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 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 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 = 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 > 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