ZonalHarmonics< T, Bands > Class Template Reference

Represents a function on the N-sphere with axial symmetry. More...

#include <geomc/function/SphericalHarmonics.h>

Public Member Functions
	ZonalHarmonics ()
	ZonalHarmonics (index_t n)
	ZonalHarmonics (const SphericalHarmonics< T, Bands > &sh)
const T *	get () const
T *	get ()
index_t	bands () const
T &	coeff (index_t n)
T	coeff (index_t n) const
template<index_t B>
T	dot (const ZonalHarmonics< T, B > &zh) const
void	generate_lambertian (index_t order=-1)
void	generate_spot (T cos_angle)
T	eval (T cos_alt) const
void	project (T cos_alt, T val)
void	convolve (const ZonalHarmonics< T, Bands > &kernel)
void	diffuse (T t)
void	normalize ()
void	clear ()

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

Protected Attributes
Dimension< Bands >::storage_t	n_bands

Detailed Description

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

Represents a function on the N-sphere with axial symmetry.

Useful as a convolution kernel for a SphericalHarmonics or another ZonalHarmonics function.

ZonalHarmonics require O(n) storage space on the number of bands and are generally much more efficient than SphericalHarmonics.

Constructor & Destructor Documentation

ZonalHarmonics() [1/3]

ZonalHarmonics ( )

inline

Construct a new ZonalHarmonics.

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

ZonalHarmonics() [2/3]

ZonalHarmonics ( index_t  n )

inline

Construct a new ZonalHarmonics (dynamic size).

Parameters

n	Number of bands to allocate. Ignored if the number of bands is not dynamic.

ZonalHarmonics() [3/3]

ZonalHarmonics ( const SphericalHarmonics< T, Bands > &  sh )

inline

Construct a new ZonalHarmonics representing the given SphericalHarmonics function smoothed by a rotation about its polar axis.

Parameters

sh	A SphericalHarmonics funciton.

Member Function Documentation

bands()

index_t bands ( ) const

inline

Returns

The number of bands in the representation.

clear()

void clear ( )

inline

Set all coefficients to zero.

coeff() [1/2]

T & coeff ( index_t  n )

inline

Returns

The nth band coefficient.

coeff() [2/2]

T coeff ( index_t  n ) const

inline

Returns

The nth band coefficient.

convolve()

void convolve ( const ZonalHarmonics< T, Bands > &  kernel )

inline

Blur this ZonalHarmonics function using kernel as a point spread funciton.

Parameters

kernel

Point spread function.

diffuse()

void diffuse ( T  t )

inline

Convert this ZonalHarmonics function to its form after t self-convolutions.

If t is 0, this function becomes an N-band approximation of the dirac (identity) kernel. If t is 1, this function remains unchanged.

Parameters

t	Real number of times to self-convolve.

dot()

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

inline

Returns

The inner product of this ZonalHarmonics with zh.

eval()

T eval ( T  cos_alt ) const

inline

Evaluate this ZonalHarmonics function at the given angle.

Parameters

cos_alt

Returns

generate_lambertian()

void generate_lambertian ( index_t  order = -1 )

inline

Replace this ZonalHarmonics function with an n-th order approximation of the Lambertian diffuse reflectance function (i.e. max(0, cos(alt))).

Parameters

order

Number of bands to use in the approximation. If no count is specified, all available bands will be used. Note that very high-order approximations may be vulernable to numerical instability.

generate_spot()

void generate_spot ( T  cos_angle )

inline

Replace this ZonalHarmonics function with an n-th order approximation of a circular spot on the sphere having value 1 and the given angular radius.

Parameters

cos_angle

Cosine of the radial angle of the spot (between -1 and 1).

get() [1/2]

T * get ( )

inline

Return a pointer to the array of coefficients.

get() [2/2]

const T * get ( ) const

inline

Return 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.

project()

void project ( T  cos_alt, T  val  )

inline

Project the sample having value val at angle given by cos_alt to this ZonalHarmonics function.

Parameters

cos_alt	Cosine of the angle from the polar axis to the sample.
val	Value of the sample.

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

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