Harmonic< D, T > Class Template Reference

The class owns basic harmonics informations. More...

#include <Hoa_Harmonics.hpp>

Public Member Functions
	Harmonic (const size_t index) hoa_noexcept
	The harmonic constructor. More...
	~Harmonic () hoa_noexcept
	The harmonic destructor.
size_t	getIndex () const hoa_noexcept
	Returns the ACN index of the harmonic.
size_t	getDegree () const hoa_noexcept
	Returns the precomputed degree of the harmonic.
long	getOrder () const hoa_noexcept
	Returns the precomputed azimuthal order of the harmonic.
std::string	getName () const hoa_noexcept
	Returns the name of the harmonic.
T	getNormalization () const hoa_noexcept
	Returns the normalization of the harmonic.
T	getSemiNormalization () const hoa_noexcept
	Returns the semi-normalization of the harmonic.

Static Public Member Functions
static long	getIndex (const size_t degree, const long order) hoa_noexcept
	Returns the index of an harmonic for a specific degree and azimuthal order. More...
static size_t	getDegree (const size_t index) hoa_noexcept
	Returns the degree of an harmonic for an index. More...
static long	getOrder (const size_t index) hoa_noexcept
	Returns the azimuthal order of an harmonic for an index. More...
static size_t	getNumberOfHarmonics (const size_t order) hoa_noexcept
	Returns the number of harmonics for an order of decomposition. More...
static size_t	getNumberOfHarmonicsInDegree (const size_t degree) hoa_noexcept
	Returns the number of harmonics for a degree. More...
static T	getNormalization (const size_t degree, const long order) hoa_noexcept
	Returns the normalization N3D or N2D of an harmonic. More...
static T	getSemiNormalization (const size_t degree, const long order) hoa_noexcept
	Returns the semi-normalization of an harmonic. More...

Detailed Description

template<Dimension D, typename T>
class hoa::Harmonic< D, T >

The class owns basic harmonics informations.

The class allows to retrieves several informations about the harmonics: the numbering (ACN), the normalization (SN3D/N3D), the degree, the aziumthal order, etc.

Definition at line 22 of file Hoa_Harmonics.hpp.

Constructor & Destructor Documentation

Harmonic ( const size_t  index )

inline

The harmonic constructor.

Parameters

index

The index must be at least 1.

Definition at line 32 of file Hoa_Harmonics.hpp.

Member Function Documentation

static long getIndex ( const size_t  degree, const long  order  )

inlinestatic

Returns the index of an harmonic for a specific degree and azimuthal order.

The computation is \(i=2|m|-(m<0)\) in 2D and \(i=(l(l+1))+m\) in 3D. with \(l\) the degree, \(m\) the azimuthal order and \(i\) the index of the harmonic.

Parameters

degree	The degree of the harmonic.
order	The order of the harmonic.

Definition at line 66 of file Hoa_Harmonics.hpp.

static size_t getDegree ( const size_t  index )

inlinestatic

Returns the degree of an harmonic for an index.

The computation is \(l=\frac{i+i\bmod{2}}{2}\) in 2D and \(l=\sqrt{i}\) in 3D. with \(l\) the degree and \(i\) the index of the harmonic.

Parameters

index

The index of the harmonic.

Definition at line 73 of file Hoa_Harmonics.hpp.

static long getOrder ( const size_t  index )

inlinestatic

Returns the azimuthal order of an harmonic for an index.

The computation is \(m=l(1-2(i\bmod{2}))\) in 2D and \(m=i-(l(l+1))\) in 3D. with \(l\) the degree, \(m\) the azimuthal order and \(i\) the index of the harmonic.

Parameters

index

The index of the harmonic.

Definition at line 81 of file Hoa_Harmonics.hpp.

static size_t getNumberOfHarmonics ( const size_t  order )

inlinestatic

Returns the number of harmonics for an order of decomposition.

The computation is \(2N+1\) in 2D and \((N+1)^{2}\) in 3D. with \(N\) the order of decomposition.

Parameters

order

The order of decomposition.

Definition at line 89 of file Hoa_Harmonics.hpp.

static size_t getNumberOfHarmonicsInDegree ( const size_t  degree )

inlinestatic

Returns the number of harmonics for a degree.

The computation is \((degree\neq0)+1\) in 2D and \(2l+1\) in 3D. with \(l\) the degree.

Parameters

degree

The degree.

Definition at line 96 of file Hoa_Harmonics.hpp.

static T getNormalization ( const size_t  degree, const long  order  )

inlinestatic

Returns the normalization N3D or N2D of an harmonic.

The semi-normalization \(k^{n2d}_{l, m}\) and \(k^{n3d}_{l, m}\) are defined by:

\[k^{n2d}_{l, m} = 1 \]

\[k^{n3d}_{l, m} = k^{sn3d}_{l, m}\sqrt{2l+1} \]

with \(l\) the degree, \(m\) the azimuthal order,

Parameters

degree	The degree of the harmonic.
order	The order of the harmonic.

Definition at line 107 of file Hoa_Harmonics.hpp.

static T getSemiNormalization ( const size_t  degree, const long  order  )

inlinestatic

Returns the semi-normalization of an harmonic.

Parameters

degree	The degree of the harmonic.
order	The order of the harmonic.

Definition at line 113 of file Hoa_Harmonics.hpp.