B.1.19 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.

htmIndex( level, lon, lat )

Gives the HTM (Hierachical Triangular Mesh) pixel index for a given sky position.

• Parameters:
  • level (integer): HTM level
  • lon (floating point): longitude in degrees
  • lat (floating point): latitude in degrees
• Return value
  • (long integer): pixel index
• See Also:
  • HTM web site

healpixNestIndex( k, lon, lat )

Gives the pixel index for a given sky position in the HEALPix NEST scheme.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • lon (floating point): longitude in degrees
  • lat (floating point): latitude in degrees
• Return value
  • (long integer): pixel index
• See Also:
  • HEALPix web site

healpixRingIndex( k, lon, lat )

Gives the pixel index for a given sky position in the HEALPix RING scheme.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • lon (floating point): longitude in degrees
  • lat (floating point): latitude in degrees
• Return value
  • (long integer): pixel index
• See Also:
  • HEALPix web site

healpixNestLon( k, index )

Returns the longitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.

Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • index (long integer): healpix index
• Return value
  • (floating point): longitude in degrees
• See Also:
  • HEALPix web site

healpixNestLat( k, index )

Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.

Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • index (long integer): healpix index
• Return value
  • (floating point): latitude in degrees
• See Also:
  • HEALPix web site

healpixRingLon( k, index )

Returns the longitude of the approximate center of the tile with a given index in the HEALPix RING scheme.

Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • index (long integer): healpix index
• Return value
  • (floating point): longitude in degrees
• See Also:
  • HEALPix web site

healpixRingLat( k, index )

Returns the latitude of the approximate center of the tile with a given index in the HEALPix RING scheme.

Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • index (long integer): healpix index
• Return value
  • (floating point): latitude in degrees
• See Also:
  • HEALPix web site

healpixNestToRing( k, nestIndex )

Converts a healpix tile index from the NEST to the RING scheme at a given order.

Note: the nestIndex parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • nestIndex (long integer): pixel index in NEST scheme
• Return value
  • (long integer): pixel index in RING scheme
• See Also:
  • HEALPix web site

healpixRingToNest( k, ringIndex )

Converts a healpix tile index from the RING to the NEST scheme at a given order.

Note: the ringIndex parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

• Parameters:
  • k (integer): HEALPix order (0..29)
  • ringIndex (long integer): pixel index in RING scheme
• Return value
  • (long integer): pixel index in NEST scheme
• See Also:
  • HEALPix web site

healpixK( pixelsize )

Gives the HEALPix resolution parameter suitable for a given pixel size. This k value (also variously known as order, level, depth) is the logarithm to base 2 of the Nside parameter.

• Parameters:
  • pixelsize (floating point): pixel size in degrees
• Return value
  • (integer): HEALPix order k
• See Also:
  • HEALPix web site

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.

• Parameters:
  • 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.

• Parameters:
  • k (integer): HEALPix order (0..29)
• Return value
  • (floating point): pixel size in steradians
• Examples:
  • healpixSteradians(5) = 0.0010226538585904274
  • 4*PI/healpixSteradians(0) = 12.0

healpixSqdeg( k )

Returns the solid angle in square degrees of each HEALPix pixel at a given order.

• Parameters:
  • k (integer): HEALPix order (0..29)
• Return value
  • (floating point): pixel size in steradians
• Examples:
  • healpixSqdeg(5) = 3.357174580844667
  • round(12 * healpixSqdeg(0)) = 41253

steradiansToSqdeg( sr )

Converts a solid angle from steradians to square degrees.

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

• Parameters:
  • sr (floating point): quantity in steradians
• Return value
  • (floating point): quantity in sqare degrees
• Example:
  • round(steradiansToSqdeg(4*PI)) = 41253

sqdegToSteradians( sqdeg )

Converts a solid angle from square degrees to steradians.

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

• Parameters:
  • sqdeg (floating point): quantity in square degrees
• Return value
  • (floating point): quantity in steradians
• Example:
  • round(sqdegToSteradians(41253)/PI) = 4

htmLevel( pixelsize )

Gives the HTM level parameter suitable for a given pixel size.

• Parameters:
  • 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.

• Parameters:
  • level (integer): HTM depth
• Return value
  • (floating point): approximate angular resolution in degrees

SQDEG

Solid angle in steradians corresponding to 1 square degree.