The high order ambisonic namespace. More...

Functions
double	min (const double v1, const double v2)
	The minimum function. More...

double	max (const double v1, const double v2)
	The maximum function. More...

double	clip_minmax (const double value, const double min, const double max)
	The clipping function. More...

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

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

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

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

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

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

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

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

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

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

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

double	wrap_360 (const double value)
	The wrapping function in degrees. More...

double	ordinate (const double radius, const double azimuth)
	The ordinate converter function. More...

double	abscissa (const double radius, const double azimuth)
	The abscissa converter function. More...

double	radius (const double x, const double y)
	The radius converter function. More...

double	azimuth (const double x, const double y)
	The azimuth converter function. More...

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

Detailed Description

The high order ambisonic namespace.

This namespace have all the standard methods and functions necessary for ambisonic processing.

Function Documentation

double Hoa::abscissa	(	const double	radius,
		const double	azimuth
	)

inline

The abscissa converter function.

This function takes a radius and an azimuth value and convert them to an abscissa value.

Parameters

radius	The radius value (greather than 0).
azimuth	The azimuth value (between \(0\) and \(2\pi\)).

Returns: The abscissa value.

See Also: ordinate

Definition at line 379 of file HoaMath.h.

double Hoa::associated_legendre	(	int	l,
		int	m,
		const double	x
	)

inline

The associated Legendre polynomials.

The function computes the associated Legendre polynomial \form#2 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 169 of file HoaMath.h.

double Hoa::azimuth	(	const double	x,
		const double	y
	)

inline

The azimuth converter function.

This function takes an abscissa and an ordinate value and convert them to an azimuth value.

Parameters

x	The abscissa value.
y	The ordinate value.

Returns: The azimuth value.

See Also: radius

Definition at line 407 of file HoaMath.h.

double Hoa::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 boundary.

Returns: The function return the clipped value.

See Also: clip_minmax; clip_min

Definition at line 102 of file HoaMath.h.

double Hoa::clip_min	(	const double	value,
		const 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 boundary.

Returns: The function return the clipped value.

See Also: clip_minmax; clip_max

Definition at line 83 of file HoaMath.h.

double Hoa::clip_minmax	(	const double	value,
		const double	min,
		const double	max
	)

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.
min	The low boundary.
max	The high boundary.

Returns: The function return the clipped value.

See Also: clip_min; clip_max

Definition at line 62 of file HoaMath.h.

unsigned long Hoa::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

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

Parameters

n	The interger.

Returns: The function return the double factorial of n.

See Also: factorial

Definition at line 140 of file HoaMath.h.

long double Hoa::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 119 of file HoaMath.h.

std::string Hoa::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 18 of file HoaUtils.h.

double Hoa::legendre_normalization	(	const int	l,
		const int	m
	)

inline

The legendre normalization.

The function normalizes the associated Legendre polynomial over \form#8 : \n

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 203 of file HoaMath.h.

double Hoa::max	(	const double	v1,
		const double	v2
	)

inline

The maximum function.

This function returns the maximum value between two values

Parameters

v1	The first value.
v2	The low boundary.

Returns: The maximum value.

See Also: min

Definition at line 42 of file HoaMath.h.

double Hoa::min	(	const double	v1,
		const double	v2
	)

inline

The minimum function.

This function returns the minimum value between two values

Parameters

v1	The first value.
v2	The low boundary.

Returns: The maximum value.

See Also: min

Definition at line 25 of file HoaMath.h.

double Hoa::ordinate	(	const double	radius,
		const double	azimuth
	)

inline

The ordinate converter function.

This function takes a radius and an azimuth value and convert them to an ordinate value.

Parameters

radius	The radius value (greather than 0).
azimuth	The azimuth value (between \(0\) and \(2\pi\)).

Returns: The ordinate value.

See Also: abscissa

Definition at line 365 of file HoaMath.h.

double Hoa::radius	(	const double	x,
		const double	y
	)

inline

The radius converter function.

This function takes an abscissa and an ordinate value and convert them to a radius value.

Parameters

x	The abscissa value.
y	The ordinate value.

Returns: The radius value.

See Also: azimuth

Definition at line 393 of file HoaMath.h.

double Hoa::spherical_harmonics	(	const int	l,
		const int	m,
		const double	phi,
		const 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 283 of file HoaMath.h.

double Hoa::spherical_harmonics_azimuth	(	const int	l,
		const int	m,
		const double	phi
	)

inline

The azimuth part of the spherical harmonics function.

The function computes the azimuth coefficient of the spherical harmonic \form#12 for an angle \form#13 in radian :\n

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 242 of file HoaMath.h.

double Hoa::spherical_harmonics_elevation	(	const int	l,
		const int	m,
		const double	theta
	)

inline

The elevation part of the spherical harmonics function.

The function computes the elevation coefficient of the the spherical harmonic \form#12  for an angle \form#17 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 265 of file HoaMath.h.

double Hoa::wrap	(	double	value,
		const double	low,
		const double	high
	)

inline

The wrapping function.

The function wraps a number between boundarys.

Parameters

value	The value to wrap.
low	The low boundary.
high	The high boundary.

Returns: The function return the wrapped value.

See Also: wrap_twopi

Definition at line 298 of file HoaMath.h.

double Hoa::wrap_360 ( const double value )

inline

The wrapping function in degrees.

The function wraps a number between \(0\) and \(360°\).

Parameters

value The value to wrap.

Returns: The wrapped value.

See Also: wrap, wrap_twopi

Definition at line 345 of file HoaMath.h.

double Hoa::wrap_twopi ( const 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, wrap_360

Definition at line 322 of file HoaMath.h.

Functions

Detailed Description

Function Documentation