Reference documentation for deal.II version GIT 921d917bf4 2023-02-06 18:40:02+00:00
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 ::ExceptionBaseSphericalAzimuth (double arg1)

static ::ExceptionBaseSphericalPolar (double arg1)

## Detailed Description

A namespace for coordinate transformations.

## ◆ 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 47 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 73 of file geometric_utilities.cc.