GeometricUtilities::Coordinates Namespace Reference

Functions
template<int dim>
std::array< double, dim >	to_spherical (const Point< dim > &point)
template<std::size_t dim>
Point< dim >	from_spherical (const std::array< double, dim > &scoord)
static ::ExceptionBase &	NegativeRadius (double arg1)
static ::ExceptionBase &	SphericalAzimuth (double arg1)
static ::ExceptionBase &	SphericalPolar (double arg1)

Detailed Description

A namespace for coordinate transformations.

Function Documentation

to_spherical()

template<int dim>

std::array< double, dim > GeometricUtilities::Coordinates::to_spherical

(

const Point< dim > &

point

)

Return spherical coordinates of a Cartesian point point. The returned array is filled with radius, azimuth angle \(\in [0,2 \pi)\) and polar/inclination angle \( \in [0,\pi]\) (omitted in 2D).

In 3D the transformation is given by

\begin{align*} r &= \sqrt{x^2+y^2+z^2} \\ \theta &= {\rm atan}(y/x) \\ \phi &= {\rm acos} (z/r) \end{align*}

The use of this function is demonstrated in step-75.

Definition at line 43 of file geometric_utilities.cc.

from_spherical()

template<std::size_t dim>

Point< dim > GeometricUtilities::Coordinates::from_spherical

(

const std::array< double, dim > &

scoord

)

Return the Cartesian coordinates of a spherical point defined by scoord which is filled with radius \(r \in [0,\infty)\), azimuth angle \(\theta \in [0,2 \pi)\) and polar/inclination angle \(\phi \in [0,\pi]\) (omitted in 2D).

In 3D the transformation is given by

\begin{align*} x &= r\, \cos(\theta) \, \sin(\phi) \\ y &= r\, \sin(\theta) \, \sin(\phi) \\ z &= r\, \cos(\phi) \end{align*}

Definition at line 69 of file geometric_utilities.cc.