
</ul>
</dd>
<dt><strong><code>htmResolution( level )</code></strong></dt>
<dd>Gives the approximate resolution in degrees for a given HTM depth level.
<ul>
<li><code>level</code> <em>(integer)</em>: HTM depth
</li>
<li>return value <em>(floating point)</em>: approximate angular resolution in degrees
</li>
</ul>
</dd>
<dt><strong><code>SQDEG</code></strong></dt>
<dd>Solid angle in steradians corresponding to 1 square degree.
<ul></ul>
</dd>
</dl>
</p>
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<hr><i>STILTS - Starlink Tables Infrastructure Library Tool Set<br>Starlink User Note256<br>STILTS web page:
<a href="http://www.starlink.ac.uk/stilts/">http://www.starlink.ac.uk/stilts/</a><br>Author email:
<a href="mailto:m.b.taylor@bristol.ac.uk">m.b.taylor@bristol.ac.uk</a><br>Mailing list:
<a href="mailto:topcat-user@jiscmail.ac.uk">topcat-user@jiscmail.ac.uk</a><br></i></body>
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