Stores a truncated real spherical harmonics representation of an L2-integrable function. More...

#include <mitsuba/core/shvector.h>

Public Member Functions
	SHVector ()
	Construct an invalid SH vector. More...

	SHVector (int bands)
	Construct a new SH vector (initialized to zero) More...

	SHVector (Stream *stream)
	Unserialize a SH vector to a binary data stream. More...

	SHVector (const SHVector &v)
	Copy constructor. More...

int	getBands () const
	Return the number of stored SH coefficient bands. More...

void	serialize (Stream *stream) const
	Serialize a SH vector to a binary data stream. More...

Float	energy (int band) const
	Get the energy per band. More...

SHVector &	operator= (const SHVector &v)
	Assignment. More...

void	clear ()
	Set all coefficients to zero. More...

SHVector &	operator+= (const SHVector &v)
	Component-wise addition. More...

SHVector	operator+ (const SHVector &v) const
	Component-wise addition. More...

SHVector &	operator-= (const SHVector &v)
	Component-wise subtraction. More...

SHVector	operator- (const SHVector &v) const
	Component-wise subtraction. More...

SHVector &	madd (Float f, const SHVector &v)
	Add a scalar multiple of another vector. More...

SHVector &	operator*= (Float f)
	Scalar multiplication. More...

SHVector	operator* (Float f) const
	Scalar multiplication. More...

SHVector &	operator/= (Float f)
	Scalar division. More...

SHVector	operator/ (Float f) const
	Scalar division. More...

SHVector	operator- () const
	Negation operator. More...

Float &	operator() (int l, int m)
	Access coefficient m (in {-l, ..., l}) on band l. More...

const Float &	operator() (int l, int m) const
	Access coefficient m (in {-l, ..., l}) on band l. More...

Float	eval (Float theta, Float phi) const
	Evaluate for a direction given in spherical coordinates. More...

Float	eval (const Vector &v) const
	Evaluate for a direction given in Cartesian coordinates. More...

Float	evalAzimuthallyInvariant (Float theta, Float phi) const
	Evaluate for a direction given in spherical coordinates. More...

Float	evalAzimuthallyInvariant (const Vector &v) const
	Evaluate for a direction given in cartesian coordinates. More...

bool	isAzimuthallyInvariant () const
	Check if this function is azumuthally invariant. More...

bool	operator== (const SHVector &v) const
	Equality comparison operator. More...

bool	operator!= (const SHVector &v) const
	Equality comparison operator. More...

void	normalize ()
	Normalize so that the represented function becomes a valid distribution. More...

Matrix3x3	mu2 () const
	Compute the second spherical moment (analytic) More...

Float	findMinimum (int res) const
	Brute-force search for the minimum value over the sphere. More...

void	addOffset (Float value)
	Add a constant value. More...

void	convolve (const SHVector &kernel)
	Convolve the SH representation with the supplied kernel. More...

template<typename Functor >
void	project (const Functor &f, int res=32)
	Project the given function onto a SH basis (using a 2D composite Simpson's rule) More...

template<typename Functor >
Float	l2Error (const Functor &f, int res=32) const
	Compute the relative L2 error. More...

std::string	toString () const
	Turn into a string representation. More...

Static Public Member Functions
static Float	normalization (int l, int m)
	Return a normalization coefficient. More...

static void	rotation (const Transform &t, SHRotation &rot)
	Recursively computes rotation matrices for each band of SH coefficients. More...

static void	staticInitialization ()
	Precomputes normalization coefficients for the first few bands. More...

static void	staticShutdown ()
	Free the memory taken up by staticInitialization() More...

Static Protected Member Functions
static void	rotationBlock (const SHRotation::Matrix &M1, const SHRotation::Matrix &Mp, SHRotation::Matrix &Mn)
	Helper function for rotation() – computes a diagonal block based on the previous level. More...

static Float	computeNormalization (int l, int m)
	Compute a normalization coefficient. More...

Friends
Float	dot (const SHVector &v1, const SHVector &v2)
	Dot product. More...

Detailed Description

Stores a truncated real spherical harmonics representation of an L2-integrable function.

Also provides some other useful functionality, such as evaluation, projection and rotation.

The Mathematica equivalent of the basis functions implemented here is:

SphericalHarmonicQ[l_, m_, \[Theta]_, \[Phi]_] :=
  Piecewise[{
     {SphericalHarmonicY[l, m, \[Theta], \[Phi]], m == 0},
     {Sqrt[2]*Re[SphericalHarmonicY[l, m, \[Theta], \[Phi]]], m > 0},
     {Sqrt[2]*Im[SphericalHarmonicY[l, -m, \[Theta], \[Phi]]], m < 0}
 }]

Constructor & Destructor Documentation

mitsuba::SHVector::SHVector ( )

inline

Construct an invalid SH vector.

mitsuba::SHVector::SHVector ( int bands )

inline

Construct a new SH vector (initialized to zero)

mitsuba::SHVector::SHVector ( Stream * stream )

Unserialize a SH vector to a binary data stream.

mitsuba::SHVector::SHVector ( const SHVector & v )

inline

Copy constructor.

Member Function Documentation

void mitsuba::SHVector::addOffset ( Float value )

Add a constant value.

void mitsuba::SHVector::clear ( )

inline

Set all coefficients to zero.

static Float mitsuba::SHVector::computeNormalization	(	int	l,
		int	m
	)

staticprotected

Compute a normalization coefficient.

void mitsuba::SHVector::convolve ( const SHVector & kernel )

Convolve the SH representation with the supplied kernel.

Based on the Funk-Hecke theorem – the kernel must be rotationally symmetric around the Z-axis.

Float mitsuba::SHVector::energy ( int band ) const

inline

Get the energy per band.

Float mitsuba::SHVector::eval	(	Float	theta,
		Float	phi
	)		const

Evaluate for a direction given in spherical coordinates.

Float mitsuba::SHVector::eval ( const Vector & v ) const

Evaluate for a direction given in Cartesian coordinates.

Float mitsuba::SHVector::evalAzimuthallyInvariant	(	Float	theta,
		Float	phi
	)		const

Evaluate for a direction given in spherical coordinates.

This function is much faster but only works for azimuthally invariant functions

Float mitsuba::SHVector::evalAzimuthallyInvariant ( const Vector & v ) const

Evaluate for a direction given in cartesian coordinates.

This function is much faster but only works for azimuthally invariant functions

Float mitsuba::SHVector::findMinimum ( int res ) const

Brute-force search for the minimum value over the sphere.

int mitsuba::SHVector::getBands ( ) const

inline

Return the number of stored SH coefficient bands.

bool mitsuba::SHVector::isAzimuthallyInvariant ( ) const

Check if this function is azumuthally invariant.

template<typename Functor >

Float mitsuba::SHVector::l2Error	(	const Functor &	f,
		int	res = `32`
	)		const

inline

Compute the relative L2 error.

SHVector& mitsuba::SHVector::madd	(	Float	f,
		const SHVector &	v
	)

inline

Add a scalar multiple of another vector.

Matrix3x3 mitsuba::SHVector::mu2 ( ) const

Compute the second spherical moment (analytic)

static Float mitsuba::SHVector::normalization	(	int	l,
		int	m
	)

inlinestatic

Return a normalization coefficient.

void mitsuba::SHVector::normalize ( )

Normalize so that the represented function becomes a valid distribution.

bool mitsuba::SHVector::operator!= ( const SHVector & v ) const

inline

Equality comparison operator.

Float& mitsuba::SHVector::operator()	(	int	l,
		int	m
	)

inline

Access coefficient m (in {-l, ..., l}) on band l.

const Float& mitsuba::SHVector::operator()	(	int	l,
		int	m
	)		const

inline

Access coefficient m (in {-l, ..., l}) on band l.

SHVector mitsuba::SHVector::operator* ( Float f ) const

inline

Scalar multiplication.

SHVector& mitsuba::SHVector::operator*= ( Float f )

inline

Scalar multiplication.

SHVector mitsuba::SHVector::operator+ ( const SHVector & v ) const

inline

Component-wise addition.

SHVector& mitsuba::SHVector::operator+= ( const SHVector & v )

inline

Component-wise addition.

SHVector mitsuba::SHVector::operator- ( const SHVector & v ) const

inline

Component-wise subtraction.

SHVector mitsuba::SHVector::operator- ( ) const

inline

Negation operator.

SHVector& mitsuba::SHVector::operator-= ( const SHVector & v )

inline

Component-wise subtraction.

SHVector mitsuba::SHVector::operator/ ( Float f ) const

inline

Scalar division.

SHVector& mitsuba::SHVector::operator/= ( Float f )

inline

Scalar division.

SHVector& mitsuba::SHVector::operator= ( const SHVector & v )

inline

Assignment.

bool mitsuba::SHVector::operator== ( const SHVector & v ) const

inline

Equality comparison operator.

template<typename Functor >

void mitsuba::SHVector::project	(	const Functor &	f,
		int	res = `32`
	)

inline

Project the given function onto a SH basis (using a 2D composite Simpson's rule)

static void mitsuba::SHVector::rotation	(	const Transform &	t,
		SHRotation &	rot
	)

static

Recursively computes rotation matrices for each band of SH coefficients.

Based on 'Rotation Matrices for Real Spherical Harmonics. Direct Determination by Recursion' by Ivanic and Ruedenberg. The implemented tables follow the notation in 'Spherical Harmonic Lighting: The Gritty Details' by Robin Green.

static void mitsuba::SHVector::rotationBlock	(	const SHRotation::Matrix &	M1,
		const SHRotation::Matrix &	Mp,
		SHRotation::Matrix &	Mn
	)

staticprotected

Helper function for rotation() – computes a diagonal block based on the previous level.

void mitsuba::SHVector::serialize ( Stream * stream ) const

Serialize a SH vector to a binary data stream.

static void mitsuba::SHVector::staticInitialization ( )

static

Precomputes normalization coefficients for the first few bands.

static void mitsuba::SHVector::staticShutdown ( )

static

Free the memory taken up by staticInitialization()

std::string mitsuba::SHVector::toString ( ) const

Turn into a string representation.

Friends And Related Function Documentation

Float dot	(	const SHVector &	v1,
		const SHVector &	v2
	)

friend

Dot product.

The documentation for this struct was generated from the following file:

include/mitsuba/core/shvector.h

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation