Functions for basic geometry and working with earth coordinate systems

Macros
#define	semilatrect(a, e)
	Calculate the semi-latus rectum of a conic section.
#define	focus(a, e)
	Calculate the focal parameter of a conic section.
#define	semimaj(p, e)
#define	eccent(a, p)

Functions
template<typename realT>
realT	mx::math::dtor (realT q)
	Convert from degrees to radians.
template<typename realT>
realT	mx::math::rtod (realT q)
	Convert from radians to degrees.
template<class angleT>
angleT::realT	mx::math::angleMod (typename angleT::realT q)
	Calculate the angle modulo full-circle, normalizing to a positive value.
template<class angleT>
angleT::realT	mx::math::angleDiff (typename angleT::realT q1, typename angleT::realT q2)
	Calculate the difference between two angles, correctly across 0/360.
template<class angleT>
angleT::realT	mx::math::angleMean (const std::vector< typename angleT::realT > &q)
	Calculate the mean of a set of angles, correctly across 0/360.
template<int degrad = 0, typename realT>
int	mx::math::continueAngles (std::vector< realT > &angles, realT threshold=0.75)
	Make a vector of angles continuous, fixing the 0/360 crossing.
template<typename realT>
void	mx::math::rotatePoint (realT &x0, realT &y0, realT angle)
	Rotate a point about the origin.

Macro Definition Documentation

◆ eccent

#define eccent	(		a,
			p )

Value:

    ( a == 0.0 ? 1e34                                                                                                  \
               : ( p >= 1e9 ? 0.0                                                                                      \
                            : ( p > 0 ? ( -p / ( 2 * a ) + 0.5 * std::sqrt( p * p / ( a * a ) + 4 ) )                  \
                                      : ( p / ( 2 * a ) + 0.5 * std::sqrt( p * p / ( a * a ) + 4 ) ) ) ) )

Calculate the eccentricity of a conic section given the semi-major axis and the focal parameter

Definition at line 67 of file geo.hpp.

◆ focus

#define focus	(		a,
			e )

Value:

( e == 0.0 ? 1e34 : ( e == 1.0 ? 2. * a : ( e < 1. ? a * ( 1 - e * e ) / e : a * ( e * e - 1 ) / e ) ) )

Calculate the focal parameter of a conic section.

Definition at line 52 of file geo.hpp.

◆ semilatrect

#define semilatrect	(		a,
			e )

Value:

( e == 0.0 ? a : ( e == 1.0 ? 2. * a : ( e < 1. ? a * ( 1 - e * e ) : a * ( e * e - 1 ) ) ) )

Calculate the semi-latus rectum of a conic section.

Definition at line 45 of file geo.hpp.

◆ semimaj

#define semimaj	(		p,
			e )

Value:

( e == 1.0 ? 1e34 : ( e < 1 ? p * e / ( 1 - e * e ) : p * e / ( e * e - 1 ) ) )

Calculate the semi-major axis of a conic section, given the focal parameter and the eccentricity

Definition at line 60 of file geo.hpp.

Function Documentation

◆ angleDiff()

template<class angleT>

angleT::realT mx::math::angleDiff	(	typename angleT::realT	q1,
		typename angleT::realT	q2 )

Calculate the difference between two angles, correctly across 0/360.

Calculates \( dq = q2- q1 \), but accounts for crossing 0/360. This implies that \( dq \le 180 \).

Returns: the difference of q2 and q1

Template Parameters

angleT	controls whether this is in degrees (0, default) or radians (1)
realT	is the type in which to do arithmetic

Parameters

[in]	q1	angle to subtract from q2.
[in]	q2	angle to subtract q1 from.

Definition at line 191 of file geo.hpp.

Referenced by mx::improc::annulusCoordsWorker(), mx::improc::maskWedge(), mx::improc::azBoxKernel< _arrayT, _kernW, _verboseT >::setKernel(), and TEST_CASE().

◆ angleMean()

template<class angleT>

angleT::realT mx::math::angleMean ( const std::vector< typename angleT::realT > & q )

Calculate the mean of a set of angles, correctly across 0/360.

Calculates the mean by decomposing into vectors and averaging the components. This accounts for crossing 0/360.

Returns: the mean angle

Template Parameters

angleT is the angle type, either radians<realT> or degrees<realT>. angleT::realT is the type in which to do arithmetic.

Parameters

[in] q vector of angles to average.

Definition at line 226 of file geo.hpp.

Referenced by mx::improc::annulusBoundingRect().

◆ angleMod()

template<class angleT>

angleT::realT mx::math::angleMod ( typename angleT::realT q )

Calculate the angle modulo full-circle, normalizing to a positive value.

The output will be betweeen 0 and 360 (or 0 and 2pi).

Returns: the value of q normalized to 0 <= q < 360[2pi]

Template Parameters

degrad	controls whether this is in degrees (0, default) or radians (1)
realT	is the type in which to do arithmetic

Parameters

[in] q the angle

Definition at line 164 of file geo.hpp.

Referenced by mx::improc::annulusCoordsWorker(), and TEST_CASE().

◆ continueAngles()

template<int degrad = 0, typename realT>

int mx::math::continueAngles	(	std::vector< realT > &	angles,
		realT	threshold = 0.75 )

Make a vector of angles continuous, fixing the 0/360 crossing.

The vector is modified so it is continuous.

Template Parameters

degrad	controls whether angles are degrees (false) or radians (true)
realT	is the type in which to do arithmetic

Parameters

[in]	angles	the vector of angles
[in]	threshold	[optional] the fraction of a full circle at which to consider a difference in angle discontinuous.

Definition at line 255 of file geo.hpp.

References two_pi().

◆ dtor()

template<typename realT>

realT mx::math::dtor ( realT q )

Convert from degrees to radians.

Parameters

q	is the angle to convert

Returns: the angle q converted to radians

Definition at line 133 of file geo.hpp.

Referenced by mx::improc::azBoxKernel< _arrayT, _kernW, _verboseT >::azBoxKernel(), mx::sigproc::makeModifiedFourierMode(), mx::astro::parAngDeg(), TEST_CASE(), TEST_CASE(), TEST_CASE(), and unitTest::improcTest::imageFiltersTest::TEST_CASE().

◆ rotatePoint()

template<typename realT>

void mx::math::rotatePoint	(	realT &	x0,
		realT &	y0,
		realT	angle )

Rotate a point about the origin.

The rotation is counter-clockwise for positive angles.

Template Parameters

realT a real floating point type

Parameters

	x0	[in.out] the x-coordinate of the point to rotate. On exit contains the rotated value.
	y0	[in.out] the y-coordinate of the point to rotate. On exit contains the rotated value.
[in]	angle	the angle by which to rotate [radians]

Definition at line 310 of file geo.hpp.

◆ rtod()

template<typename realT>

realT mx::math::rtod ( realT q )

Convert from radians to degrees.

Parameters

q	is the angle to convert

Returns: the angle q converted to degrees

Definition at line 148 of file geo.hpp.

Referenced by mx::improc::imCenterRadon< transformT >::center(), mx::improc::maskWedge(), mx::astro::parAngDeg(), and mx::astro::parAngDeg().

Macros

Functions

Macro Definition Documentation

◆ eccent

◆ focus

◆ semilatrect

◆ semimaj

Function Documentation

◆ angleDiff()

◆ angleMean()

◆ angleMod()

◆ continueAngles()

◆ dtor()

◆ rotatePoint()

◆ rtod()