Collection of static functions to manipulate geographic information. More...

#include <GeoTessUtils.h>

Public Member Functions
	GeoTessUtils ()

virtual	~GeoTessUtils ()

virtual int	class_size () const

Static Public Member Functions
static string	class_name ()

static string	getVersion ()

static double	dot (const double const v0, const double const v1)

static double	scalarTripleProduct (const double const v0, const double const v1, const double *const v2)

static double	getGeocentricLat (const double &lat)

static double	getGeographicLat (const double &lat)

static string	getLatLonString (const double *const v)

static string	getLonLatString (const double *const v)

static double	azimuthDegrees (const double const v1, const double const v2, double errorValue)

static double	azimuth (const double const v1, const double const v2, double errorValue)

static void	rotate (const double const x, const double const p, double a, double *const z)

static double **	getGreatCircle (const double const v0, const double const v1)

static void	getGreatCircle (const double const v0, const double const v1, double **const gc)

static double **	getGreatCircle (const double *const v, double azimuth)

static void	getGreatCircle (const double const v, double azimuth, double *const gc)

static int	getGreatCirclePoints (double ptA, double ptB, const double &delta, const bool &onCenters)

static double	getGreatCirclePoints (double ptA, double ptB, const int &npoints, const bool &onCenters, double **points)

static double	getGreatCirclePoints (double ptA, double ptB, const double &delta, const bool &onCenters, double **points, int &npoints)

static double	length (const double *const u)

static void	getTransform (const double const u, const double const v, double **const t)

static void	transform (const double x, double const const const t, double const g)

static void	readString (string &s, ifstream &ifs)

static void	writeString (ofstream &ofs, const string &s)

static double	angle (const double const v0, const double const v1)

static double	angleDegrees (const double const v0, const double const v1)

static double	getDistance3D (const double const v0, double r0, const double const v1, double r1)

static double	getEarthRadius (const double *const v)

static double	getLat (const double *const v)

static double	getLon (const double *const v)

static double	getLatDegrees (const double *const v)

static double	getLonDegrees (const double *const v)

static double *	getVectorDegrees (const double &lat, const double &lon)

static double *	getVectorDegrees (const double &lat, const double &lon, double *v)

static double *	getVector (const double &lat, const double &lon)

static double *	getVector (const double &lat, const double &lon, double *v)

static void	normalizeFast (double *const u)

static double	normalize (double *const u)

static void	cross (const double const v1, const double const v2, double *const rslt)

static double *	crossNormal (const double const u, const double const v)

static double	crossNormal (const double const u, const double const v, double *const w)

static double	crossNorth (const double const u, double const w)

static bool	vectorTripleProduct (const double const v0, const double const v1, const double const v2, double const rslt)

static bool	vectorTripleProductNorthPole (const double const u, double const w)

static void	circumCenter (const double const v0, const double const v1, const double const v2, double const vs)

static void	circumCenterPlus (const double const v0, const double const v1, const double const v2, double const vs)

static double *	circumCenterPlus (const double const v0, const double const v1, const double *const v2)

static void	circumCenterPlus (double const const const t, double *const vs)

static bool	moveDistAz (const double const w, double distance, double azimuth, double const u)

static void	move (const double const w, const double const vtp, double a, double *const u)

static bool	moveNorth (const double const x, double distance, double const z)

static bool	isPole (const double *const u)

static bool	parallel (const double const u, const double const v)

static double *	getGreatCirclePoint (double const const const greatCircle, double distance)

static void	getGreatCirclePoint (double const const const greatCircle, double distance, double *const v)

static double	getTriangleArea (const double const v0, const double const v1, const double *const v2)

static double	getTriangleArea (const double const v0, const double const v1, const double const v2, double work1, double work2, double work3)

static double *	center (double const const const v, int n)

static void	center (vector< double * > v, double *x)

Static Public Attributes
static bool	approximateLatitudes

Detailed Description

Collection of static functions to manipulate geographic information.

The Utils class provides basic static utility functions for GeoTess to manipulate geographic information.

Definition at line 69 of file GeoTessUtils.h.

Constructor & Destructor Documentation

◆ GeoTessUtils()

geotess::GeoTessUtils::GeoTessUtils ( )

inline

Default constructor.

Definition at line 100 of file GeoTessUtils.h.

◆ ~GeoTessUtils()

virtual geotess::GeoTessUtils::~GeoTessUtils ( )

inlinevirtual

Destructor.

Definition at line 105 of file GeoTessUtils.h.

Member Function Documentation

◆ angle()

static double geotess::GeoTessUtils::angle	(	const double *const	v0,
		const double *const	v1
	)

inlinestatic

Return the angular distance in radians between two unit vectors.

Parameters

v0	a 3 component unit vector
v1	a 3 component unit vector

Returns: angular distance in radians.

Definition at line 497 of file GeoTessUtils.h.

◆ angleDegrees()

static double geotess::GeoTessUtils::angleDegrees	(	const double *const	v0,
		const double *const	v1
	)

inlinestatic

Return the angular distance in degrees between two unit vectors.

Parameters

v0	a 3 component unit vector
v1	a 3 component unit vector

Returns: angular distance in degrees.

Definition at line 515 of file GeoTessUtils.h.

◆ azimuth()

static double geotess::GeoTessUtils::azimuth	(	const double *const	v1,
		const double *const	v2,
		double	errorValue
	)

static

Find the azimuth from unit vectors v1 to v2. Result will be between -PI and PI radians.

Parameters

v1	The point from which the azimuth will be directed toward v2.
v2	The point to which the azimuth will be directed from v1.
errorValue	if v1 and v2 are parallel, or if v1 is either the north or south pole, then return errorValue

Returns: the azimuth from v1 to v2, in radians clockwise from north, or errorValue

◆ azimuthDegrees()

static double geotess::GeoTessUtils::azimuthDegrees	(	const double *const	v1,
		const double *const	v2,
		double	errorValue
	)

static

Find the azimuth from unit vectors v1 to v2. Result will be between -180 and 180 degrees

Parameters

v1	The point from which the azimuth will be directed toward v2.
v2	The point to which the azimuth will be directed from v1.
errorValue	if v1 and v2 are parallel, or if v1 is either the north or south pole, then return errorValue

Returns: the azimuth from v1 to v2, in degrees clockwise from north, or errorValue

◆ center() [1/2]

static double* geotess::GeoTessUtils::center	(	double const const const	v,
		int	n
	)

inlinestatic

Return the normalized vector sum of the supplied unit vectors.

Parameters

v	one or more unit vectors
n	size of v

Returns: the normalized vector sum of the supplied unit vectors.

Definition at line 1173 of file GeoTessUtils.h.

◆ center() [2/2]

static void geotess::GeoTessUtils::center	(	vector< double * >	v,
		double *	x
	)

inlinestatic

Return the normalized vector sum of the supplied unit vectors.

Parameters

v	one or more unit vectors
x	the 3-element array of double in which to place the computed unit vector.

Definition at line 1197 of file GeoTessUtils.h.

◆ circumCenter()

static void geotess::GeoTessUtils::circumCenter	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2,
		double *const	vs
	)

inlinestatic

Given three unit vectors, v0, v1 and v2, find the circumcenter, vs. The circumcenter is the unit vector of the center of a small circle that has all three unit vectors on its circumference.

Parameters

v0
v1
v2
vs

Definition at line 875 of file GeoTessUtils.h.

◆ circumCenterPlus() [1/3]

static double* geotess::GeoTessUtils::circumCenterPlus	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2
	)

inlinestatic

Given three unit vectors, v0, v1 and v2, find the circumcenter, vs. The circumcenter is the unit vector of the center of a small circle that has all three unit vectors on its circumference. Vectors must be specified in clockwise order. The fourth element of returned circumcenter is the dot product of the new circumcenter with one of the vertices. In other words, cc[3] = cos(ccRadius).

Caller is responsible for deleting the double* returned by this method.

Parameters

v0
v1
v2

Returns: the circumCenter: a unit vector plus cos(ccRadius)

Definition at line 929 of file GeoTessUtils.h.

◆ circumCenterPlus() [2/3]

static void geotess::GeoTessUtils::circumCenterPlus	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2,
		double *const	vs
	)

inlinestatic

Given three unit vectors, v0, v1 and v2, find the circumcenter, vs. The circumcenter is the unit vector of the center of a small circle that has all three unit vectors on its circumference. The fourth element of vs is the dot product of the new circumcenter with one of the vertices. In other words, cc[3] = cos(ccRadius).

Parameters

v0
v1
v2
vs

Definition at line 900 of file GeoTessUtils.h.

◆ circumCenterPlus() [3/3]

static void geotess::GeoTessUtils::circumCenterPlus	(	double const const const	t,
		double *const	vs
	)

inlinestatic

Given the three unit vectors, t[0], t[1] and t[2], find the circumcenter, vs. The circumcenter is the unit vector of the center of a small circle that has all three unit vectors on its circumference. The fourth element of returned circumcenter is the dot product of the new circumcenter with one of the vertices. In other words, cc[3] = cos(ccRadius).

Parameters

t	a 3 x 3 array of doubles that contains the three unit vectors of a triangle.
vs	a 4 element array that will be populated with the unit vector and the cos(ccRadius).

Returns: true if successful, false if the three input vectors do not define a triangle.

Definition at line 959 of file GeoTessUtils.h.

◆ class_name()

static string geotess::GeoTessUtils::class_name ( )

inlinestatic

Returns the class name.

Returns: class name

Definition at line 111 of file GeoTessUtils.h.

◆ class_size()

virtual int geotess::GeoTessUtils::class_size ( ) const

inlinevirtual

Returns the class size.

Returns: class size

Definition at line 118 of file GeoTessUtils.h.

◆ cross()

static void geotess::GeoTessUtils::cross	(	const double *const	v1,
		const double *const	v2,
		double *const	rslt
	)

inlinestatic

Cross product of two 3-component vectors. Result is not normalized.

Parameters

v1	vector<double> vector one.
v2	vector<double> vector two.
rslt	set to v1 cross v2 Result is not a unit vector.

Definition at line 728 of file GeoTessUtils.h.

◆ crossNormal() [1/2]

static double* geotess::GeoTessUtils::crossNormal	(	const double *const	u,
		const double *const	v
	)

inlinestatic

Normalized cross product of two 3-component unit vectors.

Parameters

u	vector one.
v	vector two.

Returns: Normalized cross product of u x v. Will be [0,0,0] if u and v are parallel.

Definition at line 746 of file GeoTessUtils.h.

◆ crossNormal() [2/2]

static double geotess::GeoTessUtils::crossNormal	(	const double *const	u,
		const double *const	v,
		double *const	w
	)

inlinestatic

Normalized cross product of two 3-component unit vectors.

Parameters

u	vector one.
v	vector two.
w	set to u cross v, normalized to unit length. If u cross v has zero length, w will equal (0,0,0).

Returns: the length of u cross v prior to normalization. Guaranteed >= 0.

Definition at line 769 of file GeoTessUtils.h.

◆ crossNorth()

static double geotess::GeoTessUtils::crossNorth	(	const double *const	u,
		double *const	w
	)

inlinestatic

Normalized cross product of a 3-component unit vector with the north pole.

Parameters

u	vector<double> vector one.
w	set to u cross north, normalized to unit length. If u cross north has zero length, w will equal (0,0,0).

Returns: the length of u cross north prior to normalization. Guaranteed >= 0.

Definition at line 790 of file GeoTessUtils.h.

◆ dot()

static double geotess::GeoTessUtils::dot	(	const double *const	v0,
		const double *const	v1
	)

inlinestatic

Return the dot product of two vectors.

Parameters

v0	a 3 component vector
v1	a 3 component vector

Returns: dot product

Definition at line 134 of file GeoTessUtils.h.

◆ getDistance3D()

static double geotess::GeoTessUtils::getDistance3D	(	const double *const	v0,
		double	r0,
		const double *const	v1,
		double	r1
	)

inlinestatic

Given two unit vectors and their radii, return the straight line separation between their tips. Assuming that the radii are in km, the result will also be in km.

Parameters

v0	Point 0 unit vector.
r0	Point 0 length (km).
v1	Point 1 unit vector.
r1	Point 1 length (km).

Returns: Distance between tip of v0*r0 and v1*r1, in km.

Definition at line 537 of file GeoTessUtils.h.

◆ getEarthRadius()

static double geotess::GeoTessUtils::getEarthRadius ( const double *const v )

inlinestatic

Retrieve the radius of the Earth in km at the position specified by an Earth-centered unit vector. Uses the WGS84 ellipsoid.

Parameters

v	Earth-centered unit vector

Returns: radius of the Earth in km at specified position.

Definition at line 553 of file GeoTessUtils.h.

◆ getGeocentricLat()

double geotess::GeoTessUtils::getGeocentricLat ( const double & lat )

inlinestatic

Return geocentric latitude given a geographic latitude using the WGS84 ellipsoid

Parameters

lat	geographic latitude in radians

Returns: geocentric latitude in radians

Definition at line 1761 of file GeoTessUtils.h.

◆ getGeographicLat()

double geotess::GeoTessUtils::getGeographicLat ( const double & lat )

inlinestatic

Return geographic latitude given a geocentric latitude using the WGS84 ellipsoid

Parameters

lat	geocentric latitude in radians

Returns: geographic latitude in radians

Definition at line 1749 of file GeoTessUtils.h.

◆ getGreatCircle() [1/4]

static double** geotess::GeoTessUtils::getGreatCircle	(	const double *const	v,
		double	azimuth
	)

static

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array, which is the structure returned by this method. A great circle can be passed to the method getGreatCirclePoint() to retrieve a unit vector that is on the great circle and located some distance from the first point of the great circle.

This method returns a great circle that is defined by an initial point and an azimuth.

Parameters

v	a unit vector that will be the first point on the great circle.
azimuth	a direction, in radians, in which to move relative to v in order to define the great circle

Returns: a 2 x 3 array specifying two unit vectors. The first one is a clone of unit vector v passed as an argument to this method. The second is located 90 degrees away from v in the direction specified by azimuth.

Exceptions

GeoTessException if v is located at north or south pole.

◆ getGreatCircle() [2/4]

static void geotess::GeoTessUtils::getGreatCircle	(	const double *const	v,
		double	azimuth,
		double **const	gc
	)

static

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array, which is the structure returned by this method. A great circle can be passed to the method getGreatCirclePoint() to retrieve a unit vector that is on the great circle and located some distance from the first point of the great circle.

This method returns a great circle that is defined by an initial point and an azimuth.

Parameters

v	a unit vector that will be the first point on the great circle.
azimuth	a direction, in radians, in which to move relative to v in order to define the great circle
gc	a 2 x 3 array specifying two unit vectors. The first one is a clone of unit vector v passed as an argument to this method. The second is located 90 degrees away from v in the direction specified by azimuth.

Exceptions

GeoTessException if v is located at north or south pole.

◆ getGreatCircle() [3/4]

static double** geotess::GeoTessUtils::getGreatCircle	(	const double *const	v0,
		const double *const	v1
	)

static

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array, which is the structure returned by this method. A great circle can be passed to the method getGreatCirclePoint() to retrieve a unit vector that is on the great circle and located some distance from the first point of the great circle.

This method returns a great circle that is computed from two unit vectors that are not necessarily 90 degrees apart.

Parameters

v0	the first point on the great circle
v1	some other point that is also on the great circle but which is not necessarily 90 degrees away from v0.

Returns: a 2 x 3 array specifying two unit vectors. The first one is a clone of unit vector v0 passed as first argument to this method. The second is located 90 degrees away from v0.

Exceptions

GeoTessException if v0 and v1 are parallel.

◆ getGreatCircle() [4/4]

static void geotess::GeoTessUtils::getGreatCircle	(	const double *const	v0,
		const double *const	v1,
		double **const	gc
	)

static

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array, which is the structure returned by this method. A great circle can be passed to the method getGreatCirclePoint() to retrieve a unit vector that is on the great circle and located some distance from the first point of the great circle.

This method returns a great circle that is computed from two unit vectors that are not necessarily 90 degrees apart.

Parameters

v0	the first point on the great circle
v1	some other point that is also on the great circle but which is not necessarily 90 degrees away from v0.
gc	a 2 x 3 array specifying two unit vectors. The first one is a clone of unit vector v0 passed as first argument to this method. The second is located 90 degrees away from v0.

Exceptions

GeoTessException if v0 and v1 are parallel.

◆ getGreatCirclePoint() [1/2]

static double* geotess::GeoTessUtils::getGreatCirclePoint	(	double const const const	greatCircle,
		double	distance
	)

inlinestatic

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array and one can be obtained by calling one of the getGreatCircle() methods.

In this method, a great circle and a distance are specified and a point is returned which is on the great circle path and is the specified distance away from the first point of the great circle.

Parameters

greatCircle	a great circle structure
distance	distance in radians from first point of great circle

Returns: unit vector of point which is on great circle and located specified distance away from first point of great circle.

Definition at line 1087 of file GeoTessUtils.h.

◆ getGreatCirclePoint() [2/2]

static void geotess::GeoTessUtils::getGreatCirclePoint	(	double const const const	greatCircle,
		double	distance,
		double *const	v
	)

inlinestatic

A great circle is defined by two unit vectors that are 90 degrees apart. A great circle is stored in a double[2][3] array and one can be obtained by calling one of the getGreatCircle() methods.

In this method, a great circle and a distance are specified and a point is returned which is on the great circle path and is the specified distance away from the first point of the great circle.

Parameters

greatCircle	a great circle structure
distance	distance in radians from first point of great circle
v	unit vector of point which is on great circle and located specified distance away from first point of great circle.

Definition at line 1112 of file GeoTessUtils.h.

◆ getGreatCirclePoints() [1/3]

static int geotess::GeoTessUtils::getGreatCirclePoints	(	double *	ptA,
		double *	ptB,
		const double &	delta,
		const bool &	onCenters
	)

static

Retrieve the number of points that would be required to populate a great circle path from point A to point B with equally spaced points given that the spacing can be no greater than delta.

Parameters

ptA	unit vector of first point on great circle (input)
ptB	unit vector of last point on great circle (input)
delta	desired point spacing in radians (input)
onCenters	if true, returned points will be located in the centers of equal size path increments. If false, first point will coincide with ptA, last point will coincide with ptB and the remaining points will be equally spaced in between. (input)

Returns: number of points required

◆ getGreatCirclePoints() [2/3]

static double geotess::GeoTessUtils::getGreatCirclePoints	(	double *	ptA,
		double *	ptB,
		const double &	delta,
		const bool &	onCenters,
		double **	points,
		int &	npoints
	)

static

Retrieve the unit vectors of a bunch of points distributed along a great circle path between two points. Caller specifies desired spacing of the points, not the number of points. The acutal spacing will generally be somewhat less than the request spacing in order that an integral number of points can be equally spaced along the path.

Parameters

ptA	unit vector of first point on great circle (input)
ptB	unit vector of last point on great circle (input)
delta	desired point spacing in radians (input)
onCenters	if true, returned points will be located in the centers of equal size path increments. If false, first point will coincide with ptA, last point will coincide with ptB and the remaining points will be equally spaced in between. (input)
points	an npoints by 3 array that will be populated with computed points. Must be large enough to hold all the computed points.
npoints	the number of points being returned.

Returns: actual point spacing in radians

◆ getGreatCirclePoints() [3/3]

static double geotess::GeoTessUtils::getGreatCirclePoints	(	double *	ptA,
		double *	ptB,
		const int &	npoints,
		const bool &	onCenters,
		double **	points
	)

static

Retrieve the unit vectors of a bunch of points distributed along a great circle path between two points.

Parameters

ptA	unit vector of first point on great circle (input)
ptB	unit vector of last point on great circle (input)
npoints	the number of points to distribute along the great circle path (input)
onCenters	if true, returned points will be located in the centers of equal size path increments. If false, first point will coincide with ptA, last point will coincide with ptB and the remaining points will be equally spaced in between. (input)
points	an npoints by 3 array that will be populated with computed points. Must be large enough to hold all the computed points.

Returns: actual point spacing in radians

◆ getLat()

static double geotess::GeoTessUtils::getLat ( const double *const v )

inlinestatic

Convert a 3-component unit vector to geographic latitude, in radians. Uses the WGS84 ellipsoid.

Parameters

v	3-component unit vector

Returns: geographic latitude in radians.

Definition at line 563 of file GeoTessUtils.h.

◆ getLatDegrees()

static double geotess::GeoTessUtils::getLatDegrees ( const double *const v )

inlinestatic

Convert a 3-component unit vector to geographic latitude, in degrees. Uses the WGS84 ellipsoid.

Parameters

v	3-component unit vector

Returns: geographic latitude in degrees.

Definition at line 582 of file GeoTessUtils.h.

◆ getLatLonString()

static string geotess::GeoTessUtils::getLatLonString ( const double *const v )

static

Parameters

v	unit vector to be converted to lat, lon string

Returns: a String of lat,lon in degrees formatted with "%10.6f %11.6f"

◆ getLon()

static double geotess::GeoTessUtils::getLon ( const double *const v )

inlinestatic

Convert a 3-component unit vector to a longitude, in radians.

Parameters

v	3 component unit vector

Returns: longitude in radians.

Definition at line 572 of file GeoTessUtils.h.

◆ getLonDegrees()

static double geotess::GeoTessUtils::getLonDegrees ( const double *const v )

inlinestatic

Convert a 3-component unit vector to a longitude, in degrees.

Parameters

v	3 component unit vector

Returns: longitude in degrees.

Definition at line 595 of file GeoTessUtils.h.

◆ getLonLatString()

static string geotess::GeoTessUtils::getLonLatString ( const double *const v )

static

Parameters

v	unit vector to be converted to lon,lat string

Returns: a String of lon,lat in degrees formatted with "%11.6f %10.6f"

◆ getTransform()

static void geotess::GeoTessUtils::getTransform	(	const double *const	u,
		const double *const	v,
		double **const	t
	)

static

Transform is a 3 x 3 matrix such that when a vector is multiplied by transform, the vector will be projected onto the plane of this GreatCircle. The z direction will point out of the plane of the great circle in the direction of the observer (lastPoint cross firstPoint; parallel to normal). The y direction will correspond to the mean of firstPoint and lastPoint. The x direction will correspond to y cross z, forming a right handed coordinate system.

Parameters

u	a 3-component unit vector defining start of great circle
v	a 3-component unit vector defining end of great circle
t	3 x 3 array that will be populated with the transform

◆ getTriangleArea() [1/2]

static double geotess::GeoTessUtils::getTriangleArea	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2
	)

inlinestatic

Parameters

v0	first corner of triangle
v1	second corner of triangle
v2	third corner of triangle

Returns: the area of a triangle defined by three 3-component vectors

Definition at line 1129 of file GeoTessUtils.h.

◆ getTriangleArea() [2/2]

static double geotess::GeoTessUtils::getTriangleArea	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2,
		double *	work1,
		double *	work2,
		double *	work3
	)

inlinestatic

Parameters

v0	first corner of triangle
v1	second corner of triangle
v2	third corner of triangle
work1	a double[3] used as work space
work2	a double[3] used as work space
work3	a double[3] used as work space

Returns: the area of a triangle defined by three 3-component vectors

Definition at line 1148 of file GeoTessUtils.h.

◆ getVector() [1/2]

static double* geotess::GeoTessUtils::getVector	(	const double &	lat,
		const double &	lon
	)

inlinestatic

Convert geographic lat, lon into a geocentric unit vector. The x-component points toward lat,lon = 0, 0. The y-component points toward lat,lon = 0, PI/2. The z-component points toward north pole. Uses the WGS84 ellipsoid.

Parameters

lat	geographic latitude in radians.
lon	longitude in radians.

Returns: 3 component unit vector.

Definition at line 641 of file GeoTessUtils.h.

◆ getVector() [2/2]

static double* geotess::GeoTessUtils::getVector	(	const double &	lat,
		const double &	lon,
		double *	v
	)

inlinestatic

Convert geographic lat, lon into a geocentric unit vector. The x-component points toward lat,lon = 0, 0. The y-component points toward lat,lon = 0, PI/2 The z-component points toward north pole. Uses the WGS84 ellipsoid.

Parameters

lat	geographic latitude in radians.
lon	longitude in radians.
v	3-component unit vector.

Returns: a pointer to v

Definition at line 659 of file GeoTessUtils.h.

◆ getVectorDegrees() [1/2]

static double* geotess::GeoTessUtils::getVectorDegrees	(	const double &	lat,
		const double &	lon
	)

inlinestatic

Convert geographic lat, lon into a geocentric unit vector. The x-component points toward lat,lon = 0, 0. The y-component points toward lat,lon = 0, 90. The z-component points toward north pole. Uses the WGS84 ellipsoid.

Parameters

lat	geographic latitude in degrees.
lon	longitude in degrees.

Returns: 3 component unit vector.

Definition at line 610 of file GeoTessUtils.h.

◆ getVectorDegrees() [2/2]

static double* geotess::GeoTessUtils::getVectorDegrees	(	const double &	lat,
		const double &	lon,
		double *	v
	)

inlinestatic

Convert geographic lat, lon into a geocentric unit vector. The x-component points toward lat,lon = 0, 0. The y-component points toward lat,lon = 0, 90. The z-component points toward north pole. Uses the WGS84 ellipsoid.

Parameters

lat	geographic latitude in degrees.
lon	longitude in degrees.
v	3 component unit vector.

Returns: pointer to v

Definition at line 625 of file GeoTessUtils.h.

◆ getVersion()

static string geotess::GeoTessUtils::getVersion ( )

inlinestatic

The current GeoTess version.

Returns: the current GeoTess version

Definition at line 125 of file GeoTessUtils.h.

◆ isPole()

static bool geotess::GeoTessUtils::isPole ( const double *const u )

inlinestatic

Returns true if unit vector u is very close to [0, 0, +/- 1]

Parameters

u	unit vector

Returns: true if unit vector u is very close to [0, 0, +/- 1]

Definition at line 1052 of file GeoTessUtils.h.

◆ length()

static double geotess::GeoTessUtils::length ( const double *const u )

inlinestatic

Find the length of a 3-element vector.

Parameters

u double[]

Returns: the length of the vector. Guaranteed to be >= 0.

Definition at line 420 of file GeoTessUtils.h.

◆ move()

static void geotess::GeoTessUtils::move	(	const double *const	w,
		const double *const	vtp,
		double	a,
		double *const	u
	)

inlinestatic

Move unit vector w in direction of vtp by distance a and store result in u. vtp is assumed to be a unit vector normal to w on input.

Parameters

w	double[]
vtp	double[]
a	double
u	double[]

Definition at line 1005 of file GeoTessUtils.h.

◆ moveDistAz()

static bool geotess::GeoTessUtils::moveDistAz	(	const double *const	w,
		double	distance,
		double	azimuth,
		double *const	u
	)

inlinestatic

Move unit vector w specified distance in direction given by azimuth and return the result in u. If w is north or south pole, u will be equal to the same pole and method returns false.

Parameters

w	double[] unit vector of starting position
distance	distance to move in radians
azimuth	direction to move in radians
u	double[] unit vector of resulting position.

Returns: true if successful, false if w is north or south pole

Definition at line 977 of file GeoTessUtils.h.

◆ moveNorth()

static bool geotess::GeoTessUtils::moveNorth	(	const double *const	x,
		double	distance,
		double *const	z
	)

inlinestatic

Return a unit vector that is distance radians due north of positon x. If x is the north or south pole, then z is set equal to x.

Parameters

x	the position to be moved.
distance	the distance, in radians, that x is to be moved toward the north.
z	the 3-element unit vector representing the position after having moved distance north.

Returns: true if operation successful, false if x is north or south pole.

Definition at line 1029 of file GeoTessUtils.h.

◆ normalize()

static double geotess::GeoTessUtils::normalize ( double *const u )

inlinestatic

Normalize the input vector to unit length. Returns the length of the vector prior to normalization.

Parameters

u	vector<double>

Returns: length of the vector prior to normalization ( >= 0.)

Definition at line 701 of file GeoTessUtils.h.

◆ normalizeFast()

static void geotess::GeoTessUtils::normalizeFast ( double *const u )

inlinestatic

Normalize the input vector to unit length. Unlike normalize(), this method does not check to ensure that the length of the input vector is not zero. Only call this version if certain that the length of the vector is > 0.

Parameters

u	vector<double>

Definition at line 685 of file GeoTessUtils.h.

◆ parallel()

static bool geotess::GeoTessUtils::parallel	(	const double *const	u,
		const double *const	v
	)

inlinestatic

Returns true if unit vector u and v are parallel or very close to it

Parameters

u	a unit vector
v	another unit vector

Returns: 1.-abs(dot(u,v)) < 2e-15

Definition at line 1066 of file GeoTessUtils.h.

◆ readString()

static void geotess::GeoTessUtils::readString	(	string &	s,
		ifstream &	ifs
	)

inlinestatic

Read a string from the input file stream and set into s

Parameters

s	the string that will be populated with results
ifs	input stream

Definition at line 469 of file GeoTessUtils.h.

◆ rotate()

static void geotess::GeoTessUtils::rotate	(	const double *const	x,
		const double *const	p,
		double	a,
		double *const	z
	)

static

Rotate unit vector x clockwise around unit vector p, by angle a. x and z may be references to the same array. Clockwise rotation as viewed from outside the unit sphere is positive.

Parameters

x	vector to be rotated
p	pole about which rotation is to occur.
a	double the amount of rotation, in radians.
z	the rotated vector, normalized to unit length.

◆ scalarTripleProduct()

static double geotess::GeoTessUtils::scalarTripleProduct	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2
	)

inlinestatic

Calculate the scalar triple product of 3 3-component vectors: (v0 cross v1) dot v2

Parameters

v0	double[]
v1	double[]
v2	double[]

Returns: scalar triple product (v0 cross v1) dot v2

Definition at line 146 of file GeoTessUtils.h.

◆ transform()

static void geotess::GeoTessUtils::transform	(	const double *	x,
		double const const const	t,
		double *const	g
	)

inlinestatic

Project vector x onto the plane of a great circle. Consider a great circle defined by two unti vectors, u and v. Find the transform of x by calling t = getTransform(u, v). Then call this method: transform(x, t, g), which will calculate unit vector g such that

g[2] is the z direction, i.e., the component of x that points out of the plane of the great circle, toward the observer (v cross u).
g[1] is the y direction, i.e., the mean of u and v, and
g[0] is the x direction, i.e, g[1] cross g2.

Parameters

x	unit vector to be transformed
t	transform obtained with call to getTransform()
g	transformed unit vector

Definition at line 456 of file GeoTessUtils.h.

◆ vectorTripleProduct()

static bool geotess::GeoTessUtils::vectorTripleProduct	(	const double *const	v0,
		const double *const	v1,
		const double *const	v2,
		double *const	rslt
	)

inlinestatic

Compute the normalized vector triple product (v0 x v1) x v2 and store result in rslt. It is ok if rslt is a reference to one of the input vectors. Local variables are used to ensure memory is not corrupted.

Parameters

v0	double[]
v1	double[]
v2	double[]
rslt	double[]

Returns: true if rslt has finite length, false if length(rslt) is zero.

Definition at line 822 of file GeoTessUtils.h.

◆ vectorTripleProductNorthPole()

static bool geotess::GeoTessUtils::vectorTripleProductNorthPole	(	const double *const	u,
		double *const	w
	)

inlinestatic

Compute the normalized vector triple product (u x northPole) x u and store result in w. Returns false is u is north or south pole.

Parameters

u	double[]
w	double[]

Returns: true if w has finite length, false if length(w) is zero.

Definition at line 856 of file GeoTessUtils.h.

◆ writeString()

static void geotess::GeoTessUtils::writeString	(	ofstream &	ofs,
		const string &	s
	)

inlinestatic

Write the string s to the output file stream.

Parameters

ofs	output stream
s	the string to write the output stream.

Definition at line 484 of file GeoTessUtils.h.

Member Data Documentation

◆ approximateLatitudes

bool geotess::GeoTessUtils::approximateLatitudes

static

If true, then an approximate algorithm will be used to convert back and forth between geocentric and geographic latitudes. The approximation incurs an error of about 0.1 meters in latitude calculations but is faster than the correct calculation.

Note that the existence of this static, mutable variable technically violates thread-safety of this class. But given the assumption that the approximation is just as good as the true conversions, this is not a significant violation.

Definition at line 95 of file GeoTessUtils.h.

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

rstt/GeoTessCPP/include/GeoTessUtils.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ GeoTessUtils()

◆ ~GeoTessUtils()

Member Function Documentation

◆ angle()

◆ angleDegrees()

◆ azimuth()

◆ azimuthDegrees()

◆ center() [1/2]

◆ center() [2/2]

◆ circumCenter()

◆ circumCenterPlus() [1/3]

◆ circumCenterPlus() [2/3]

◆ circumCenterPlus() [3/3]

◆ class_name()

◆ class_size()

◆ cross()

◆ crossNormal() [1/2]

◆ crossNormal() [2/2]

◆ crossNorth()

◆ dot()

◆ getDistance3D()

◆ getEarthRadius()

◆ getGeocentricLat()

◆ getGeographicLat()

◆ getGreatCircle() [1/4]

◆ getGreatCircle() [2/4]

◆ getGreatCircle() [3/4]

◆ getGreatCircle() [4/4]

◆ getGreatCirclePoint() [1/2]

◆ getGreatCirclePoint() [2/2]

◆ getGreatCirclePoints() [1/3]

◆ getGreatCirclePoints() [2/3]

◆ getGreatCirclePoints() [3/3]

◆ getLat()

◆ getLatDegrees()

◆ getLatLonString()

◆ getLon()

◆ getLonDegrees()

◆ getLonLatString()

◆ getTransform()

◆ getTriangleArea() [1/2]

◆ getTriangleArea() [2/2]

◆ getVector() [1/2]

◆ getVector() [2/2]

◆ getVectorDegrees() [1/2]

◆ getVectorDegrees() [2/2]

◆ getVersion()

◆ isPole()

◆ length()

◆ move()

◆ moveDistAz()

◆ moveNorth()

◆ normalize()

◆ normalizeFast()

◆ parallel()

◆ readString()

◆ rotate()

◆ scalarTripleProduct()

◆ transform()

◆ vectorTripleProduct()

◆ vectorTripleProductNorthPole()

◆ writeString()

Member Data Documentation

◆ approximateLatitudes