coordConv Namespace Reference

Namespaces
	testUtils
	version

Classes
class	Coord
class	CoordSys
class	MeanCoordSys
class	ApparentCoordSys
class	ICRSCoordSys
class	FK5CoordSys
class	FK4CoordSys
class	GalCoordSys
class	AppGeoCoordSys
class	AppTopoCoordSys
class	ObsCoordSys
class	OtherCoordSys
class	NoneCoordSys
class	PVT
class	PVTCoord
class	Site

Enumerations
enum	DateTypeEnum { DateType_Julian, DateType_Besselian, DateType_TAI, DateType_None }

Functions
bool	angSideAng (double &angA, double &sideB, double &angC, double sideA, double angB, double sideC)
Coord	appGeoFromAppTopo (Coord const &appTopoCoord, Site const &site, double tai)
Coord	appTopoFromAppGeo (Coord const &appGeoCoord, Site const &site, double tai)
Coord	appTopoFromObs (Coord const &obsCoord, Site const &site)
void	azAltFromHADec (Eigen::Vector3d &azAlt, Eigen::Vector3d const &haDec, double lat)
double	distanceFromParallax (double parallax)
double	parallaxFromDistance (double dist)
std::ostream &	operator<< (std::ostream &out, Coord const &coord)
CoordSys::Ptr	makeCoordSys (std::string const &name, double date)
std::ostream &	operator<< (std::ostream &out, CoordSys const &coordSys)
void	haDecFromAzAlt (Eigen::Vector3d &haDec, Eigen::Vector3d const &azAlt, double lat)
void	rot2D (double &rotX, double &rotY, double x, double y, double ang)
double	wrapPos (double ang)
double	wrapCtr (double ang)
double	wrapNear (double ang, double refAng)
double	hypot (double x, double y)
double	sind (double ang)
	sine of angle in degrees More...
double	cosd (double ang)
	cosine of angle in degrees More...
double	tand (double ang)
	tangent of angle in degrees More...
double	asind (double x)
	arcsine in degrees More...
double	acosd (double x)
	arccosine in degrees More...
double	atand (double x)
	arctangent in degrees More...
double	atan2d (double x, double y)
	arctangent2 in degrees More...
bool	polarFromXY (double &r, double &theta, double x, double y)
void	xyFromPolar (double &x, double &y, double r, double theta)
void	computeRotationMatrix (Eigen::Matrix3d &rotMat, Eigen::Vector3d const &axis, double rotAngle)
Coord	obsFromAppTopo (Coord const &appTopoCoord, Site const &site)
bool	polarFromXY (PVT &r, PVT &theta, PVT const &x, PVT const &y, double tai)
void	xyFromPolar (PVT &x, PVT &y, PVT const &r, PVT const &theta, double tai)
void	rot2D (PVT &rotX, PVT &rotY, PVT const &x, PVT const &y, double ang, double tai)
PVT	wrapPos (PVT const &pvt)
PVT	wrapCtr (PVT const &pvt)
std::ostream &	operator<< (std::ostream &os, PVT const &pvt)
std::ostream &	operator<< (std::ostream &os, PVTCoord const &pvtCoord)
void	rotEqPol (Eigen::Vector3d &toVec, Eigen::Vector3d const &fromVec, double eqAng, double polarAng)
void	rotXY (Eigen::Vector3d &toVec, Eigen::Vector3d const &fromVec, double xAng, double yAng)
std::ostream &	operator<< (std::ostream &out, Site const &site)
double	lastFromTAI (double tai, Site const &site)
double	julianEpochFromTAI (double mjdSec)
double	taiFromJulianEpoch (double julianEpoch)
double	besselianEpochFromTAI (double mjdSec)
double	taiFromBesselianEpoch (double besselianEpoch)

Variables
const double	MinParallax = 1e-7
const double	DeltaTForPos = 0.01
	by computing position at two nearby times (sec) More...
const double	DoubleEpsilon = std::numeric_limits<double>::epsilon()
const double	DoubleMax = std::numeric_limits<double>::max()
const double	DoubleMin = std::numeric_limits<double>::min()
const double	DoubleNaN = std::numeric_limits<double>::quiet_NaN()
const double	Pi = std::atan(1.0)*4
const double	HoursPerDeg = 24.0 / 360.0
const double	RadPerDeg = Pi / 180.0
const double	KmPerAU = 149597871.0
const double	AUPerParsec = 206264.8062470964
const double	ArcsecPerDeg = 3600.0
const double	SecPerDay = 24.0 * 3600.0
const double	DaysPerYear = 365.25
const double	VLight = 299792.458 / KmPerAU
const double	DegK_DegC = 273.15
const double	MJD_UnixTime = 40587 * SecPerDay
const double	MJDJ2000 = 51544.5
const double	AngstromsPerMicron = 1.0e4
const double	PascalsPerMillibar = 100.0
const double	TT_TAI = 32.184
const double	SiderealPerSolar = 1.00273790934

Enumeration Type Documentation

enum coordConv::DateTypeEnum

Enumerator
DateType_Julian	Julian years.
DateType_Besselian	Besselian years.
DateType_TAI	TAI (MJD, seconds)
DateType_None	date is irrelevant

Definition at line 18 of file coordSys.h.

Function Documentation

double coordConv::acosd ( double  x )

inline

arccosine in degrees

Definition at line 64 of file mathUtils.h.

bool coordConv::angSideAng	(	double &	angA,
		double &	sideB,
		double &	angC,
		double	sideA,
		double	angB,
		double	sideC
	)

Solve for two sides and the included angle of a spherical triangle

Parameters

[out]	angA	interior angle opposite side A (deg)
[out]	sideB	length of side B (deg)
[out]	angC	interior angle opposite side C (deg)
[in]	sideA	length of side A (deg)
[in]	angB	interior angle opposite side B (deg)
[in]	sideC	length of side C (deg)

Returns

unknownAng: if true: sideB is so near 0 or 180 (see Special Cases below) that angA and angC cannot not be computed; angA and angC are set to 90 (hence their sum is 180, which is essentially correct) and sideB will be 0 or 180 (again, essentially correct).

Exceptions

runtime_error

if the inputs are too small to allow computation

Special Cases (in the order they are handled):

sideA angB sideC angA sideB angC

~0 any ~0 unknown(90) 0 unknown(90) ~0 any ~180 unknown(90) 180 unknown(90) ~0 any !pole 0 sideC 180-angB

~180 any ~0 unknown(90) 180 unknown(90) ~180 any ~180 unknown(90) 0 unknown(90) ~180 any !pole 180 180-sideC angB

!pole any ~0 180-angB sideA 0 !pole any ~180 angB 180-sideA 180

any ~0 ~=sideA unknown(90) 0 unknown(90) any ~0 <sideA 180 sideA-sideC 0 any ~0 >sideA 0 sideC-sideA 180

where:

• !pole means not nearly 0 and not nearly 180 (modulo 360)
• unknown(90) means unknownAng = true is returned
• All relations are modulo 360. For example ~0 means approximately zero, 360, etc.

Note

: allowing angles in the 3rd and 4th quadrants is unusual.

References: Selby, Standard Math Tables, crc, 15th ed, 1967, p161 (Spherical Trig.)

Definition at line 9 of file angSideAng.cc.

Coord coordConv::appGeoFromAppTopo	(	Coord const &	appTopoCoord,
		Site const &	site,
		double	tai
	)

Convert apparent geocentric coordinates to apparent topocentric at a specified date

Parameters

[in]	appTopoCoord	apparent topocentric coord at the specified TAI date
[in]	site	site information
[in]	tai	TAI date (MJD, sec)

Returns

position in apparent topocentric coordinates at the specified TAI date

Definition at line 8 of file appGeoFromAppTopo.cc.

Coord coordConv::appTopoFromAppGeo	(	Coord const &	appGeoCoord,
		Site const &	site,
		double	tai
	)

Convert apparent geocentric coordinates to apparent topocentric at a specified date

Parameters

[in]	appGeoCoord	apparent geocentric coord at the specified TAI date
[in]	site	site information
[in]	tai	TAI date (MJD, sec)

Returns

position in apparent geocentric coordinates at the specified TAI date

Definition at line 8 of file appTopoFromAppGeo.cc.

Coord coordConv::appTopoFromObs	(	Coord const &	obsCoord,
		Site const &	site
	)

Convert observed coordinates (refracted apparent topocentric) to apparent topocentric coordinates

Parameters

[in]	obsCoord	observed (refracted apparent topocentric) coord
[in]	site	site information; refCoA and refCoB are read

Returns

position in observed coordinates

Definition at line 7 of file appTopoFromObs.cc.

double coordConv::asind ( double  x )

inline

arcsine in degrees

Definition at line 61 of file mathUtils.h.

double coordConv::atan2d ( double  x, double  y  )

inline

arctangent2 in degrees

Definition at line 70 of file mathUtils.h.

double coordConv::atand ( double  x )

inline

arctangent in degrees

Definition at line 67 of file mathUtils.h.

void coordConv::azAltFromHADec	(	Eigen::Vector3d &	azAlt,
		Eigen::Vector3d const &	haDec,
		double	lat
	)

Convert HA/Dec position to Alt/Az.

Parameters

[out]	azAlt	cartesian Az/Alt (same units as haDec); Sign convention: (1,0,0) is south, (0,1,0) is east.
[in]	haDec	cartesian -HA, Dec (any units)
[in]	lat	latitude (degrees)

Definition at line 6 of file azAltFromHADec.cc.

double coordConv::besselianEpochFromTAI

(

double

mjdSec

)

Convert TAI (MJD seconds) to Besselian epoch

Parameters

[in]

mjdSec

MJD date (sec)

Definition at line 39 of file time.cc.

void coordConv::computeRotationMatrix	(	Eigen::Matrix3d &	rotMat,
		Eigen::Vector3d const &	axis,
		double	rotAngle
	)

Compute a rotation matrix given an axis and rotation angle

Parameters

[out]	rotMat	rotation matrix
[in]	axis	axis of rotation (magnitude is ignored, but must be finite and nonzero)
[in]	rotAngle	rotation angle (deg)

Definition at line 33 of file mathUtils.cc.

double coordConv::cosd ( double  ang )

inline

cosine of angle in degrees

Definition at line 55 of file mathUtils.h.

double coordConv::distanceFromParallax

(

double

parallax

)

Definition at line 12 of file coord.cc.

void coordConv::haDecFromAzAlt	(	Eigen::Vector3d &	haDec,
		Eigen::Vector3d const &	azAlt,
		double	lat
	)

Convert Az/Alt position to HA/Dec

Parameters

[out]	haDec	cartesian -HA, Dec (same units as azAlt)
[in]	azAlt	cartesian Az/Alt (any units) Sign convention: (1,0,0) is south, (0,1,0) is east.
[in]	lat	latitude (degrees)

Compute HA/Dec position from alt/az position

Parameters

[out]	haDec	cartesian -HA, Dec (same units as azAlt)
[in]	lat	latitude (degrees)
[in]	azAlt	cartesian Az/Alt (any units) Sign convention: (1,0,0) is south, (0,1,0) is east.

Definition at line 14 of file haDecFromAzAlt.cc.

double coordConv::hypot	(	double	x,
		double	y
	)

Hypotenuse function (also present in C++11, which I'm not using yet)

Parameters

[in]

x,y:

sides of right triangle

Returns

hypotenuse of right triangle

Definition at line 8 of file mathUtils.cc.

double coordConv::julianEpochFromTAI

(

double

mjdSec

)

Convert TAI (MJD seconds) to Julian epoch

Parameters

[in]

mjdSec

MJD date (sec)

Definition at line 31 of file time.cc.

double coordConv::lastFromTAI	(	double	tai,
		Site const &	site
	)

Compute local apparent sidereal time from TAI

Parameters

[in]	tai	universal time (MJD, seconds)
[in]	site	site information (a coordConv::Site) read fields: ut1_tai, longitude

Returns

Local mean sidereal time, in degrees, in range [0, 360)

Definition at line 18 of file time.cc.

CoordSys::Ptr coordConv::makeCoordSys	(	std::string const &	name,
		double	date
	)

Return a coordinate system given its name

Parameters

[in]	name	name of coordinate system (case matters)
[in]	date	date of coordinate system (units depend on the coordinate system); if 0 then the coordSys is current, except FK4 defaults to 1950 and FK5 defaults to 2000

Returns

the specified coordinate system at the specified date

Exceptions

std::invalid_argument

(ValueError in python) if name is not recognized.

Warning

this will not construct an OtherCoordSys, since those have arbitary names (but it will construct a NoneCoordSys)

Definition at line 74 of file coordSys.cc.

Coord coordConv::obsFromAppTopo	(	Coord const &	appTopoCoord,
		Site const &	site
	)

Convert apparent topocentric coordinates to observed (refracted apparent topocentric)

Parameters

[in]	appTopoCoord	apparent topocentric coord
[in]	site	site information; refCoA and refCoB are read

Returns

position in observed coordinates

Definition at line 7 of file obsFromAppTopo.cc.

std::ostream & coordConv::operator<<	(	std::ostream &	out,
		Site const &	site
	)

Definition at line 82 of file site.cc.

std::ostream & coordConv::operator<<	(	std::ostream &	os,
		PVTCoord const &	pvtCoord
	)

Definition at line 191 of file pvtCoord.cc.

std::ostream & coordConv::operator<<	(	std::ostream &	out,
		Coord const &	coord
	)

Definition at line 263 of file coord.cc.

std::ostream & coordConv::operator<<	(	std::ostream &	os,
		PVT const &	pvt
	)

Append a formatted PVT to a stream

The format is:

PVT(pos, vel, time)

where all values are shown in decimal format (rather than exponential notation):

• pos and vel are shown to 7 digits after the decimal point (0.0003 arcsec resolution)
• time is shown to 6 digits (because time is commonly given to the nearest microsecond)

Parameters

[in,out]	os	stream to which to append the formatted value
[in]	pvt	PVT to format and append to the stream

Definition at line 49 of file pvt.cc.

std::ostream & coordConv::operator<<	(	std::ostream &	out,
		CoordSys const &	coordSys
	)

Definition at line 98 of file coordSys.cc.

double coordConv::parallaxFromDistance

(

double

dist

)

Definition at line 16 of file coord.cc.

bool coordConv::polarFromXY	(	double &	r,
		double &	theta,
		double	x,
		double	y
	)

Convert cartesian coordinates to polar coordinates.

Parameters

[out]	r	magnitude of vector (same units as "x" and "y")
[out]	theta	angle of vector (degrees) 0 along x, 90 along y and in the range (-180, 180)
[in]	x	x component of vector (arbitrary units)
[in]	y	y component of vector (same units as "x")

Returns

true if |r| is so small that theta cannot be computed and sets theta to 0

Definition at line 14 of file mathUtils.cc.

bool coordConv::polarFromXY	(	PVT &	r,
		PVT &	theta,
		PVT const &	x,
		PVT const &	y,
		double	tai
	)

Convert cartesian coordinates to polar coordinates.

Parameters

[out]	r	magnitude of vector (same units as "x" and "y")
[out]	theta	angle of vector (degrees) 0 along x, 90 along y and in the range (-180, 180)
[in]	x	x component of vector (arbitrary units)
[in]	y	y component of vector (same units as "x")
[in]	tai	TAI date (MJD, sec)

Returns

true if |r| is so small that theta cannot be computed and sets theta to 0

Definition at line 17 of file pvt.cc.

void coordConv::rot2D ( double &  rotX, double &  rotY, double  x, double  y, double  ang  )

inline

Rotate a 2-dimensional vector by a given angle.

Parameters

[out]	rotX	rotated x value
[out]	rotY	rotated y value
[in]	x:	unrotated x value
[in]	y:	unrotated y value
[in]	ang:	angle by which to rotate (deg)

Using rot2D to change coordinate systems: Given a coordinate system A and a coordinate system B, such that:

• B's origin is at B_A_xy in A
• B's orientation is B_A_ang in A Then a point P can be transformed as follows between these systems:
• P_B_xy = rot2D(P_A_xy - B_A_xy, -B_A_ang)
• P_A_xy = B_A_xy + rot2D(P_B_xy, +B_A_ang)

Definition at line 12 of file mathUtils.cc.

void coordConv::rot2D	(	PVT &	rotX,
		PVT &	rotY,
		PVT const &	x,
		PVT const &	y,
		double	ang,
		double	tai
	)

Rotate a 2-dimensional PVT vector by a given angle.

Parameters

[out]	rotX	rotated x value
[out]	rotY	rotated y value
[in]	x:	unrotated x value
[in]	y:	unrotated y value
[in]	ang:	angle by which to rotate (deg)
[in]	tai	TAI date (MJD, sec)

Using rot2D to change coordinate systems: Given a coordinate system A and a coordinate system B, such that:

• B's origin is at B_A_xy in A
• B's orientation is B_A_ang in A Then a point P can be transformed as follows between these systems:
• P_B_xy = rot2D(P_A_xy - B_A_xy, -B_A_ang)
• P_A_xy = B_A_xy + rot2D(P_B_xy, +B_A_ang)

Definition at line 39 of file pvt.cc.

void coordConv::rotEqPol	(	Eigen::Vector3d &	toVec,
		Eigen::Vector3d const &	fromVec,
		double	eqAng,
		double	polarAng
	)

Rotate a 3-vector described by equatorial and polar angles, as follows: The plane of rotation contains the z axis and a line in the x-y plane at angle eqAng from the x axis towards y. The amount of rotation is angle polarAng from the z axis towards the line in the x-y plane.

Parameters

[out]	toVec	rotated 3-vector
[in]	fromVec	input 3-vector
[in]	eqAng	angle of line in x-y plane (from x to y); the plane of rotation includes this line and z
[in]	polarAng	angle of rotation (from z axis to line in x-y plane)

Definition at line 5 of file rotEqPol.cc.

void coordConv::rotXY	(	Eigen::Vector3d &	toVec,
		Eigen::Vector3d const &	fromVec,
		double	xAng,
		double	yAng
	)

Rotate a 3-vector, first about the x axis, then about the y axis. Warning: toVec cannot replace fromVec

Inputs:

Parameters

[out]	toVec	rotated 3-vector
[in]	fromVec	input 3-vector
[in]	xAng	angle about x axis (deg); positive rotation is from y to z.
[in]	yAng	angle about original y axis (deg); positive rotation is from z to x.

Definition at line 5 of file rotXY.cc.

double coordConv::sind ( double  ang )

inline

sine of angle in degrees

Definition at line 52 of file mathUtils.h.

double coordConv::taiFromBesselianEpoch

(

double

besselianEpoch

)

Convert Besselian epoch to TAI (MJD seconds)

Parameters

[in]

besselianEpoch

date as a Besselian epoch (years)

Definition at line 43 of file time.cc.

double coordConv::taiFromJulianEpoch

(

double

julianEpoch

)

Convert Julian epoch to TAI (MJD seconds)

Parameters

[in]

julianEpoch

date as a Julian epoch (years)

Definition at line 35 of file time.cc.

double coordConv::tand ( double  ang )

inline

tangent of angle in degrees

Definition at line 58 of file mathUtils.h.

double coordConv::wrapCtr ( double  ang )

inline

Compute angle wrapped into range: -180 <= wrapped ang < 180 deg

Parameters

[in]

ang

angle to wrap (deg)

Returns

wrapped angle (deg)

Definition at line 33 of file mathUtils.cc.

PVT coordConv::wrapCtr ( PVT const &  pvt )

inline

Compute PVT angle wrapped into range [-180, 180) deg; only the pos differs

Parameters

pvt	input PVT angle (pos in deg)

Definition at line 244 of file pvt.h.

double coordConv::wrapNear ( double  ang, double  refAng  )

inline

Wrap one angle to be within 180 degrees of a reference angle: 180 <= wrapped ang - refAng < 180

Parameters

[in]	ang	angle to wrap (deg)
[in]	refAng	result is wrapped to be near this reference angle (deg)

Returns

wrapped angle (deg)

Definition at line 52 of file mathUtils.cc.

double coordConv::wrapPos ( double  ang )

inline

Compute angle wrapped into range: 0 <= wrapped ang < 360 deg

Parameters

[in]

ang

angle to wrap (deg)

Returns

wrapped angle (deg)

Definition at line 20 of file mathUtils.cc.

PVT coordConv::wrapPos ( PVT const &  pvt )

inline

Compute PVT angle wrapped into range [0, 360) deg; only the pos differs

Parameters

pvt	input PVT angle (pos in deg)

Definition at line 233 of file pvt.h.

void coordConv::xyFromPolar	(	double &	x,
		double &	y,
		double	r,
		double	theta
	)

Convert polar coordinates to cartesian coordinates.

Parameters

[out]	x	x component of vector (same units as "r")
[out]	y	y component of vector (same units as "r")
[in]	r	magnitude of vector (arbitrary units)
[in]	theta	angle of vector from x axis (degrees)

Definition at line 28 of file mathUtils.cc.

void coordConv::xyFromPolar	(	PVT &	x,
		PVT &	y,
		PVT const &	r,
		PVT const &	theta,
		double	tai
	)

Convert polar coordinates to cartesian coordinates.

Parameters

[out]	x	x component of vector (same units as "r")
[out]	y	y component of vector (same units as "r")
[in]	r	magnitude of vector (arbitrary units)
[in]	theta	angle of vector from x axis (degrees)
[in]	tai	TAI date (MJD, sec)

Definition at line 29 of file pvt.cc.

Variable Documentation

const double coordConv::AngstromsPerMicron = 1.0e4

Definition at line 31 of file physConst.h.

const double coordConv::ArcsecPerDeg = 3600.0

Definition at line 22 of file physConst.h.

const double coordConv::AUPerParsec = 206264.8062470964

Definition at line 21 of file physConst.h.

const double coordConv::DaysPerYear = 365.25

Definition at line 24 of file physConst.h.

const double coordConv::DegK_DegC = 273.15

Definition at line 26 of file physConst.h.

const double coordConv::DeltaTForPos = 0.01

by computing position at two nearby times (sec)

delta time to use when computing velocity

Definition at line 15 of file coordSys.h.

const double coordConv::DoubleEpsilon = std::numeric_limits<double>::epsilon()

Definition at line 13 of file mathUtils.h.

const double coordConv::DoubleMax = std::numeric_limits<double>::max()

Definition at line 14 of file mathUtils.h.

const double coordConv::DoubleMin = std::numeric_limits<double>::min()

Definition at line 15 of file mathUtils.h.

const double coordConv::DoubleNaN = std::numeric_limits<double>::quiet_NaN()

Definition at line 16 of file mathUtils.h.

const double coordConv::HoursPerDeg = 24.0 / 360.0

Definition at line 18 of file physConst.h.

const double coordConv::KmPerAU = 149597871.0

Definition at line 20 of file physConst.h.

const double coordConv::MinParallax = 1e-7

Definition at line 10 of file coord.h.

const double coordConv::MJD_UnixTime = 40587 * SecPerDay

Definition at line 27 of file physConst.h.

const double coordConv::MJDJ2000 = 51544.5

Definition at line 30 of file physConst.h.

const double coordConv::PascalsPerMillibar = 100.0

Definition at line 32 of file physConst.h.

const double coordConv::Pi = std::atan(1.0)*4

Definition at line 17 of file physConst.h.

const double coordConv::RadPerDeg = Pi / 180.0

Definition at line 19 of file physConst.h.

const double coordConv::SecPerDay = 24.0 * 3600.0

Definition at line 23 of file physConst.h.

const double coordConv::SiderealPerSolar = 1.00273790934

Definition at line 39 of file physConst.h.

const double coordConv::TT_TAI = 32.184

Definition at line 35 of file physConst.h.

const double coordConv::VLight = 299792.458 / KmPerAU

Definition at line 25 of file physConst.h.