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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 48 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 78 of file geometric_utilities.cc.