PYME.Analysis.points.spherical_harmonics module

Estimate spherical harmonics from a point data set

PYME.Analysis.points.spherical_harmonics.cart2sph(x, y, z)
PYME.Analysis.points.spherical_harmonics.r_sph_harm(m, n, theta, phi)

return real valued spherical harmonics. Uses the convention that m > 0 corresponds to the cosine terms, m < zero the sine terms

Parameters:

m : int

n : int

theta : ndarray

the azimuth angle in [0, 2pi]

phi : ndarray

the elevation in [0, pi]

PYME.Analysis.points.spherical_harmonics.reconstruct_from_modes(modes, coeffs, theta, phi)
PYME.Analysis.points.spherical_harmonics.sph2cart(az, el, r)

Convert sperical coordinates into cartesian

Parameters:

az : ndarray

azimuth (angle in x,y plane)

el : ndarray

elevation (angle from z axis)

r : ndarray

radius

Returns:

x, y, z

PYME.Analysis.points.spherical_harmonics.sphere_expansion(x, y, z, mmax=3, centre_points=True)

Project coordinates onto spherical harmonics

Parameters:

x : ndarray

x coordinates

y : ndarray

y coordinates

z : ndarray

z coordinates

mmax : int

Maximum order to calculate to

centre_points : bool

Subtract the mean from the co-ordinates before projecting

Returns:

modes : list of tuples

a list of the (m, n) modes projected onto

c : ndarray

the mode coefficients

centre : tuple

the x, y, z centre of the object (if we centred the points pripr to calculation).

PYME.Analysis.points.spherical_harmonics.sphere_expansion_clean(x, y, z, mmax=3, centre_points=True, nIters=2, tol_init=0.3)

Project coordinates onto spherical harmonics

Parameters:

x : ndarray

x coordinates

y : ndarray

y coordinates

z : ndarray

z coordinates

mmax : int

Maximum order to calculate to

centre_points : bool

Subtract the mean from the co-ordinates before projecting

Returns:

modes : list of tuples

a list of the (m, n) modes projected onto

c : ndarray

the mode coefficients

centre : tuple

the x, y, z centre of the object (if we centred the points prior to calculation).

PYME.Analysis.points.spherical_harmonics.visualize_reconstruction(modes, coeffs, d_phi=0.1, zscale=1.0)