def __init__(self, radius=1.):
"""
Arguments:
radius - Set as the sphere's radius.
Private attributes:
_rad - radius of the sphere, a float.
"""
QuadricGM.__init__(self)
self.set_radius(radius)
def __init__(self, a=1.0, b=1.0):
"""
Arguments:
a, b - describe the paraboloid as z = (x/a)**2 + (y/b)**2
(sorry, legacy)
Private attributes:
a, b - describe the paraboloid as z = a*x**2 + b*y**2
"""
QuadricGM.__init__(self)
self.a = 1.0 / (a ** 2)
self.b = 1.0 / (b ** 2)
def __init__(self, a=1., b=1., c=1., d=0., e=0., f=0.): """ Arguments: a, b, c, d, e, f: z = ax**2 + by**2 + cxy + dx + ey + f """ QuadricGM.__init__(self) self.a = a self.b = b self.c = c self.d = d self.e = e self.f = f
def __init__(self, c = 1., a = 0.):
"""
Arguments:
c - cone gradient (r/h)
a - position of cone apex on z axis
Cone equation is x**2 + y**2 = (c*(z-a))**2
Private attributes:
c - cone gradient (r/h)
a - position of cone apex on z axis
"""
QuadricGM.__init__(self)
self.c = float(c)
self.a = float(a)
def _select_coords(self, coords, prm): """ Choose between two intersection points on a quadric surface. This implementation extends QuadricGM's behaviour by not choosing intersections outside the rectangular aperture. Arguments: coords - a 2 by 3 by n array whose each column is the global coordinates of one intersection point of a ray with the sphere. prm - the corresponding parametric location on the ray where the intersection occurs. Returns: The index of the selected intersection, or None if neither will do. """ select = QuadricGM._select_coords(self, coords, prm) coords = N.concatenate((coords, N.ones((2,1,coords.shape[2]))), axis = 1) # assumed no additional parameters to coords, axis = 1 local = N.sum(N.linalg.inv(self._working_frame)[None,:2,:,None] * \ coords[:,None,:,:], axis=2) abs_x = abs(local[:,0,:]) abs_y = abs(local[:,1,:]) outside = abs_x > self._w outside |= abs_y > self._h inside = (~outside) & (prm > 1e-6) select[~N.logical_or(*inside)] = N.nan one_hit = N.logical_xor(*inside) select[one_hit] = N.nonzero(inside.T[one_hit,:])[1] return select
def _select_coords(self, coords, prm):
"""
Choose between two intersection points on a quadric surface.
This implementation extends QuadricGM's behaviour by not choosing
intersections outside the circular aperture.
Arguments:
coords - a 2 by 3 by n array whose each column is the global coordinates
of one intersection point of a ray with the sphere.
prm - the corresponding parametric location on the ray where the
intersection occurs.
Returns:
The index of the selected intersection, or None if neither will do.
"""
select = QuadricGM._select_coords(self, coords, prm) # defaults
coords = N.concatenate((coords, N.ones((2, 1, coords.shape[2]))), axis=1)
local_z = N.sum(N.linalg.inv(self._working_frame)[None, 2, :, None] * coords, axis=1)
under_cut = (local_z <= self._h) & (prm > 0)
select[~N.logical_or(*under_cut)] = N.nan
one_hit = N.logical_xor(*under_cut)
select[one_hit] = N.nonzero(under_cut.T[one_hit, :])[1]
return select
def _select_coords(self, coords, prm):
"""
Choose between two intersection points on a quadric surface.
This implementation extends QuadricGM's behaviour by not choosing
intersections outside the hexagon aperture.
Arguments:
coords - a 2 by 3 by n array whose each column is the global coordinates
of one intersection point of a ray with the sphere. Why 2 by three here, doesn't concatenate with
prm - the corresponding parametric location on the ray where the
intersection occurs.
Returns:
The index of the selected intersection, or None if neither will do.
"""
select = QuadricGM._select_coords(self, coords, prm) # defaults
coords = N.concatenate(
(coords, N.ones((2, 1, coords.shape[2]))), axis=1
) # n rays two clusters of row matrices with n elements of one concatenated horizontally 2*4*n ats.
local = N.sum(N.linalg.inv(self._working_frame)[None, :2, :, None] * coords[:, None, :, :], axis=2)
# working frame, a 4*4 homogeneous transform array representing the surface frame in the global coordinates. This is an elementwise multiplication, interesting.
# 2*4 and three extra layers. Imitation of a dot product. Now the coordinates transferred back to the local ones.
abs_x = abs(local[:, 0, :])
abs_y = abs(local[:, 1, :])
outside = abs_x > N.sqrt(3) * self._R / 2.0
outside |= abs_y > self._R - N.tan(N.pi / 6.0) * abs_x
inside = (~outside) & (prm > 1e-9)
select[~N.logical_or(*inside)] = N.nan
one_hit = N.logical_xor(*inside)
select[one_hit] = N.nonzero(inside.T[one_hit, :])[1]
return select
def _select_coords(self, coords, prm):
select = QuadricGM._select_coords(self, coords, prm) # defaults
coords = N.concatenate((coords, N.ones((2,1,coords.shape[2]))), axis=1)
local = N.sum(N.linalg.inv(self._working_frame)[None,:,:,None] * coords[:,None,:,:], axis=2)
bottom_hem = (local[:,2,:] <= 0) & (prm > 0)
in_facet = (N.abs(local[:,0,:])<=self.lx/2.) & (N.abs(local[:,1,:])<=self.ly/2.)
good = N.logical_and(bottom_hem,in_facet)
select[~N.logical_or(*good)] = N.nan
one_hit = N.logical_xor(*good)
select[one_hit] = N.nonzero(good[:,one_hit])[0]
return select
def _select_coords(self, coords, prm):
"""
Select from dual intersections by vetting out rays in the upper
hemisphere, or if both are below use the default behaviour of choosing
the first hit.
"""
select = QuadricGM._select_coords(self, coords, prm) # defaults
coords = N.concatenate((coords, N.ones((2,1,coords.shape[2]))), axis=1)
local = N.sum(N.linalg.inv(self._working_frame)[None,:,:,None] * \
coords[:,None,:,:], axis=2)
bottom_hem = (local[:,2,:] <= 0) & (prm > 0)
select[~N.logical_or(*bottom_hem)] = N.nan
one_hit = N.logical_xor(*bottom_hem)
select[one_hit] = N.nonzero(bottom_hem[:,one_hit])[0]
return select
def _select_coords(self, coords, prm):
"""
Select from dual intersections by vetting out rays in the upper
hemisphere, or if both are below use the default behaviour of choosing
the first hit.
"""
select = QuadricGM._select_coords(self, coords, prm) # defaults
coords = N.concatenate((coords, N.ones((2, 1, coords.shape[2]))),
axis=1)
local = N.sum(N.linalg.inv(self._working_frame)[None,:,:,None] * \
coords[:,None,:,:], axis=2)
bottom_hem = (local[:, 2, :] <= 0) & (prm > 1e-6)
select[~N.logical_or(*bottom_hem)] = N.nan
one_hit = N.logical_xor(*bottom_hem)
select[one_hit] = N.nonzero(bottom_hem[:, one_hit])[0]
return select
