org.locationtech.proj4j.geodesic

Class GeoMath

java.lang.Object

org.locationtech.proj4j.geodesic.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 and Description
static 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 and 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

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

Field Detail

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:

Constant Field Values

Method Detail

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:

u - the first number in the sum.

v - the second number in the sum.

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.

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 p_s+n x^N−n. Return 0 if N < 0. Return p_s, 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:

x - the first angle in degrees.

y - the second angle in degrees.

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).

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°.