The 3D ambisonic classes. More...

Classes
class	Ambisonic
	The ambisonic class. More...

class	Decoder
	The ambisonic decoder. More...

class	Encoder
	The ambisonic encoder. More...

class	Map
	The ambisonic multi-encoder with distance compensation. More...

class	Meter
	The planewaves peak level meter. More...

class	Optim
	The ambisonic optimization. More...

class	Planewaves
	The planewaves class. More...

class	Rotate
	The ambisonic rotate. More...

class	Scope
	The ambisonic scope. More...

class	Vector
	The planewaves vector. More...

class	Wider
	The ambisonic wider. More...

Functions
unsigned long	factorial (long n)
	The factorial. More...

unsigned long	double_factorial (long n)
	The double factorial. More...

double	associated_legendre (int l, int m, double x)
	The associated Legendre polynomials. More...

double	legendre_normalization (int l, int m)
	The legendre normalization. More...

double	spherical_harmonics_azimuth (int l, int m, double phi)
	The azimuth part of the spherical harmonics function. More...

double	spherical_harmonics_elevation (int l, int m, double theta)
	The elevation part of the spherical harmonics function. More...

double	spherical_harmonics (int l, int m, double phi, double theta)
	The spherical harmonics function. More...

double	wrap (double value, double low, double high)
	The wrapping function. More...

double	wrap_twopi (double value)
	The wrapping function over \(2\pi\). More...

double	clip_minmax (double value, double low, double high)
	The clipping function. More...

double	clip_min (double value, double low)
	The minimum clipping function. More...

double	clip_max (const double value, const double high)
	The maximum clipping function. More...

std::string	int_to_string (int aValue)
	The int to string conversion. More...

Detailed Description

The 3D ambisonic classes.

The 3D high order ambisonic namespace.

All the 3D ambisonic and planewaves classes will be part of this namespace

All the 3D ambisonic classes will be part of this namespace

Function Documentation

double Hoa3D::associated_legendre	(	int	l,
		int	m,
		double	x
	)

inline

The associated Legendre polynomials.

The function computes the associated Legendre polynomial \(P(l, m)\) that is a part of the formula that compute the spherical harmonic coefficient where l is the band and the m is the argument of a spherical harmonic and x is the cosinus of the elevation. It uses three recurrence formulas :

\[P(l, l)(x) = (-1)^l \times (2l - 1)!! \times (1 - x^2)^{0.5l}\]

\[P(l + 1, l)(x) = x \times (2l + 1) \times P(l, l)\]

\[P(l + 1, m)(x) = \frac{(2l + 1) \times x \times P(m, l) - (l + m) \times P(m, l - 1)}{(l - m + 1)}\]

with \(0 \leq l\) and \(-l \leq m \leq +l\)

Parameters

l	The band of the spherical harmonic.
m	The argument of the spherical harmonic.
x	The cosinus of the elevation.

Returns: The function return the associated Legendre polynomial of x for l and m.

See Also: legendre_normalization; spherical_harmonics

Definition at line 104 of file Tools.h.

double Hoa3D::clip_max	(	const double	value,
		const double	high
	)

inline

The maximum clipping function.

The function clips a number at a maximum value.
If \(x > max\), \(f(x) = max\) else \(f(x) = x\).

Parameters

value	The value to clip.
high	The high boundarie.

Returns: The function return the clipped value.

See Also: clip_minmax; clip_min

Definition at line 324 of file Tools.h.

double Hoa3D::clip_min	(	double	value,
		double	low
	)

inline

The minimum clipping function.

The function clips a number at a minimum value.
If \(x < min\), \(f(x) = min\) else \(f(x) = x\).

Parameters

value	The value to clip.
low	The low boundarie.

Returns: The function return the clipped value.

See Also: clip_minmax; clip_max

Definition at line 305 of file Tools.h.

double Hoa3D::clip_minmax	(	double	value,
		double	low,
		double	high
	)

inline

The clipping function.

The function clips a number between boundaries.
If \(x < min\), \(f(x) = min\) else if \(x > max\), \(f(x) = max\) else \(f(x) = x\).

Parameters

value	The value to clip.
low	The low boundarie.
high	The high boundarie.

Returns: The function return the clipped value.

See Also: clip_min; clip_max

Definition at line 284 of file Tools.h.

unsigned long Hoa3D::double_factorial ( long n )

inline

The double factorial.

The function computes the double factorial, the product of all the odd integers up to some odd positive integer :

\[n!! = n \times (n - 2) \times (n - 4) \times {...} \]

Parameters

n	The interger.

Returns: The function return the double factorial of n.

See Also: factorial

Definition at line 75 of file Tools.h.

unsigned long Hoa3D::factorial ( long n )

inline

The factorial.

The function computes the factorial, the product of all positive integers less than or equal to an integer.

\[n! = n \times (n - 1) \times (n - 2) \times {...} \]

Parameters

n	The interger.

Returns: The function return the factorial of n.

See Also: double_factorial

Definition at line 54 of file Tools.h.

std::string Hoa3D::int_to_string ( int aValue )

inline

The int to string conversion.

The function converts a interger to a string.

Parameters

value The value to convert.

Returns: The function return value in a string format.

Definition at line 398 of file Tools.h.

double Hoa3D::legendre_normalization	(	int	l,
		int	m
	)

inline

The legendre normalization.

The function normalizes the associated Legendre polynomial over \(2\pi\) :
if \( m = 0\)

\[K(l) = \sqrt{\frac{2 \times l + 1}{4\pi}}\]

else

\[K(l, m) = \sqrt{2 \times \frac{2 \times l + 1}{4\pi} \times \frac{(l - |m|)!}{(l + |m|)!}}\]

with \(0 \leq l\) and \(-l \leq m \leq +l\)

Parameters

l	The band of the spherical harmonic.
m	The argument of the spherical harmonic.

Returns: The function return the normalization of the associated Legendre polynomial for l and m.

See Also: associated_legendre; spherical_harmonics

Definition at line 138 of file Tools.h.

double Hoa3D::spherical_harmonics	(	int	l,
		int	m,
		double	phi,
		double	theta
	)

inline

The spherical harmonics function.

The function computes the spherical harmonics coefficient for the angles \(\phi\) and \(\theta\) in radian.

\[Y(l, m, \phi, \theta) = Y_{azimuth}(l, m, \phi) \times Y_{elevation}(l, m, \theta)\]

Parameters

l	The band of the spherical harmonic.
m	The argument of the spherical harmonic.
phi	The azimuth.
theta	The elevation.

Returns: The function return the coefficient for phi and theta for the spherical harmonics of band l and argument m.

See Also: spherical_harmonics_azimuth; spherical_harmonics_elevation

Definition at line 218 of file Tools.h.

double Hoa3D::spherical_harmonics_azimuth	(	int	l,
		int	m,
		double	phi
	)

inline

The azimuth part of the spherical harmonics function.

The function computes the azimuth coefficient of the spherical harmonic \([l, m]\) for an angle \(\phi\) in radian :
if \( m \geq 0\)

\[Y_{azimuth}(l, m, \phi) = cos(m \times \phi)\]

else

\[Y_{azimuth}(l, m, \phi) = sin(-m \times \phi)\]

with \(0 \leq l\) and \(-l \leq m \leq +l\)

Parameters

l	The band of the spherical harmonic.
m	The argument of the spherical harmonic.
phi	The azimuth.

Returns: The function return the azimuth coefficient for phi of the spherical harmonic of band l and argument m.

See Also: spherical_harmonics_elevation; spherical_harmonics

Definition at line 177 of file Tools.h.

double Hoa3D::spherical_harmonics_elevation	(	int	l,
		int	m,
		double	theta
	)

inline

The elevation part of the spherical harmonics function.

The function computes the elevation coefficient of the the spherical harmonic \([l, m]\) for an angle \(\theta\) in radian. It uses the associated Legendre polynomial and applies the Legendre normalization :

\[Y_{elevation}(l, m, \theta) = N(l, m) \times P(l, m, cos(/theta)\]

with \(0 \leq l\), \(-l \leq m \leq +l\) and \(N\) the normalization and \(P\) the associated Legendre polynomial.

Parameters

l	The band of the spherical harmonic.
m	The argument of the spherical harmonic.
theta	The elevation.

Returns: The function return the elevation coefficient for theta of the spherical harmonic of band l and argument m.

See Also: legendre_normalization; associated_legendre; spherical_harmonics_azimuth; spherical_harmonics

Definition at line 200 of file Tools.h.

double Hoa3D::wrap	(	double	value,
		double	low,
		double	high
	)

inline

The wrapping function.

The function wraps a number between boundaries.

Parameters

value	The value to wrap.
low	The low boundarie.
high	The high boundarie.

Returns: The function return the wrapped value.

See Also: wrap_twopi

Definition at line 233 of file Tools.h.

double Hoa3D::wrap_twopi ( double value )

inline

The wrapping function over \(2\pi\).

The function wraps a number between 0 and \(2\pi\).

Parameters

value The value to wrap.

Returns: The function return the wrapped value.

See Also: wrap

Definition at line 257 of file Tools.h.

Classes

Functions

Detailed Description

Function Documentation