def ring_patch(rin, rout, inc_deg, tilt_deg, tau, dr=([0, 0])):
'''
this function makes a Patch in the shape of a tilted annulus
Parameters
----------
rin : float
inner radius of the annulus
rout : float
outer radius of the annulus
inc_deg : float
inclination of the annulus in degrees
tilt_deg : float
tilt of the annulus (w.r.t. x-axis) in degress
tau : float
opacity of the annulus
dr : tuple:
(x,y) centre of the annulus
Returns
-------
newP : matplotlib.patch
path object to be added to figures
'''
# conversion to radians
inc = np.deg2rad(inc_deg)
tilt = np.deg2rad(tilt_deg)
# get an Ellipse patch that has an ellipse defined with eight CURVE4 Bezier
# curves actual parameters are irrelevant - get_path() returns only a
# normalised Bezier curve ellipse which we then subsequently transform
e1 = Ellipse((1, 1), 1, 1, 0)
# get the Path points for the ellipse (8 Bezier curves with 3 additional
# control points)
e1p = e1.get_path()
# create a rotation matrix
c = np.cos(tilt)
s = np.sin(tilt)
rotm = np.array([[c, s], [s, -c]])
# transform the vertices
i = np.cos(inc)
a1 = e1p.vertices * ([1., i])
a2 = e1p.vertices * ([-1., i])
e1r = np.dot(a1 * rout, rotm) + dr
e2r = np.dot(a2 * rin, rotm) + dr
# create the vertices and fix the path
new_verts = np.vstack((e1r, e2r))
new_cmds = np.hstack((e1p.codes, e1p.codes))
newp = Path(new_verts, new_cmds)
newP = PathPatch(newp, facecolor='black', edgecolor='none', alpha=tau)
return newP
