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### B.1.2 Tilings

Pixel tiling functions for the celestial sphere.

The `k` 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 `k`, there are 12*4^k pixels on the sphere.

`healpixNestIndex( k, lon, lat )`
  Gives the pixel index for a given sky position in the HEALPix NEST scheme.
  - `k` (integer): HEALPix order (0..29)
  - `lon` (floating point): longitude in degrees
  - `lat` (floating point): latitude in degrees
  - return value (long integer): pixel index
`healpixRingIndex( k, lon, lat )`
  Gives the pixel index for a given sky position in the HEALPix RING scheme.
  - `k` (integer): HEALPix order (0..29)
  - `lon` (floating point): longitude in degrees
  - `lat` (floating point): latitude in degrees
  - return value (long integer): pixel index
`healpixNestLon( k, index )`
  Returns the longitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
  - `k` (integer): HEALPix order (0..29)
  - `index` (long integer): healpix index
  - return value (floating point): longitude in degrees
`healpixNestLat( k, index )`
  Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
  - `k` (integer): HEALPix order (0..29)
  - `index` (long integer): healpix index
  - return value (floating point): latitude in degrees
`healpixRingLon( k, index )`
  Returns the longitude of the approximate center of the tile with a given index in the HEALPix RING scheme.
  - `k` (integer): HEALPix order (0..29)
  - `index` (long integer): healpix index
  - return value (floating point): longitude in degrees
`healpixRingLat( k, index )`
  Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
  - `k` (integer): HEALPix order (0..29)
  - `index` (long integer): healpix index
  - return value (floating point): latitude in degrees
`healpixNestToRing( k, nestIndex )`
  Converts a healpix ring index from the NEST to the RING scheme at a given order.
  - `k` (integer): HEALPix order (0..29)
  - `nestIndex` (long integer): pixel index in NEST scheme
  - return value (long integer): pixel index in RING scheme
`healpixRingToNest( k, ringIndex )`
  Converts a healpix ring index from the RING to the NEST scheme at a given order.
  - `k` (integer): HEALPix order (0..29)
  - `ringIndex` (long integer): pixel index in RING scheme
  - return value (long integer): pixel index in NEST scheme
`healpixK( pixelsize )`
  Gives the HEALPix resolution parameter suitable for a given pixel size. This `k` value is the logarithm to base 2 of the Nside parameter.
  - `pixelsize` (floating point): pixel size in degrees
  - return value (integer): HEALPix order `k`
`healpixResolution( k )`
  Gives the approximate resolution in degrees for a given HEALPix resolution parameter `k` This `k` value is the logarithm to base 2 of the Nside parameter.
  - `k` (integer): HEALPix order (0..29)
  - return value (floating point): approximate angular resolution in degrees
`healpixSteradians( k )`
  Returns the solid angle in steradians of each HEALPix pixel at a given order.
  - `k` (integer): HEALPix order (0..29)
  - return value (floating point): pixel size in steradians
`healpixSqdeg( k )`
  Returns the solid angle in square degrees of each HEALPix pixel at a given order.
  - `k` (integer): HEALPix order (0..29)
  - return value (floating point): pixel size in steradians
`steradiansToSqdeg( sr )`
  Converts a solid angle from steradians to square degrees.

  The unit sphere is 4*PI steradians = 360*360/PI square degrees.

  - `sr` (floating point): quantity in steradians
  - return value (floating point): quantity in sqare degrees
`sqdegToSteradians( sqdeg )`
  Converts a solid angle from square degrees to steradians.

  The unit sphere is 4*PI steradians = 360*360/PI square degrees.

  - `sqdeg` (floating point): quantity in square degrees
  - return value (floating point): quantity in steradians
`htmLevel( pixelsize )`
  Gives the HTM `level` parameter suitable for a given pixel size.
  - `pixelsize` (floating point): required resolution in degrees
  - return value (integer): HTM level parameter
`htmResolution( level )`
  Gives the approximate resolution in degrees for a given HTM depth level.
  - `level` (integer): HTM depth
  - return value (floating point): approximate angular resolution in degrees
`SQDEG`
  Solid angle in steradians corresponding to 1 square degree.

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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
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