Package org.esa.snap.core.util.math

Class MathUtils

java.lang.Object
org.esa.snap.core.util.math.MathUtils
public class MathUtils extends Object
A utility class providing frequently used mathematical functions which are not found in the java.lang.Math class.

All functions have been implemented with extreme caution in order to provide a maximum performance.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final double
    DTOR
    Conversion factor for degrees to radians for the double data type.
    static final float
    DTOR_F
    Conversion factor for degrees to radians for the float data type.
    static final double
    EPS
    The epsilon value for the double data type.
    static final float
    EPS_F
    The epsilon value for the float data type.
    static final double
    HALFPI
    Pi half
    static final double
    LOG10
    The natural logarithm of 10 as given by Math.logging(10)
    static final double
    RTOD
    Conversion factor for radians to degrees for the double data type.
    static final float
    RTOD_F
    Conversion factor for radians to degrees for the float data type.

  • Constructor Summary

    Constructors
    Constructor
    Description
    MathUtils()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static int
    ceilInt(double x)
    Returns (int) Math.ceil(x).
    static long
    ceilLong(double x)
    Returns (long) Math.ceil(x).
    static double
    computeRoundFactor(double min, double max, int numDigits)
    Computes a rounding factor suitable for the given value range and number of significant digits after the decimal point.
    static float
    computeRoundFactor(float min, float max, int numDigits)
    Computes a rounding factor suitable for the given value range and number of significant digits.
    static byte[]
    createGammaCurve(double gamma, byte[] f)
    Creates a quantized gamma (correction) curve for 256 samples in range from 0 to 1.
    static byte
    crop(byte val, byte min, byte max)
    Crops the value to the range min to max.
    static double
    crop(double val, double min, double max)
    Crops the value to the range min to max.
    static float
    crop(float val, float min, float max)
    Crops the value to the range min to max.
    static int
    crop(int val, int min, int max)
    Crops the value to the range min to max.
    static long
    crop(long val, long min, long max)
    Crops the value to the range min to max.
    static short
    crop(short val, short min, short max)
    Crops the value to the range min to max.
    static boolean
    equalValues(double x1, double x2)
    Compares two double values for equality within the fixed epsilon.
    static boolean
    equalValues(double x1, double x2, double eps)
    Compares two double values for equality within the given epsilon.
    static boolean
    equalValues(float x1, float x2)
    Compares two float values for equality within the fixed epsilon.
    static boolean
    equalValues(float x1, float x2, float eps)
    Compares two float values for equality within the given epsilon.
    static Dimension
    fitDimension(int n, double a, double b)
    Computes an integer dimension for a given integer area that best fits the rectangle given by floating point width and height.
    static int
    floorAndCrop(double x, int min, int max)
    First calls Math.floor with x and then crops the resulting value to the range min to max.
    static int
    floorInt(double value)
    Returns (int) Math.floor(value).
    static long
    floorLong(double x)
    Returns (long) Math.floor(x).
    static double
    getOrderOfMagnitude(double x)
    Returns the order of magnitude for the value x.
    static double
    interpolate2D(double wi, double wj, double x00, double x10, double x01, double x11)
    Performs a fast linear interpolation in two dimensions i and j.
    static float
    interpolate2D(float wi, float wj, float x00, float x10, float x01, float x11)
    Performs a fast linear interpolation in two dimensions i and j.
    static double
    log10(double x)
    Computes the common logarithm (to the base 10).
    static double
    round(double x, double roundFactor)
    Computes a rounded value for the given rounding factor.
    static float
    round(float x, float roundFactor)
    Computes a rounded value for the given rounding factor.
    static long
    roundAndCrop(double value, long min, long max)
    First calls Math.round with value and then crops the resulting value to the range min to max.
    static int
    roundAndCrop(float x, int min, int max)
    First calls Math.round with x and then crops the resulting value to the range min to max.
    static final double
    sphereDistance(double sphereRadius, double lambda1_rad, double phi1_rad, double lambda2_rad, double phi2_rad)
     
    static final double
    sphereDistanceDeg(double sphereRadius, double lambda1_deg, double phi1_deg, double lambda2_deg, double phi2_deg)
     
    static Rectangle[]
    subdivideRectangle(int width, int height, int numTilesX, int numTilesY, int extraBorder)
    Subdivides a rectangle into tiles.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • EPS_F

      public static final float EPS_F
      The epsilon value for the float data type. The exact value of this constant is 1.0E-6.
      See Also:

    • EPS

      public static final double EPS
      The epsilon value for the double data type. The exact value of this constant is 1.0E-12.
      See Also:

    • DTOR

      public static final double DTOR
      Conversion factor for degrees to radians for the double data type.
      See Also:

    • RTOD

      public static final double RTOD
      Conversion factor for radians to degrees for the double data type.
      See Also:

    • DTOR_F

      public static final float DTOR_F
      Conversion factor for degrees to radians for the float data type.
      See Also:

    • RTOD_F

      public static final float RTOD_F
      Conversion factor for radians to degrees for the float data type.
      See Also:

    • LOG10

      public static final double LOG10
      The natural logarithm of 10 as given by Math.logging(10)

    • HALFPI

      public static final double HALFPI
      Pi half
      See Also:

  • Constructor Details

    • MathUtils

      public MathUtils()

  • Method Details

    • equalValues

      public static boolean equalValues(float x1, float x2)
      Compares two float values for equality within the fixed epsilon.
      Parameters:
      x1 - the first value
      x2 - the second value

    • equalValues

      public static boolean equalValues(double x1, double x2)
      Compares two double values for equality within the fixed epsilon.
      Parameters:
      x1 - the first value
      x2 - the second value

    • equalValues

      public static boolean equalValues(float x1, float x2, float eps)
      Compares two float values for equality within the given epsilon.
      Parameters:
      x1 - the first value
      x2 - the second value
      eps - the maximum allowed difference

    • equalValues

      public static boolean equalValues(double x1, double x2, double eps)
      Compares two double values for equality within the given epsilon.
      Parameters:
      x1 - the first value
      x2 - the second value
      eps - the maximum allowed difference

    • interpolate2D

      public static float interpolate2D(float wi, float wj, float x00, float x10, float x01, float x11)
      Performs a fast linear interpolation in two dimensions i and j.
      Parameters:
      wi - weight in i-direction, a weight of 0.0 corresponds to i, 1.0 to i+1
      wj - weight in j-direction, a weight of 0.0 corresponds to j, 1.0 to j+1
      x00 - first anchor point located at (i,j)
      x10 - second anchor point located at (i+1,j)
      x01 - third anchor point located at (i,j+1)
      x11 - forth anchor point located at (i+1,j+1)
      Returns:
      the interpolated value

    • interpolate2D

      public static double interpolate2D(double wi, double wj, double x00, double x10, double x01, double x11)
      Performs a fast linear interpolation in two dimensions i and j.
      Parameters:
      wi - weight in i-direction, a weight of 0.0 corresponds to i, 1.0 to i+1
      wj - weight in j-direction, a weight of 0.0 corresponds to j, 1.0 to j+1
      x00 - first anchor point located at (i,j)
      x10 - second anchor point located at (i+1,j)
      x01 - third anchor point located at (i,j+1)
      x11 - forth anchor point located at (i+1,j+1)
      Returns:
      the interpolated value

    • floorAndCrop

      public static int floorAndCrop(double x, int min, int max)
      First calls Math.floor with x and then crops the resulting value to the range min to max.

    • roundAndCrop

      public static int roundAndCrop(float x, int min, int max)
      First calls Math.round with x and then crops the resulting value to the range min to max.

    • roundAndCrop

      public static long roundAndCrop(double value, long min, long max)
      First calls Math.round with value and then crops the resulting value to the range min to max.
      Parameters:
      value - the value to round and crop
      min - the minimum value of the crop range
      max - the maximum value of the crop range
      Returns:
      the rounded and cropped value

    • floorInt

      public static int floorInt(double value)
      Returns (int) Math.floor(value).
      Parameters:
      value - the double value to be converted
      Returns:
      the integer value corresponding to the floor of value

    • floorLong

      public static long floorLong(double x)
      Returns (long) Math.floor(x).
      Parameters:
      x - the value to be converted
      Returns:
      the long integer value corresponding to the floor of x

    • ceilInt

      public static int ceilInt(double x)
      Returns (int) Math.ceil(x).
      Parameters:
      x - the value to be converted
      Returns:
      the integer value corresponding to the ceil of x

    • ceilLong

      public static long ceilLong(double x)
      Returns (long) Math.ceil(x).
      Parameters:
      x - the value to be converted
      Returns:
      the long value corresponding to the ceil of x

    • computeRoundFactor

      public static float computeRoundFactor(float min, float max, int numDigits)
      Computes a rounding factor suitable for the given value range and number of significant digits.
      Parameters:
      min - the minimum value of the range
      max - the maximum value of the range
      numDigits - the number of significant digits, must be =0
      Returns:
      the rounded value, always a power to the base 10
      See Also:

    • computeRoundFactor

      public static double computeRoundFactor(double min, double max, int numDigits)
      Computes a rounding factor suitable for the given value range and number of significant digits after the decimal point.
      Parameters:
      min - the minimum value of the range
      max - the maximum value of the range
      numDigits - the number of significant digits after the decimal point, must be =0
      Returns:
      the rounded value, always a power to the base 10
      See Also:

    • round

      public static float round(float x, float roundFactor)
      Computes a rounded value for the given rounding factor. The given value is pre-multiplied with the rounding factor, then rounded to the closest int and then again divided by the the rounding factor.

      The rounding factor can be computed for a given value range and accuracy with the computeRoundFactor method.

      Parameters:
      x - the value to be rounded
      roundFactor - the rounding factor specifying the accuracy, should always be a power to the base 10
      Returns:
      the rounded value
      See Also:

    • round

      public static double round(double x, double roundFactor)
      Computes a rounded value for the given rounding factor. The given value is pre-multiplied with the rounding factor, then rounded to the closest int and then again divided by the the rounding factor.

      The rounding factor can be computed for a given value range and accuracy with the computeRoundFactor method.

      Parameters:
      x - the value to be rounded
      roundFactor - the rounding factor specifying the accuracy, should always be a power to the base 10
      Returns:
      the rounded value
      See Also:

    • getOrderOfMagnitude

      public static double getOrderOfMagnitude(double x)
      Returns the order of magnitude for the value x.
      Parameters:
      x - the input
      Returns:
      the order of magnitude: Math.floor(log10(x))

    • log10

      public static double log10(double x)
      Computes the common logarithm (to the base 10).
      Parameters:
      x - the input
      Returns:
      the common logarithm: Math.logging(x)/LOG10

    • createGammaCurve

      public static byte[] createGammaCurve(double gamma, byte[] f)
      Creates a quantized gamma (correction) curve for 256 samples in range from 0 to 1. The array returned for can be used as a lookup table for gamma transformations. In order to interpret the value correctly use the following code snippet: 
          byte[] f = MathUtils.createGammaCurve(gamma, null);
    for (int i = 0; i < 256; i++) {
         // transform i --> j
         j = f[i] & 0xff;
         // now use j instead of i
    }
      Parameters:
      gamma - the gamma value, reasonable range is 1/10 to 10, if 1 then each f[i] & 0xff will be i.
      f - the curve as an array of length 256. If not null, the method used this array as returen value after values have been written into it. If null, the method creates a new array and returns it.
      Returns:
      a quantized gamma (correction) curve for 256 samples

    • crop

      public static byte crop(byte val, byte min, byte max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • crop

      public static short crop(short val, short min, short max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • crop

      public static int crop(int val, int min, int max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • crop

      public static long crop(long val, long min, long max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • crop

      public static float crop(float val, float min, float max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • crop

      public static double crop(double val, double min, double max)
      Crops the value to the range min to max.
      Parameters:
      val - the value to crop
      min - the minimum crop limit
      max - the maximum crop limit

    • fitDimension

      public static Dimension fitDimension(int n, double a, double b)
      Computes an integer dimension for a given integer area that best fits the rectangle given by floating point width and height.
      Parameters:
      n - the integer area
      a - the rectangle's width
      b - the rectangle's height
      Returns:
      an integer dimension, never null

    • subdivideRectangle

      public static Rectangle[] subdivideRectangle(int width, int height, int numTilesX, int numTilesY, int extraBorder)
      Subdivides a rectangle into tiles. The coordinates of each returned tile rectangle are guaranteed to be within the given rectangle.
      Parameters:
      width - the rectangle's width
      height - the rectangle's height
      numTilesX - the number of tiles in X direction
      numTilesY - the number of tiles in Y direction
      extraBorder - an extra border size to extend each tile
      Returns:
      the tile coordinates as rectangles

    • sphereDistanceDeg

      public static final double sphereDistanceDeg(double sphereRadius, double lambda1_deg, double phi1_deg, double lambda2_deg, double phi2_deg)
      Parameters:
      sphereRadius - the radius of the sphere
      lambda1_deg - the lambda angle of point one, in degree
      phi1_deg - the phi angle of point one, in degree
      lambda2_deg - the lambda angle of point two, in degree
      phi2_deg - the phi angle of point one, in degree
      Returns:
      the distance described by the two given points (lambda/phi) on the top of sphere described by the given radius

    • sphereDistance

      public static final double sphereDistance(double sphereRadius, double lambda1_rad, double phi1_rad, double lambda2_rad, double phi2_rad)
      Parameters:
      sphereRadius - the radius of the sphere
      lambda1_rad - the lambda angle of point one, in radians
      phi1_rad - the phi angle of point one, in radians
      lambda2_rad - the lambda angle of point two, in radians
      phi2_rad - the phi angle of point one, in radians
      Returns:
      the distance described by the two given points (lambda/phi) on the top of sphere described by the given radius