Classes
class	InverseData

class	InverseStartV

class	Lambda12V

class	LengthsV

Public Member Functions
GeodesicData	ArcDirect (double lat1, double lon1, double azi1, double a12)

GeodesicData	ArcDirect (double lat1, double lon1, double azi1, double a12, int outmask)

GeodesicLine	ArcDirectLine (double lat1, double lon1, double azi1, double a12)

GeodesicLine	ArcDirectLine (double lat1, double lon1, double azi1, double a12, int caps)

GeodesicData	Direct (double lat1, double lon1, double azi1, boolean arcmode, double s12_a12, int outmask)

GeodesicData	Direct (double lat1, double lon1, double azi1, double s12)

GeodesicData	Direct (double lat1, double lon1, double azi1, double s12, int outmask)

GeodesicLine	DirectLine (double lat1, double lon1, double azi1, double s12)

GeodesicLine	DirectLine (double lat1, double lon1, double azi1, double s12, int caps)

double	EllipsoidArea ()

double	Flattening ()

GeodesicLine	GenDirectLine (double lat1, double lon1, double azi1, boolean arcmode, double s12_a12, int caps)

	Geodesic (double a, double f)

GeodesicData	Inverse (double lat1, double lon1, double lat2, double lon2)

GeodesicData	Inverse (double lat1, double lon1, double lat2, double lon2, int outmask)

GeodesicLine	InverseLine (double lat1, double lon1, double lat2, double lon2)

GeodesicLine	InverseLine (double lat1, double lon1, double lat2, double lon2, int caps)

GeodesicLine	Line (double lat1, double lon1, double azi1)

GeodesicLine	Line (double lat1, double lon1, double azi1, int caps)

double	MajorRadius ()

Static Public Attributes
static final Geodesic	WGS84

Protected Member Functions
void	A3coeff ()

double	A3f (double eps)

void	C3coeff ()

void	C3f (double eps, double c[])

void	C4coeff ()

void	C4f (double eps, double c[])

Static Protected Member Functions
static double	A1m1f (double eps)

static double	A2m1f (double eps)

static void	C1f (double eps, double c[])

static void	C1pf (double eps, double c[])

static void	C2f (double eps, double c[])

static double	SinCosSeries (boolean sinp, double sinx, double cosx, double c[])

Protected Attributes
double	_a

Static Protected Attributes
static final int	GEOGRAPHICLIB_GEODESIC_ORDER = 6

static final int	nA1_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nA2_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nA3_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nA3x_ = nA3_

static final int	nC1_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nC1p_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nC2_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nC3_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nC3x_ = (nC3_ * (nC3_ - 1)) / 2

static final int	nC4_ = GEOGRAPHICLIB_GEODESIC_ORDER

static final int	nC4x_ = (nC4_ * (nC4_ + 1)) / 2

static final double	tiny_ = Math.sqrt(GeoMath.min)

Private Member Functions
InverseData	InverseInt (double lat1, double lon1, double lat2, double lon2, int outmask)

InverseStartV	InverseStart (double sbet1, double cbet1, double dn1, double sbet2, double cbet2, double dn2, double lam12, double slam12, double clam12, double C1a[], double C2a[])

Lambda12V	Lambda12 (double sbet1, double cbet1, double dn1, double sbet2, double cbet2, double dn2, double salp1, double calp1, double slam120, double clam120, boolean diffp, double C1a[], double C2a[], double C3a[])

LengthsV	Lengths (double eps, double sig12, double ssig1, double csig1, double dn1, double ssig2, double csig2, double dn2, double cbet1, double cbet2, int outmask, double C1a[], double C2a[])

Static Private Member Functions
static double	Astroid (double x, double y)

Private Attributes
double	_A3x []

double	_n

Static Private Attributes
static final int	maxit1_ = 20

static final int	maxit2_ = maxit1_ + GeoMath.digits + 10

static final double	tol0_ = GeoMath.epsilon

static final double	tol1_ = 200 * tol0_

static final double	tol2_ = Math.sqrt(tol0_)

static final double	tolb_ = tol0_ * tol2_

static final double	xthresh_ = 1000 * tol2_

Detailed Description

Geodesic calculations.

The shortest path between two points on a ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic. Its length is s12 and the geodesic from point 1 to point 2 has azimuths azi1 and azi2 at the two end points. (The azimuth is the heading measured clockwise from north. azi2 is the "forward" azimuth, i.e., the heading that takes you beyond point 2 not back to point 1.)

Given lat1, lon1, azi1, and s12, we can determine lat2, lon2, and azi2. This is the direct geodesic problem and its solution is given by the function Direct. (If s12 is sufficiently large that the geodesic wraps more than halfway around the earth, there will be another geodesic between the points with a smaller s12.)

Given lat1, lon1, lat2, and lon2, we can determine azi1, azi2, and s12. This is the inverse geodesic problem, whose solution is given by Inverse. Usually, the solution to the inverse problem is unique. In cases where there are multiple solutions (all with the same s12, of course), all the solutions can be easily generated once a particular solution is provided.

The standard way of specifying the direct problem is the specify the distance s12 to the second point. However it is sometimes useful instead to specify the arc length a12 (in degrees) on the auxiliary sphere. This is a mathematical construct used in solving the geodesic problems. The solution of the direct problem in this form is provided by ArcDirect. An arc length in excess of 180° indicates that the geodesic is not a shortest path. In addition, the arc length between an equatorial crossing and the next extremum of latitude for a geodesic is 90°.

This class can also calculate several other quantities related to geodesics. These are:

reduced length. If we fix the first point and increase azi1 by dazi1 (radians), the second point is displaced m12 dazi1 in the direction azi2 + 90°. The quantity m12 is called the "reduced length" and is symmetric under interchange of the two points. On a curved surface the reduced length obeys a symmetry relation, m12 + m21 = 0. On a flat surface, we have m12 = s12. The ratio s12/m12 gives the azimuthal scale for an azimuthal equidistant projection.
geodesic scale. Consider a reference geodesic and a second geodesic parallel to this one at point 1 and separated by a small distance dt. The separation of the two geodesics at point 2 is M12 dt where M12 is called the "geodesic scale". M21 is defined similarly (with the geodesics being parallel at point 2). On a flat surface, we have M12 = M21 = 1. The quantity 1/M12 gives the scale of the Cassini-Soldner projection.
area. The area between the geodesic from point 1 to point 2 and the equation is represented by S12; it is the area, measured counter-clockwise, of the geodesic quadrilateral with corners (lat1,lon1), (0,lon1), (0,lon2), and (lat2,lon2). It can be used to compute the area of any simple geodesic polygon.

The quantities m12, M12, M21 which all specify the behavior of nearby geodesics obey addition rules. If points 1, 2, and 3 all lie on a single geodesic, then the following rules hold:

s13 = s12 + s23
a13 = a12 + a23
S13 = S12 + S23
m13 = m12 M23 + m23 M21
M13 = M12 M23 − (1 − M12 M21) m23 / m12
M31 = M32 M21 − (1 − M23 M32) m12 / m23

The results of the geodesic calculations are bundled up into a {} object which includes the input parameters and all the computed results, i.e., lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12. The functions Direct, ArcDirect, and Inverse include an optional final argument outmask which allows you specify which results should be computed and returned. If you omit outmask, then the "standard" geodesic results are computed (latitudes, longitudes, azimuths, and distance). outmask is bitor'ed combination of {} values. For example, if you wish just to compute the distance between two points you would call, e.g., GeodesicData g = Geodesic.WGS84.Inverse(lat1, lon1, lat2, lon2, GeodesicMask.DISTANCE); <p<blockquote> Additional functionality is provided by the GeodesicLine class, which allows a sequence of points along a geodesic to be computed.

The shortest distance returned by the solution of the inverse problem is (obviously) uniquely defined. However, in a few special cases there are multiple azimuths which yield the same shortest distance. Here is a catalog of those cases:

lat1 = −lat2 (with neither point at a pole). If azi1 = azi2, the geodesic is unique. Otherwise there are two geodesics and the second one is obtained by setting [azi1, azi2] → [azi2, azi1], [M12, M21] → [M21, M12], S12 → −S12. (This occurs when the longitude difference is near ±180° for oblate ellipsoids.)
lon2 = lon1 ± 180° (with neither point at a pole). If azi1 = 0° or ±180°, the geodesic is unique. Otherwise there are two geodesics and the second one is obtained by setting [ azi1, azi2] → [−azi1, −azi2], S12 → − S12. (This occurs when lat2 is near −lat1 for prolate ellipsoids.)
Points 1 and 2 at opposite poles. There are infinitely many geodesics which can be generated by setting [azi1, azi2] → [azi1, azi2] + [d, −d], for arbitrary d. (For spheres, this prescription applies when points 1 and 2 are antipodal.)
s12 = 0 (coincident points). There are infinitely many geodesics which can be generated by setting [azi1, azi2] → [azi1, azi2] + [d, d], for arbitrary d.

The calculations are accurate to better than 15 nm (15 nanometers) for the WGS84 ellipsoid. See Sec. 9 of arXiv:1102.1215v1 for details. The algorithms used by this class are based on series expansions using the flattening f as a small parameter. These are only accurate for |f| < 0.02; however reasonably accurate results will be obtained for |f| < 0.2. Here is a table of the approximate maximum error (expressed as a distance) for an ellipsoid with the same equatorial radius as the WGS84 ellipsoid and different values of the flattening.

    |f|      error
    0.01     25 nm
    0.02     30 nm
    0.05     10 um
    0.1     1.5 mm
    0.2     300 mm

<p<blockquote>

The algorithms are described in

C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013) (addenda).

Example of use:

// Solve the direct geodesic problem.
 
// This program reads in lines with lat1, lon1, azi1, s12 and prints
// out lines with lat2, lon2, azi2 (for the WGS84 ellipsoid).
 
import java.util.*;
import net.sf.geographiclib.*;
public class Direct {
  public static void main(String[] args) {
    try {
      Scanner in = new Scanner(System.in);
      double lat1, lon1, azi1, s12;
      while (true) {
        lat1 = in.nextDouble(); lon1 = in.nextDouble();
        azi1 = in.nextDouble(); s12 = in.nextDouble();
        GeodesicData g = Geodesic.WGS84.Direct(lat1, lon1, azi1, s12);
        System.out.println(g.lat2 + " " + g.lon2 + " " + g.azi2);
      }
    }
    catch (Exception e) {}
  }
}

Definition at line 202 of file Geodesic.java.

Constructor & Destructor Documentation

◆ Geodesic()

net.sf.geographiclib.Geodesic.Geodesic	(	double	a,
		double	f
	)

inline

Constructor for a ellipsoid with

Parameters

a	equatorial radius (meters).
f	flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.

Exceptions

GeographicErr if a or (1 − f ) a is not positive.

Definition at line 250 of file Geodesic.java.

Member Function Documentation

◆ A1m1f()

static double net.sf.geographiclib.Geodesic.A1m1f ( double eps )

inlinestaticprotected

Definition at line 1676 of file Geodesic.java.

◆ A2m1f()

static double net.sf.geographiclib.Geodesic.A2m1f ( double eps )

inlinestaticprotected

Definition at line 1743 of file Geodesic.java.

◆ A3coeff()

void net.sf.geographiclib.Geodesic.A3coeff ( )

inlineprotected

Definition at line 1782 of file Geodesic.java.

◆ A3f()

double net.sf.geographiclib.Geodesic.A3f ( double eps )

inlineprotected

Definition at line 1644 of file Geodesic.java.

◆ ArcDirect() [1/2]

GeodesicData net.sf.geographiclib.Geodesic.ArcDirect	(	double	lat1,
		double	lon1,
		double	azi1,
		double	a12
	)

inline

Solve the direct geodesic problem where the length of the geodesic is specified in terms of arc length.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
a12	arc length between point 1 and point 2 (degrees); it can be negative.

Returns: a GeodesicData object with the following fields: lat1, lon1, azi1, lat2, lon2, azi2, s12, a12.

lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°].

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)

Definition at line 366 of file Geodesic.java.

◆ ArcDirect() [2/2]

GeodesicData net.sf.geographiclib.Geodesic.ArcDirect	(	double	lat1,
		double	lon1,
		double	azi1,
		double	a12,
		int	outmask
	)

inline

Solve the direct geodesic problem where the length of the geodesic is specified in terms of arc length and with a subset of the geodesic results returned.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
a12	arc length between point 1 and point 2 (degrees); it can be negative.
outmask	a bitor'ed combination of GeodesicMask values specifying which results should be returned.

Returns: a GeodesicData object with the fields specified by outmask computed.

lat1, lon1, azi1, and a12 are always included in the returned result. The value of lon2 returned is in the range [−180°, 180°], unless the outmask includes the {} flag.

Definition at line 391 of file Geodesic.java.

◆ ArcDirectLine() [1/2]

GeodesicLine net.sf.geographiclib.Geodesic.ArcDirectLine	(	double	lat1,
		double	lon1,
		double	azi1,
		double	a12
	)

inline

Define a GeodesicLine in terms of the direct geodesic problem specified in terms of arc length with all capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
a12	arc length between point 1 and point 2 (degrees); it can be negative.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.

lat1 should be in the range [−90°, 90°].

Definition at line 523 of file Geodesic.java.

◆ ArcDirectLine() [2/2]

GeodesicLine net.sf.geographiclib.Geodesic.ArcDirectLine	(	double	lat1,
		double	lon1,
		double	azi1,
		double	a12,
		int	caps
	)

inline

Define a GeodesicLine in terms of the direct geodesic problem specified in terms of arc length with a subset of the capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
a12	arc length between point 1 and point 2 (degrees); it can be negative.
caps	bitor'ed combination of GeodesicMask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine.Position.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.

lat1 should be in the range [−90°, 90°].

Definition at line 549 of file Geodesic.java.

◆ Astroid()

static double net.sf.geographiclib.Geodesic.Astroid	(	double	x,
		double	y
	)

inlinestaticprivate

Definition at line 1324 of file Geodesic.java.

◆ C1f()

static void net.sf.geographiclib.Geodesic.C1f	(	double	eps,
		double	c[]
	)

inlinestaticprotected

Definition at line 1687 of file Geodesic.java.

◆ C1pf()

static void net.sf.geographiclib.Geodesic.C1pf	(	double	eps,
		double	c[]
	)

inlinestaticprotected

Definition at line 1715 of file Geodesic.java.

◆ C2f()

static void net.sf.geographiclib.Geodesic.C2f	(	double	eps,
		double	c[]
	)

inlinestaticprotected

Definition at line 1754 of file Geodesic.java.

◆ C3coeff()

void net.sf.geographiclib.Geodesic.C3coeff ( )

inlineprotected

Definition at line 1806 of file Geodesic.java.

◆ C3f()

void net.sf.geographiclib.Geodesic.C3f	(	double	eps,
		double	c[]
	)

inlineprotected

Definition at line 1649 of file Geodesic.java.

◆ C4coeff()

void net.sf.geographiclib.Geodesic.C4coeff ( )

inlineprotected

Definition at line 1849 of file Geodesic.java.

◆ C4f()

void net.sf.geographiclib.Geodesic.C4f	(	double	eps,
		double	c[]
	)

inlineprotected

Definition at line 1662 of file Geodesic.java.

◆ Direct() [1/3]

GeodesicData net.sf.geographiclib.Geodesic.Direct	(	double	lat1,
		double	lon1,
		double	azi1,
		boolean	arcmode,
		double	s12_a12,
		int	outmask
	)

inline

The general direct geodesic problem. Direct and ArcDirect are defined in terms of this function.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
arcmode	boolean flag determining the meaning of the s12_a12.
s12_a12	if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative.
outmask	a bitor'ed combination of GeodesicMask values specifying which results should be returned.

Returns: a GeodesicData object with the fields specified by outmask computed.

The GeodesicMask values possible for outmask are

outmask |= GeodesicMask#LATITUDE for the latitude lat2;
outmask |= GeodesicMask#LONGITUDE for the latitude lon2;
outmask |= GeodesicMask#AZIMUTH for the latitude azi2;
outmask |= GeodesicMask#DISTANCE for the distance s12;
outmask |= GeodesicMask#REDUCEDLENGTH for the reduced length m12;
outmask |= GeodesicMask#GEODESICSCALE for the geodesic scales M12 and M21;
outmask |= GeodesicMask#AREA for the area S12;
outmask |= GeodesicMask#ALL for all of the above;
outmask |= GeodesicMask#LONG_UNROLL, if set then lon1 is unchanged and lon2 − lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid. Otherwise lon1 and lon2 are both reduced to the range [−180°, 180°].

The function value a12 is always computed and returned and this equals s12_a12 is arcmode is true. If outmask includes GeodesicMask#DISTANCE and arcmode is false, then s12 = s12_a12. It is not necessary to include {} in outmask; this is automatically included is arcmode is false.

Definition at line 452 of file Geodesic.java.

◆ Direct() [2/3]

GeodesicData net.sf.geographiclib.Geodesic.Direct	(	double	lat1,
		double	lon1,
		double	azi1,
		double	s12
	)

inline

Solve the direct geodesic problem where the length of the geodesic is specified in terms of distance.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
s12	distance between point 1 and point 2 (meters); it can be negative.

Returns: a GeodesicData object with the following fields: lat1, lon1, azi1, lat2, lon2, azi2, s12, a12.

lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°].

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)

Definition at line 313 of file Geodesic.java.

◆ Direct() [3/3]

GeodesicData net.sf.geographiclib.Geodesic.Direct	(	double	lat1,
		double	lon1,
		double	azi1,
		double	s12,
		int	outmask
	)

inline

Solve the direct geodesic problem where the length of the geodesic is specified in terms of distance and with a subset of the geodesic results returned.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
s12	distance between point 1 and point 2 (meters); it can be negative.
outmask	a bitor'ed combination of GeodesicMask values specifying which results should be returned.

Returns: a GeodesicData object with the fields specified by outmask computed.

lat1, lon1, azi1, s12, and a12 are always included in the returned result. The value of lon2 returned is in the range [−180°, 180°], unless the outmask includes the GeodesicMask#LONG_UNROLL flag.

Definition at line 337 of file Geodesic.java.

◆ DirectLine() [1/2]

GeodesicLine net.sf.geographiclib.Geodesic.DirectLine	(	double	lat1,
		double	lon1,
		double	azi1,
		double	s12
	)

inline

Define a GeodesicLine in terms of the direct geodesic problem specified in terms of distance with all capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
s12	distance between point 1 and point 2 (meters); it can be negative.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.

lat1 should be in the range [−90°, 90°].

Definition at line 477 of file Geodesic.java.

◆ DirectLine() [2/2]

GeodesicLine net.sf.geographiclib.Geodesic.DirectLine	(	double	lat1,
		double	lon1,
		double	azi1,
		double	s12,
		int	caps
	)

inline

Define a GeodesicLine in terms of the direct geodesic problem specified in terms of distance with a subset of the capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
s12	distance between point 1 and point 2 (meters); it can be negative.
caps	bitor'ed combination of GeodesicMask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine.Position.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.

lat1 should be in the range [−90°, 90°].

Definition at line 502 of file Geodesic.java.

◆ EllipsoidArea()

double net.sf.geographiclib.Geodesic.EllipsoidArea ( )

inline

Returns: total area of ellipsoid in meters². The area of a polygon encircling a pole can be found by adding EllipsoidArea()/2 to the sum of S12 for each side of the polygon.

Definition at line 1201 of file Geodesic.java.

◆ Flattening()

double net.sf.geographiclib.Geodesic.Flattening ( )

inline

Returns: f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 1194 of file Geodesic.java.

◆ GenDirectLine()

GeodesicLine net.sf.geographiclib.Geodesic.GenDirectLine	(	double	lat1,
		double	lon1,
		double	azi1,
		boolean	arcmode,
		double	s12_a12,
		int	caps
	)

inline

Define a GeodesicLine in terms of the direct geodesic problem specified in terms of either distance or arc length with a subset of the capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
arcmode	boolean flag determining the meaning of the s12_a12.
s12_a12	if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative.
caps	bitor'ed combination of GeodesicMask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine.Position.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.

lat1 should be in the range [−90°, 90°].

Definition at line 577 of file Geodesic.java.

◆ Inverse() [1/2]

GeodesicData net.sf.geographiclib.Geodesic.Inverse	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2
	)

inline

Solve the inverse geodesic problem.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
lat2	latitude of point 2 (degrees).
lon2	longitude of point 2 (degrees).

Returns: a GeodesicData object with the following fields: lat1, lon1, azi1, lat2, lon2, azi2, s12, a12.

lat1 and lat2 should be in the range [−90°, 90°]. The values of azi1 and azi2 returned are in the range [−180°, 180°].

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), taking the limit ε → 0+.

The solution to the inverse problem is found using Newton's method. If this fails to converge (this is very unlikely in geodetic applications but does occur for very eccentric ellipsoids), then the bisection method is used to refine the solution.

Definition at line 615 of file Geodesic.java.

◆ Inverse() [2/2]

GeodesicData net.sf.geographiclib.Geodesic.Inverse	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2,
		int	outmask
	)

inline

Solve the inverse geodesic problem with a subset of the geodesic results returned.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
lat2	latitude of point 2 (degrees).
lon2	longitude of point 2 (degrees).
outmask	a bitor'ed combination of GeodesicMask values specifying which results should be returned.

Returns: a GeodesicData object with the fields specified by outmask computed.

The GeodesicMask values possible for outmask are

outmask |= GeodesicMask#DISTANCE for the distance s12;
outmask |= GeodesicMask#AZIMUTH for the latitude azi2;
outmask |= GeodesicMask#REDUCEDLENGTH for the reduced length m12;
outmask |= GeodesicMask#GEODESICSCALE for the geodesic scales M12 and M21;
outmask |= GeodesicMask#AREA for the area S12;
outmask |= GeodesicMask#ALL for all of the above.
outmask |= GeodesicMask#LONG_UNROLL, if set then lon1 is unchanged and lon2 − lon1 indicates whether the geodesic is east going or west going. Otherwise lon1 and lon2 are both reduced to the range [−180°, 180°].

lat1, lon1, lat2, lon2, and a12 are always included in the returned result.

Definition at line 1049 of file Geodesic.java.

◆ InverseInt()

InverseData net.sf.geographiclib.Geodesic.InverseInt	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2,
		int	outmask
	)

inlineprivate

Definition at line 629 of file Geodesic.java.

◆ InverseLine() [1/2]

GeodesicLine net.sf.geographiclib.Geodesic.InverseLine	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2
	)

inline

Define a GeodesicLine in terms of the inverse geodesic problem with all capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
lat2	latitude of point 2 (degrees).
lon2	longitude of point 2 (degrees).

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the inverse geodesic problem.

lat1 and lat2 should be in the range [−90°, 90°].

Definition at line 1077 of file Geodesic.java.

◆ InverseLine() [2/2]

GeodesicLine net.sf.geographiclib.Geodesic.InverseLine	(	double	lat1,
		double	lon1,
		double	lat2,
		double	lon2,
		int	caps
	)

inline

Define a GeodesicLine in terms of the inverse geodesic problem with a subset of the capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
lat2	latitude of point 2 (degrees).
lon2	longitude of point 2 (degrees).
caps	bitor'ed combination of GeodesicMask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine.Position.

Returns: a GeodesicLine object.

This function sets point 3 of the GeodesicLine to correspond to point 2 of the inverse geodesic problem.

lat1 and lat2 should be in the range [−90°, 90°].

Definition at line 1102 of file Geodesic.java.

◆ InverseStart()

InverseStartV net.sf.geographiclib.Geodesic.InverseStart	(	double	sbet1,
		double	cbet1,
		double	dn1,
		double	sbet2,
		double	cbet2,
		double	dn2,
		double	lam12,
		double	slam12,
		double	clam12,
		double	C1a[],
		double	C2a[]
	)

inlineprivate

Definition at line 1387 of file Geodesic.java.

◆ Lambda12()

Lambda12V net.sf.geographiclib.Geodesic.Lambda12	(	double	sbet1,
		double	cbet1,
		double	dn1,
		double	sbet2,
		double	cbet2,
		double	dn2,
		double	salp1,
		double	calp1,
		double	slam120,
		double	clam120,
		boolean	diffp,
		double	C1a[],
		double	C2a[],
		double	C3a[]
	)

inlineprivate

Definition at line 1556 of file Geodesic.java.

◆ Lengths()

LengthsV net.sf.geographiclib.Geodesic.Lengths	(	double	eps,
		double	sig12,
		double	ssig1,
		double	csig1,
		double	dn1,
		double	ssig2,
		double	csig2,
		double	dn2,
		double	cbet1,
		double	cbet2,
		int	outmask,
		double	C1a[],
		double	C2a[]
	)

inlineprivate

Definition at line 1262 of file Geodesic.java.

◆ Line() [1/2]

GeodesicLine net.sf.geographiclib.Geodesic.Line	(	double	lat1,
		double	lon1,
		double	azi1
	)

inline

Set up to compute several points on a single geodesic with all capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).

Returns: a GeodesicLine object.

lat1 should be in the range [−90°, 90°]. The full set of capabilities is included.

If the point is at a pole, the azimuth is defined by keeping the lon1 fixed, writing lat1 = ±(90 − ε), taking the limit ε → 0+.

Definition at line 1130 of file Geodesic.java.

◆ Line() [2/2]

GeodesicLine net.sf.geographiclib.Geodesic.Line	(	double	lat1,
		double	lon1,
		double	azi1,
		int	caps
	)

inline

Set up to compute several points on a single geodesic with a subset of the capabilities included.

Parameters

lat1	latitude of point 1 (degrees).
lon1	longitude of point 1 (degrees).
azi1	azimuth at point 1 (degrees).
caps	bitor'ed combination of GeodesicMask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to {GeodesicLine.Position}. a GeodesicLine} object. The GeodesicMask values are caps \|= GeodesicMask#LATITUDE for the latitude lat2; this is added automatically; caps \|= GeodesicMask#LONGITUDE for the latitude lon2; caps \|= GeodesicMask#AZIMUTH for the azimuth azi2; this is added automatically; caps \|= GeodesicMask#DISTANCE for the distance s12; caps \|= GeodesicMask#REDUCEDLENGTH for the reduced length m12; caps \|= GeodesicMask#GEODESICSCALE for the geodesic scales M12 and M21; caps \|= GeodesicMask#AREA for the area S12; caps \|= GeodesicMask#DISTANCE_IN permits the length of the geodesic to be given in terms of s12; without this capability the length can only be specified in terms of arc length; caps \|= GeodesicMask#ALL for all of the above.

If the point is at a pole, the azimuth is defined by keeping lon1 fixed, writing lat1 = ±(90 − ε), and taking the limit ε → 0+.

Definition at line 1180 of file Geodesic.java.

◆ MajorRadius()

double net.sf.geographiclib.Geodesic.MajorRadius ( )

inline

Returns: a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 1188 of file Geodesic.java.

◆ SinCosSeries()

static double net.sf.geographiclib.Geodesic.SinCosSeries	(	boolean	sinp,
		double	sinx,
		double	cosx,
		double	c[]
	)

inlinestaticprotected

Definition at line 1229 of file Geodesic.java.

Member Data Documentation

◆ _a

double net.sf.geographiclib.Geodesic._a

protected

Definition at line 237 of file Geodesic.java.

◆ _A3x

double net.sf.geographiclib.Geodesic._A3x[]

private

Definition at line 239 of file Geodesic.java.

◆ _n

double net.sf.geographiclib.Geodesic._n

private

Definition at line 238 of file Geodesic.java.

◆ GEOGRAPHICLIB_GEODESIC_ORDER

final int net.sf.geographiclib.Geodesic.GEOGRAPHICLIB_GEODESIC_ORDER = 6

staticprotected

The order of the expansions used by Geodesic.

Definition at line 207 of file Geodesic.java.

◆ maxit1_

final int net.sf.geographiclib.Geodesic.maxit1_ = 20

staticprivate

Definition at line 220 of file Geodesic.java.

◆ maxit2_

final int net.sf.geographiclib.Geodesic.maxit2_ = maxit1_ + GeoMath.digits + 10

staticprivate

Definition at line 221 of file Geodesic.java.

◆ nA1_

final int net.sf.geographiclib.Geodesic.nA1_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 209 of file Geodesic.java.

◆ nA2_

final int net.sf.geographiclib.Geodesic.nA2_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 212 of file Geodesic.java.

◆ nA3_

final int net.sf.geographiclib.Geodesic.nA3_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 214 of file Geodesic.java.

◆ nA3x_

final int net.sf.geographiclib.Geodesic.nA3x_ = nA3_

staticprotected

Definition at line 215 of file Geodesic.java.

◆ nC1_

final int net.sf.geographiclib.Geodesic.nC1_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 210 of file Geodesic.java.

◆ nC1p_

final int net.sf.geographiclib.Geodesic.nC1p_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 211 of file Geodesic.java.

◆ nC2_

final int net.sf.geographiclib.Geodesic.nC2_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 213 of file Geodesic.java.

◆ nC3_

final int net.sf.geographiclib.Geodesic.nC3_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 216 of file Geodesic.java.

◆ nC3x_

final int net.sf.geographiclib.Geodesic.nC3x_ = (nC3_ * (nC3_ - 1)) / 2

staticprotected

Definition at line 217 of file Geodesic.java.

◆ nC4_

final int net.sf.geographiclib.Geodesic.nC4_ = GEOGRAPHICLIB_GEODESIC_ORDER

staticprotected

Definition at line 218 of file Geodesic.java.

◆ nC4x_

final int net.sf.geographiclib.Geodesic.nC4x_ = (nC4_ * (nC4_ + 1)) / 2

staticprotected

Definition at line 219 of file Geodesic.java.

◆ tiny_

final double net.sf.geographiclib.Geodesic.tiny_ = Math.sqrt(GeoMath.min)

staticprotected

Definition at line 226 of file Geodesic.java.

◆ tol0_

final double net.sf.geographiclib.Geodesic.tol0_ = GeoMath.epsilon

staticprivate

Definition at line 227 of file Geodesic.java.

◆ tol1_

final double net.sf.geographiclib.Geodesic.tol1_ = 200 * tol0_

staticprivate

Definition at line 231 of file Geodesic.java.

◆ tol2_

final double net.sf.geographiclib.Geodesic.tol2_ = Math.sqrt(tol0_)

staticprivate

Definition at line 232 of file Geodesic.java.

◆ tolb_

final double net.sf.geographiclib.Geodesic.tolb_ = tol0_ * tol2_

staticprivate

Definition at line 234 of file Geodesic.java.

◆ WGS84

final Geodesic net.sf.geographiclib.Geodesic.WGS84

static

Initial value:

=

new Geodesic(Constants.WGS84_a, Constants.WGS84_f)

A global instantiation of Geodesic with the parameters for the WGS84 ellipsoid.

Definition at line 1207 of file Geodesic.java.

◆ xthresh_

final double net.sf.geographiclib.Geodesic.xthresh_ = 1000 * tol2_

staticprivate

Definition at line 235 of file Geodesic.java.

The documentation for this class was generated from the following file:

Geodesic.java

Classes

Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Geodesic()

Member Function Documentation

◆ A1m1f()

◆ A2m1f()

◆ A3coeff()

◆ A3f()

◆ ArcDirect() [1/2]

◆ ArcDirect() [2/2]

◆ ArcDirectLine() [1/2]

◆ ArcDirectLine() [2/2]

◆ Astroid()

◆ C1f()

◆ C1pf()

◆ C2f()

◆ C3coeff()

◆ C3f()

◆ C4coeff()

◆ C4f()

◆ Direct() [1/3]

◆ Direct() [2/3]

◆ Direct() [3/3]

◆ DirectLine() [1/2]

◆ DirectLine() [2/2]

◆ EllipsoidArea()

◆ Flattening()

◆ GenDirectLine()

◆ Inverse() [1/2]

◆ Inverse() [2/2]

◆ InverseInt()

◆ InverseLine() [1/2]

◆ InverseLine() [2/2]

◆ InverseStart()

◆ Lambda12()

◆ Lengths()

◆ Line() [1/2]

◆ Line() [2/2]

◆ MajorRadius()

◆ SinCosSeries()

Member Data Documentation

◆ _a

◆ _A3x

◆ _n

◆ GEOGRAPHICLIB_GEODESIC_ORDER

◆ maxit1_

◆ maxit2_

◆ nA1_

◆ nA2_

◆ nA3_

◆ nA3x_

◆ nC1_

◆ nC1p_

◆ nC2_

◆ nC3_

◆ nC3x_

◆ nC4_

◆ nC4x_

◆ tiny_

◆ tol0_

◆ tol1_

◆ tol2_

◆ tolb_

◆ WGS84

◆ xthresh_