def test_sph_to_cart():
"""Test conversion between sphere and cartesian."""
# Simple test, expected value (11, 0, 0)
r, theta, phi = 11., 0., np.pi / 2.
z = r * np.cos(phi)
rsin_phi = r * np.sin(phi)
x = rsin_phi * np.cos(theta)
y = rsin_phi * np.sin(theta)
coord = _sph_to_cart(np.array([[r, theta, phi]]))[0]
assert_allclose(coord, (x, y, z), atol=1e-7)
assert_allclose(coord, (r, 0, 0), atol=1e-7)
rng = np.random.RandomState(0)
# round-trip test
coords = rng.randn(10, 3)
assert_allclose(_sph_to_cart(_cart_to_sph(coords)), coords, atol=1e-5)
# equivalence tests to old versions
for coord in coords:
sph = _cart_to_sph(coord[np.newaxis])
cart = _sph_to_cart(sph)
sph_old = np.array(_cartesian_to_sphere(*coord))
cart_old = _sphere_to_cartesian(*sph_old)
sph_old[1] = np.pi / 2. - sph_old[1] # new convention
assert_allclose(sph[0], sph_old[[2, 0, 1]], atol=1e-7)
assert_allclose(cart[0], cart_old, atol=1e-7)
assert_allclose(cart[0], coord, atol=1e-7)
def test_sph_to_cart():
"""Test conversion between sphere and cartesian."""
# Simple test, expected value (11, 0, 0)
r, theta, phi = 11., 0., np.pi / 2.
z = r * np.cos(phi)
rsin_phi = r * np.sin(phi)
x = rsin_phi * np.cos(theta)
y = rsin_phi * np.sin(theta)
coord = _sph_to_cart(np.array([[r, theta, phi]]))[0]
assert_allclose(coord, (x, y, z), atol=1e-7)
assert_allclose(coord, (r, 0, 0), atol=1e-7)
rng = np.random.RandomState(0)
# round-trip test
coords = rng.randn(10, 3)
assert_allclose(_sph_to_cart(_cart_to_sph(coords)), coords, atol=1e-5)
# equivalence tests to old versions
for coord in coords:
sph = _cart_to_sph(coord[np.newaxis])
cart = _sph_to_cart(sph)
sph_old = np.array(_cartesian_to_sphere(*coord))
cart_old = _sphere_to_cartesian(*sph_old)
sph_old[1] = np.pi / 2. - sph_old[1] # new convention
assert_allclose(sph[0], sph_old[[2, 0, 1]], atol=1e-7)
assert_allclose(cart[0], cart_old, atol=1e-7)
assert_allclose(cart[0], coord, atol=1e-7)
def _make_radial_coord_system(points, origin):
"""Compute a radial coordinate system at the given points.
For each point X, a set of three unit vectors is computed that point along
the axes of a radial coordinate system. The first axis of the coordinate
system is in the direction of the line between X and the origin point. The
second and third axes are perpendicular to the first axis.
Parameters
----------
points : ndarray, shape (n_points, 3)
For each point, the XYZ carthesian coordinates.
origin : (x, y, z)
A tuple (or other array-like) containing the XYZ carthesian coordinates
of the point of origin. This can for example be the center of a sphere
fitted through the points.
Returns
-------
radial : ndarray, shape (n_points, 3)
For each point X, a unit vector pointing in the radial direction, i.e.,
the direction of the line between X and the origin point. This is the
first axis of the coordinate system.
tan1 : ndarray, shape (n_points, 3)
For each point, a unit vector perpendicular to both ``radial`` and
``tan2``. This is the second axis of the coordinate system.
tan2 : ndarray, shape (n_points, 3)
For each point, a unit vector perpendicular to both ``radial`` and
``tan1``. This is the third axis of the coordinate system.
"""
radial = (points - origin)
radial /= np.linalg.norm(radial, axis=1)[:, np.newaxis]
theta = _cart_to_sph(radial)[:, 1]
# Compute tangential directions
tan1 = np.vstack((-np.sin(theta), np.cos(theta), np.zeros(len(points)))).T
tan2 = np.cross(radial, tan1)
return radial, tan1, tan2
