def surf_grid_3D(r, theta, phi, scale_radius=False, **mesh_args):
"""Draw a function r = f(theta, phi), evaluated on a grid, on the sphere.
Parameters
----------
r : (M, N) ndarray
Function values.
theta : (M,) ndarray
Inclination / polar angles of function values.
phi : (N,) ndarray
Azimuth angles of function values.
scale_radius : bool
Whether to scale the radius with the function value (changes the
surface height to reflect function values).
ax : mpl axis, optional
If specified, draw onto this existing axis instead.
mesh_args : dict / kwds
Keyword arguments passed to the ``mlab.mesh`` call.
"""
phi, theta = np.meshgrid(phi, theta)
if scale_radius:
x, y, z = coord.sph2car(theta, phi, r)
else:
x, y, z = coord.sph2car(theta, phi)
return get_mlab().mesh(x, y, z, scalars=r, **mesh_args)
def scatter_3D(theta, phi, scalar=None, **points3d_args):
points3d_args.setdefault('scale_factor', 0.1)
points3d_args.setdefault('color', (1, 0, 0))
if scalar is None:
scalar = np.ones_like(theta)
x, y, z = coord.sph2car(theta, phi)
get_mlab().points3d(x, y, z, scalar, **points3d_args)
def saff_kuijlaars(N): k = np.arange(N) h = -1 + 2 * k / (N - 1) theta = np.arccos(h) phi = np.zeros_like(h) for i in range(1, N - 1): phi[i] = (phi[i - 1] + 3.6 / np.sqrt(N * (1 - h[i]**2))) % (2 * np.pi) x,y,z = coord.sph2car(theta, phi) return x, y, z, len(x)
def saff_kuijlaars(N):
k = np.arange(N)
h = -1 + 2 * k / (N - 1)
theta = np.arccos(h)
phi = np.zeros_like(h)
for i in range(1, N - 1):
phi[i] = (phi[i - 1] + 3.6 / np.sqrt(N * (1 - h[i]**2))) % (2 * np.pi)
x, y, z = coord.sph2car(theta, phi)
return x, y, z, len(x)
rotation = np.eye(3)
out_shape = r.shape[:r.ndim - 1]
R = np.asarray(rotation)
Di = np.linalg.inv(R.dot(np.diag(evals)).dot(R.T))
r = r.reshape(-1, 3)
P = np.zeros(len(r))
for (i, u) in enumerate(r):
P[i] = u.T.dot(Di).dot(u)**(3 / 2)
return (1 / (4 * np.pi * np.prod(evals)**(1/2) * P)).reshape(out_shape)
if __name__ == "__main__":
import sphere, coord, plot
npts = 150
theta, phi = sphere.mesh(npts)
xyz = np.dstack(coord.sph2car(theta, phi))
ODF = single_tensor_ODF(xyz, rotation=None)
signal = single_tensor(gradients=xyz,
bvals=1000 * np.ones(npts * npts), rotation=None,
S0=1, SNR=None)
plot.surf_grid_3D(ODF, theta, phi, scale_radius=True)
plot.show()
plot.surf_grid_3D(signal, theta, phi, scale_radius=True)
plot.show()