Utilities::Geometry::SphericalPoint< T > Class Template Reference

represents a point in spherical coordinates, theta = 0 is equator More...

#include <geometry.h>

Public Member Functions
	SphericalPoint (T r, T theta, T phi)
	SphericalPoint (Point_3d< T > &x)
SphericalPoint &	operator= (const SphericalPoint &p)
SphericalPoint &	operator= (Point_3d< T > &x)
bool	operator== (const SphericalPoint &p) const
SphericalPoint	operator* (T a)
SphericalPoint &	operator*= (T a)
T	operator* (const SphericalPoint< T > &p)
	dot product
void	TOcartisian (T x[]) const
	output Cartesian coordinates of the point
Point_3d< T >	TOcartisian () const
	output cartisian coordinates of the point
void	cartisianTOspherical (T const x[])
	set the spherical coordinates of the point from the cartisian coordinates
void	TOspherical (Point_3d< T > &x)
void	StereographicProjection (const SphericalPoint &central, T x[]) const
	Calculates the stereographic projection of the point onto a plane.
void	StereographicProjection (const SphericalPoint &central, Point_2d &x) const
Point_2d	StereographicProjection (const SphericalPoint &central) const
void	OrthographicProjection (const SphericalPoint &central, T x[]) const
	Calculates the orthographic projection of the point onto a plane.
Point_2d	OrthographicProjection (const SphericalPoint &central) const
void	InverseOrthographicProjection (const SphericalPoint &central, T const x[])
	Convert from an orthographic projection of the plane onto the unit sphere.
void	InverseOrthographicProjection (const SphericalPoint &central, const Point_2d &x)
SphericalPoint< T >	InverseOrthographicProjection (const Point_2d &x)
T	angular_separation (SphericalPoint &p)
	angle between points. This uses the haversine formula that is more stable for small angles than the more commin formula
Point_3d< T >	unitPhi ()
	unit vector in phi direction
Point_3d< T >	unitTheta ()
	unit vector in theta direction
T	OrthographicAngleTheta (const SphericalPoint &central)
	the angle between the orthographic x-axis and the constant theta curve
T	OrthographicAnglePhi (const SphericalPoint &central)
	the angle between the orthographic x-axis and the constant Phi curve
Point_3d< T >	theta_hat () const
Point_3d< T >	phi_hat () const

Public Attributes
T	r
T	theta
T	phi

Detailed Description

template<typename T = double>
class Utilities::Geometry::SphericalPoint< T >

represents a point in spherical coordinates, theta = 0 is equator

Member Function Documentation

InverseOrthographicProjection() [1/3]

template<typename T>

SphericalPoint< T > Utilities::Geometry::SphericalPoint< T >::InverseOrthographicProjection

(

const Point_2d &

x

)

Parameters

x	2D coordinate on projection

InverseOrthographicProjection() [2/3]

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::InverseOrthographicProjection	(	const SphericalPoint< T > &	central,
		const Point_2d &	x )

Parameters

central	point on the sphere where the tangent plane touches
x	2D output coordinate on projection

InverseOrthographicProjection() [3/3]

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::InverseOrthographicProjection	(	const SphericalPoint< T > &	central,
		T const	x[] )

Convert from an orthographic projection of the plane onto the unit sphere.

Parameters

central	point on the sphere where the tangent plane touches
x	2D output coordinate on projection

OrthographicAnglePhi()

template<typename T>

T Utilities::Geometry::SphericalPoint< T >::OrthographicAnglePhi

(

const SphericalPoint< T > &

central

)

the angle between the orthographic x-axis and the constant Phi curve

Parameters

central

point on the sphere where the tangent plane touches

OrthographicAngleTheta()

template<typename T>

T Utilities::Geometry::SphericalPoint< T >::OrthographicAngleTheta

(

const SphericalPoint< T > &

central

)

the angle between the orthographic x-axis and the constant theta curve

Parameters

central

point on the sphere where the tangent plane touches

OrthographicProjection() [1/2]

template<typename T>

Point_2d Utilities::Geometry::SphericalPoint< T >::OrthographicProjection

(

const SphericalPoint< T > &

central

)

const

Parameters

central

point on the sphere where the tangent plane touches

OrthographicProjection() [2/2]

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::OrthographicProjection	(	const SphericalPoint< T > &	central,
		T	x[] ) const

Calculates the orthographic projection of the point onto a plane.

The result is in radian units. Near the central point this is a rectolinear projection onto a tangent plane. Points in the oposite hemosphere are maped to points on the border at |x| = 1

Parameters

central	point on the sphere where the tangent plane touches
x	2D output coordinate on projection

StereographicProjection() [1/3]

template<typename T>

Point_2d Utilities::Geometry::SphericalPoint< T >::StereographicProjection

(

const SphericalPoint< T > &

central

)

const

Parameters

central

point on the sphere where the tangent plane touches

StereographicProjection() [2/3]

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::StereographicProjection	(	const SphericalPoint< T > &	central,
		Point_2d &	x ) const

Parameters

central	point on the sphere where the tangent plane touches
x	2D output coordinate on projection

StereographicProjection() [3/3]

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::StereographicProjection	(	const SphericalPoint< T > &	central,
		T	x[] ) const

Calculates the stereographic projection of the point onto a plane.

The result is in radian units. Near the central point this is a rectolinear projection onto a tangent plane.

Parameters

central	point on the sphere where the tangent plane touches
x	2D output coordinate on projection

TOcartisian()

template<typename T>

void Utilities::Geometry::SphericalPoint< T >::TOcartisian

(

T

x[]

)

const

output Cartesian coordinates of the point

output cartisian coordinates

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

• SLsimLib/include/geometry.h