Class and methods for representing band-limited functions on the surface of a 3D sphere. More...

#include <geomc/function/SphericalHarmonics.h>

Public Member Functions
	SphericalHarmonics ()

	SphericalHarmonics (index_t bands)

template<index_t B>
	SphericalHarmonics (const ZonalHarmonics< T, B > &zh)

template<index_t B>
	SphericalHarmonics (const ZonalHarmonics< T, B > &zh, Vec< T, 3 > new_axis)

T	coeff (index_t l, index_t m) const

T &	coeff (index_t l, index_t m)

T *	get ()

const T *	get () const

index_t	size () const

index_t	bands () const

T	dot (const SphericalHarmonics< T, Bands > &other) const

void	normalize ()

template<index_t ZH_Bands>
void	convolve (const ZonalHarmonics< T, ZH_Bands > &zh)

T	eval (Vec< T, 3 > d) const

T	eval (T alt, T azi) const

void	project (Vec< T, 3 > d, T val)

void	project (T alt, T azi, T val)

void	clear ()

SphericalHarmonics< T, Bands > &	operator- ()

SphericalHarmonics< T, Bands > &	operator*= (T k)

SphericalHarmonics< T, Bands > &	operator/= (T k)

SphericalHarmonics< T, Bands > &	operator+= (T k)

SphericalHarmonics< T, Bands > &	operator+= (const SphericalHarmonics< T, Bands > &sh)

SphericalHarmonics< T, Bands >	operator+ (const SphericalHarmonics< T, Bands > &sh)

Static Public Member Functions
static SphericalHarmonics< T, Bands >	basis (Vec< T, 3 > d, index_t n=Bands)
	Construct a SphericalHarmonics basis for the direction given by `d`. More...

Public Attributes
UniqueStorage< T, Bands *Bands >	coeffs
	Coefficient vector.

Protected Member Functions
T	_eval (T cos_alt, T azi) const

void	_project (T cos_alt, T azi, T val)

Protected Attributes
Dimension< Bands >::storage_t	n_bands

Detailed Description

template<typename T, index_t Bands>
class geom::SphericalHarmonics< T, Bands >

Class and methods for representing band-limited functions on the surface of a 3D sphere.

Template Parameters

T	Type of evaluated function.
Bands	Number of bands to represent, or 0 if the band count is dynamic.

Memory requirements are O(n²) on the number of bands.

This implementation uses the Condon-Shortley phase convention.

Complex-valued SH functions are not yet natively supported.

Constructor & Destructor Documentation

◆ SphericalHarmonics() [1/4]

SphericalHarmonics ( )

inline

Construct a new SphericalHarmonics.

If dynamically sized, only a single DC band will be allocated.

◆ SphericalHarmonics() [2/4]

SphericalHarmonics ( index_t bands )

inlineexplicit

Construct a new SphericalHarmonics. (Dynamic size).

Parameters

bands Number of bands to represent. Ignored unless the template parameter Bands is 0 (dynamic).

◆ SphericalHarmonics() [3/4]

SphericalHarmonics ( const ZonalHarmonics< T, B > & zh )

inline

Construct a new SphericalHarmonics matching the function described by the given ZonalHarmonics.

◆ SphericalHarmonics() [4/4]

SphericalHarmonics	(	const ZonalHarmonics< T, B > &	zh,
		Vec< T, 3 >	new_axis
	)

inline

Construct a new SphericalHarmonics matching the given ZonalHarmonics, re-oriented so that the axis of symmetry aligns with new_axis.

Parameters

zh	ZonalHarmonics funciton.
new_axis	New axis of rotational symmetry.

Member Function Documentation

◆ bands()

index_t bands ( ) const

inline

Returns: Number of bands stored.

◆ basis()

static SphericalHarmonics< T, Bands > basis	(	Vec< T, 3 >	d,
		index_t	n = `Bands`
	)

inlinestatic

Construct a SphericalHarmonics basis for the direction given by d.

Parameters

d	Direction for basis.
n	Number of bands to use, if dynamic.

◆ clear()

void clear ( )

inline

Set all coefficients to zero.

◆ coeff() [1/2]

T & coeff	(	index_t	l,
		index_t	m
	)

inline

Get the stored SH coefficient for band l and sub-band m.

Parameters

l	Integer in `[0, bands())`.
m	Integer in `[-l, l]`.

◆ coeff() [2/2]

T coeff	(	index_t	l,
		index_t	m
	)		const

inline

Get the stored SH coefficient for band l and sub-band m.

Parameters

l	Integer in `[0, bands())`.
m	Integer in `[-l, l]`.

◆ convolve()

void convolve ( const ZonalHarmonics< T, ZH_Bands > & zh )

inline

Convolve this SphericalHarmonics with a point spread function described by zh.

Parameters

zh	Point spread (kernel) function.

◆ dot()

T dot ( const SphericalHarmonics< T, Bands > & other ) const

inline

Compute the inner product of this SH function with other.

Returns: Sum of products of respective coefficients between this and other.

◆ eval() [1/2]

T eval	(	T	alt,
		T	azi
	)		const

inline

Evaluate this SphericalHarmonics function in the direction described by alt and azi.

Parameters

alt	Angle from the polar axis.
azi	Azimuthal (longitude) angle.

Returns: Reconstructed function value.

◆ eval() [2/2]

T eval ( Vec< T, 3 > d ) const

inline

Evaluate this SphericalHarmonics function in given direction. The polar direction is aligned with z+, and the x-axis has zero azimuthal angle.

Parameters

d	Direction along which to sample the funciton.

Returns: Reconstructed function value.

◆ get() [1/2]

T * get ( )

inline

Get a pointer to the array of coefficients.

◆ get() [2/2]

const T * get ( ) const

inline

Get a pointer to the array of coefficients.

◆ normalize()

void normalize ( )

inline

Ensure the integral over the entire sphere is 1. If the integral is currently 0, no change will be made.

◆ operator*=()

SphericalHarmonics< T, Bands > & operator*= ( T k )

inline

Multiply this SphericalHarmonics function by a constant value.

Parameters

k	Gain factor.

◆ operator+()

SphericalHarmonics< T, Bands > operator+ ( const SphericalHarmonics< T, Bands > & sh )

inline

Construct a SphericalHarmonics function which is the sum of this and another.

◆ operator+=() [1/2]

SphericalHarmonics< T, Bands > & operator+= ( const SphericalHarmonics< T, Bands > & sh )

inline

Add another SphericalHarmonics function to this one.

◆ operator+=() [2/2]

SphericalHarmonics< T, Bands > & operator+= ( T k )

inline

Add a constant value to this SphericalHarmonics function.

Parameters

k Bias.

◆ operator-()

SphericalHarmonics< T, Bands > & operator- ( )

inline

Negate the values of this SphericalHarmonics function.

◆ operator/=()

SphericalHarmonics< T, Bands > & operator/= ( T k )

inline

Divide this SphericalHarmonics function by a constant value.

Parameters

k Divisor.

◆ project() [1/2]

void project	(	T	alt,
		T	azi,
		T	val
	)

inline

Project the Dirac delta function with direction given by alt and azi, and integral val onto the spherical harmonic basis. The projection will be added to the current representation. In other words, "add" the supplied sample to the representation.

To represent a known function on the sphere, draw many samples from it and project each sample, then divide by the number of samples.

Parameters

d	Direction of sample to project.
val	Value of sample.

◆ project() [2/2]

void project	(	Vec< T, 3 >	d,
		T	val
	)

inline

Project the Dirac delta function with direction d and integral val onto the spherical harmonic basis. The projection will be added to the current representation. In other words, "add" the supplied sample to the representation.

To represent a known function on the sphere, draw many samples from it and project each sample, then divide by 4π times the number of samples.

Parameters

alt	Angle from the polar axis.
azi	Azimuthal (longitude) angle.
val	Value of sample.

◆ size()

index_t size ( ) const

inline

Returns: Number of coefficients stored.

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

geomc/function/FunctionTypes.h
geomc/function/SphericalHarmonics.h

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SphericalHarmonics() [1/4]

◆ SphericalHarmonics() [2/4]

◆ SphericalHarmonics() [3/4]

◆ SphericalHarmonics() [4/4]

Member Function Documentation

◆ bands()

◆ basis()

◆ clear()

◆ coeff() [1/2]

◆ coeff() [2/2]

◆ convolve()

◆ dot()

◆ eval() [1/2]

◆ eval() [2/2]

◆ get() [1/2]

◆ get() [2/2]

◆ normalize()

◆ operator*=()

◆ operator+()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator/=()

◆ project() [1/2]

◆ project() [2/2]

◆ size()