Package net.sf.geographiclib

Class GeoMath

java.lang.Object
net.sf.geographiclib.GeoMath
public class GeoMath extends Object
Mathematical functions needed by GeographicLib.

Define mathematical functions and constants so that any version of Java can be used.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final int
    digits
    The number of binary digits in the fraction of a double precision number (equivalent to C++'s numeric_limits<double>::digits).

  • Method Summary

    Modifier and Type
    Method
    Description
    static void
    AngDiff(Pair p, double x, double y)
    The exact difference of two angles reduced to [−180°, 180°].
    static double
    AngNormalize(double x)
    Normalize an angle.
    static double
    AngRound(double x)
    Coarsen a value close to zero.
    static double
    atan2d(double y, double x)
    Evaluate the atan2 function with the result in degrees
    static double
    atanh(double x)
    The inverse hyperbolic tangent function.
    static double
    LatFix(double x)
    Normalize a latitude.
    static void
    norm(Pair p, double sinx, double cosx)
    Normalize a sine cosine pair.
    static double
    polyval(int N, double[] p, int s, double x)
    Evaluate a polynomial.
    static void
    sincosd(Pair p, double x)
    Evaluate the sine and cosine function with the argument in degrees
    static void
    sincosde(Pair p, double x, double t)
    Evaluate the sine and cosine function with reduced argument plus correction
    static double
    sq(double x)
    Square a number.
    static void
    sum(Pair p, double u, double v)
    The error-free sum of two numbers.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • digits

      public static final int digits
      The number of binary digits in the fraction of a double precision number (equivalent to C++'s numeric_limits<double>::digits).
      See Also:

  • Method Details

    • sq

      public static double sq(double x)
      Square a number.

      Parameters:
      x - the argument.
      Returns:
      x2.

    • atanh

      public static double atanh(double x)
      The inverse hyperbolic tangent function. This is defined in terms of Math.log1p(x) in order to maintain accuracy near x = 0. In addition, the odd parity of the function is enforced.

      Parameters:
      x - the argument.
      Returns:
      atanh(x).

    • norm

      public static void norm(Pair p, double sinx, double cosx)
      Normalize a sine cosine pair.

      Parameters:
      p - return parameter for normalized quantities with sinx2 + cosx2 = 1.
      sinx - the sine.
      cosx - the cosine.

    • sum

      public static void sum(Pair p, double u, double v)
      The error-free sum of two numbers.

      Parameters:
      p - output Pair(s, t) with s = round(u + v) and t = u + v - s.

      See D. E. Knuth, TAOCP, Vol 2, 4.2.2, Theorem B.

      u - the first number in the sum.
      v - the second number in the sum.

    • polyval

      public static double polyval(int N, double[] p, int s, double x)
      Evaluate a polynomial.

      Parameters:
      N - the order of the polynomial.
      p - the coefficient array (of size N + s + 1 or more).
      s - starting index for the array.
      x - the variable.
      Returns:
      the value of the polynomial.

      Evaluate y = ∑n=0..N ps+n xN−n. Return 0 if N < 0. Return ps, if N = 0 (even if x is infinite or a nan). The evaluation uses Horner's method.

    • AngRound

      public static double AngRound(double x)
      Coarsen a value close to zero.

      Parameters:
      x - the argument
      Returns:
      the coarsened value.

      This makes the smallest gap in x = 1/16 − nextafter(1/16, 0) = 1/257 for reals = 0.7 pm on the earth if x is an angle in degrees. (This is about 1000 times more resolution than we get with angles around 90 degrees.) We use this to avoid having to deal with near singular cases when x is non-zero but tiny (e.g., 10−200). This converts −0 to +0; however tiny negative numbers get converted to −0.

    • AngNormalize

      public static double AngNormalize(double x)
      Normalize an angle.

      Parameters:
      x - the angle in degrees.
      Returns:
      the angle reduced to the range [−180°, 180°).

      The range of x is unrestricted.

    • LatFix

      public static double LatFix(double x)
      Normalize a latitude.

      Parameters:
      x - the angle in degrees.
      Returns:
      x if it is in the range [−90°, 90°], otherwise return NaN.

    • AngDiff

      public static void AngDiff(Pair p, double x, double y)
      The exact difference of two angles reduced to [−180°, 180°].

      Parameters:
      p - output Pair(d, e) with d being the rounded difference and e being the error.

      This computes z = y − x exactly, reduced to [−180°, 180°]; and then sets z = d + e where d is the nearest representable number to z and e is the truncation error. If z = ±0° or ±180°, then the sign of d is given by the sign of y − x. The maximum absolute value of e is 2−26 (for doubles).

      x - the first angle in degrees.
      y - the second angle in degrees.

    • sincosd

      public static void sincosd(Pair p, double x)
      Evaluate the sine and cosine function with the argument in degrees
      Parameters:
      p - return Pair(s, t) with s = sin(x) and c = cos(x).
      x - in degrees.

      The results obey exactly the elementary properties of the trigonometric functions, e.g., sin 9° = cos 81° = − sin 123456789°.

    • sincosde

      public static void sincosde(Pair p, double x, double t)
      Evaluate the sine and cosine function with reduced argument plus correction
      Parameters:
      p - return Pair(s, t) with s = sin(x + t) and c = cos(x + t).
      x - reduced angle in degrees.
      t - correction in degrees.

      This is a variant of GeoMath.sincosd allowing a correction to the angle to be supplied. x x must be in [−180°, 180°] and t is assumed to be a small correction. GeoMath.AngRound is applied to the reduced angle to prevent problems with x + t being extremely close but not exactly equal to one of the four cardinal directions.

    • atan2d

      public static double atan2d(double y, double x)
      Evaluate the atan2 function with the result in degrees
      Parameters:
      y - the sine of the angle
      x - the cosine of the angle
      Returns:
      atan2(y, x) in degrees.

      The result is in the range [−180° 180°]. N.B., atan2d(±0, −1) = ±180°.