Directivity

The directivity module provides tools to work with directivity.

The following conventions are used within this module:

• The inclination angle \(\theta\) has a range \([0, \pi]\).
• The azimuth angle \(\phi\) has a range \([0 , 2 \pi]\).

class acoustics.directivity.Cardioid(rotation=None)

Cardioid directivity.

class acoustics.directivity.Custom(theta=None, phi=None, r=None)

A class to work with directivity.

__init__(theta=None, phi=None, r=None)

Constructor.

phi = None

Longitude. 1-D array.

r = None

Magnitude or radius. 2-D array.

theta = None

Latitude. 1-D array.

class acoustics.directivity.Directivity(rotation=None)

Abstract directivity class.

This class defines several methods to be implemented by subclasses.

__init__(rotation=None)

Initialize self. See help(type(self)) for accurate signature.

plot(filename=None, include_rotation=True)

Directivity plot. Plot to filename when given.

Parameters:

• filename – Filename
• include_rotation – Apply the rotation to the directivity. By default the rotation is applied in this figure.

rotation = None

Rotation of the directivity pattern.

using_cartesian(x, y, z, include_rotation=True)

Return the directivity for given cartesian coordinates.

Parameters:

• x – x
• y – y
• z – z

using_spherical(r, theta, phi, include_rotation=True)

Return the directivity for given spherical coordinates.

Parameters:

• r – norm
• theta – angle \(\theta\)
• phi – angle \(\phi\)

class acoustics.directivity.FigureEight(rotation=None)

Directivity of a figure of eight.

class acoustics.directivity.Omni(rotation=None)

Class to work with omni-directional directivity.

class acoustics.directivity.SphericalHarmonic(rotation=None, m=None, n=None)

Directivity of a spherical harmonic of degree n and order m.

__init__(rotation=None, m=None, n=None)

Initialize self. See help(type(self)) for accurate signature.

m = None

Order m.

n = None

Degree n.

acoustics.directivity.cardioid(theta, a=1.0, k=1.0)

A cardioid pattern.

Parameters:

• a – a
• k – k

acoustics.directivity.cartesian_to_spherical(x, y, z)

Convert cartesian coordinates to spherical coordinates.

Parameters:

• x – x
• y – y
• z – z

\[r = \sqrt{\left( x^2 + y^2 + z^2 \right)}\]

\[\theta = \arccos{\frac{z}{r}}\]

\[\phi = \arccos{\frac{y}{x}}\]

acoustics.directivity.figure_eight(theta, phi=0.0)

A figure-of-eight pattern.

Parameters:theta – angle \(\theta\)

acoustics.directivity.plot(d, sphere=False)

Plot directivity d.

Parameters:d (Directivity) – Directivity Returns:Figure

acoustics.directivity.spherical_harmonic(theta, phi, m=0, n=0)

Spherical harmonic of order m and degree n.

Note

The degree n is often denoted l.

See also

scipy.special.sph_harm()

acoustics.directivity.spherical_to_cartesian(r, theta, phi)

Convert spherical coordinates to cartesian coordinates.

Parameters:

• r – norm
• theta – angle \(\theta\)
• phi – angle \(\phi\)

\[x = r \sin{\theta}\cos{\phi}\]

\[y = r \sin{\theta}\sin{\phi}\]

\[z = r \cos{\theta}\]