Package uk.ac.starlink.ttools.func

Class Tilings

  • public class Tilings
extends java.lang.Object
    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.

    Since:
    6 Dec 2007
    Author:
    Mark Taylor
    See Also:
    HTM web site, HEALPix web site

    • Field Summary

      Fields 
      Modifier and Type Field Description
      static double SQDEG
      Solid angle in steradians corresponding to 1 square degree.

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static int healpixK​(double pixelsize)
      Gives the HEALPix resolution parameter suitable for a given pixel size.
      static long healpixNestIndex​(int k, double lon, double lat)
      Gives the pixel index for a given sky position in the HEALPix NEST scheme.
      static double healpixNestLat​(int k, long index)
      Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
      static double healpixNestLon​(int k, long index)
      Returns the longitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
      static long healpixNestToRing​(int k, long nestIndex)
      Converts a healpix tile index from the NEST to the RING scheme at a given order.
      static double healpixResolution​(int 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.
      static long healpixRingIndex​(int k, double lon, double lat)
      Gives the pixel index for a given sky position in the HEALPix RING scheme.
      static double healpixRingLat​(int k, long index)
      Returns the latitude of the approximate center of the tile with a given index in the HEALPix RING scheme.
      static double healpixRingLon​(int k, long index)
      Returns the longitude of the approximate center of the tile with a given index in the HEALPix RING scheme.
      static long healpixRingToNest​(int k, long ringIndex)
      Converts a healpix tile index from the RING to the NEST scheme at a given order.
      static double healpixSqdeg​(int k)
      Returns the solid angle in square degrees of each HEALPix pixel at a given order.
      static double healpixSteradians​(int k)
      Returns the solid angle in steradians of each HEALPix pixel at a given order.
      static int htmLevel​(double pixelsize)
      Gives the HTM level parameter suitable for a given pixel size.
      static double htmResolution​(int level)
      Gives the approximate resolution in degrees for a given HTM depth level.
      static double sqdegToSteradians​(double sqdeg)
      Converts a solid angle from square degrees to steradians.
      static double steradiansToSqdeg​(double sr)
      Converts a solid angle from steradians to square degrees.

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • SQDEG

        public static final double SQDEG
        Solid angle in steradians corresponding to 1 square degree.
        See Also:
        Constant Field Values

    • Method Detail

      • healpixNestIndex

        public static long healpixNestIndex​(int k,
                                    double lon,
                                    double lat)
        Gives the pixel index for a given sky position in the HEALPix NEST scheme.
        Parameters:
        k - HEALPix order (0..29)
        lon - longitude in degrees
        lat - latitude in degrees
        Returns:
        pixel index
        See Also:
        HEALPix web site

      • healpixRingIndex

        public static long healpixRingIndex​(int k,
                                    double lon,
                                    double lat)
        Gives the pixel index for a given sky position in the HEALPix RING scheme.
        Parameters:
        k - HEALPix order (0..29)
        lon - longitude in degrees
        lat - latitude in degrees
        Returns:
        pixel index
        See Also:
        HEALPix web site

      • healpixNestLon

        public static double healpixNestLon​(int k,
                                    long 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 - HEALPix order (0..29)
        index - healpix index
        Returns:
        longitude in degrees
        See Also:
        HEALPix web site

      • healpixNestLat

        public static double healpixNestLat​(int k,
                                    long 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 - HEALPix order (0..29)
        index - healpix index
        Returns:
        latitude in degrees
        See Also:
        HEALPix web site

      • healpixRingLon

        public static double healpixRingLon​(int k,
                                    long 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 - HEALPix order (0..29)
        index - healpix index
        Returns:
        longitude in degrees
        See Also:
        HEALPix web site

      • healpixRingLat

        public static double healpixRingLat​(int k,
                                    long 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 - HEALPix order (0..29)
        index - healpix index
        Returns:
        latitude in degrees
        See Also:
        HEALPix web site

      • healpixNestToRing

        public static long healpixNestToRing​(int k,
                                     long 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 - HEALPix order (0..29)
        nestIndex - pixel index in NEST scheme
        Returns:
        pixel index in RING scheme
        See Also:
        HEALPix web site

      • healpixRingToNest

        public static long healpixRingToNest​(int k,
                                     long 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 - HEALPix order (0..29)
        ringIndex - pixel index in RING scheme
        Returns:
        pixel index in NEST scheme
        See Also:
        HEALPix web site

      • healpixK

        public static int healpixK​(double 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 - pixel size in degrees
        Returns:
        HEALPix order k
        See Also:
        HEALPix web site

      • healpixResolution

        public static double healpixResolution​(int 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 - HEALPix order (0..29)
        Returns:
        approximate angular resolution in degrees

      • healpixSteradians

        public static double healpixSteradians​(int k)
        Returns the solid angle in steradians of each HEALPix pixel at a given order.
        Parameters:
        k - HEALPix order (0..29)
        Returns:
        pixel size in steradians
        Examples:
        healpixSteradians(5) = 0.0010226538585904274, 4*PI/healpixSteradians(0) = 12.0

      • healpixSqdeg

        public static double healpixSqdeg​(int k)
        Returns the solid angle in square degrees of each HEALPix pixel at a given order.
        Parameters:
        k - HEALPix order (0..29)
        Returns:
        pixel size in steradians
        Examples:
        healpixSqdeg(5) = 3.357174580844667, round(12 * healpixSqdeg(0)) = 41253

      • steradiansToSqdeg

        public static double steradiansToSqdeg​(double sr)
        Converts a solid angle from steradians to square degrees.

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

        Parameters:
        sr - quantity in steradians
        Returns:
        quantity in sqare degrees
        Examples:
        round(steradiansToSqdeg(4*PI)) = 41253

      • sqdegToSteradians

        public static double sqdegToSteradians​(double sqdeg)
        Converts a solid angle from square degrees to steradians.

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

        Parameters:
        sqdeg - quantity in square degrees
        Returns:
        quantity in steradians
        Examples:
        round(sqdegToSteradians(41253)/PI) = 4

      • htmLevel

        public static int htmLevel​(double pixelsize)
        Gives the HTM level parameter suitable for a given pixel size.
        Parameters:
        pixelsize - required resolution in degrees
        Returns:
        HTM level parameter

      • htmResolution

        public static double htmResolution​(int level)
        Gives the approximate resolution in degrees for a given HTM depth level.
        Parameters:
        level - HTM depth
        Returns:
        approximate angular resolution in degrees