def edge_rays_bundle(num_rays, center, direction, radius, ang_range, flux=None, radius_in=0.): radius = float(radius) radius_in = float(radius_in) a = edge_rays_directions(num_rays, ang_range) # Rotate to a frame in which <direction> is Z: perp_rot = rotation_to_z(direction) directions = N.sum(perp_rot[...,None] * a[None,...], axis=1) # Locations: # See [1] xi1 = random.uniform(size=num_rays) thetas = random.uniform(high=2.*N.pi, size=num_rays) rs = N.sqrt(radius_in**2.+xi1*(radius**2.-radius_in**2.)) xs = rs * N.cos(thetas) ys = rs * N.sin(thetas) # Rotate locations to the plane defined by <direction>: vertices_local = N.vstack((xs, ys, N.zeros(num_rays))) vertices_global = N.dot(perp_rot, vertices_local) rayb = RayBundle(vertices=vertices_global + center, directions=directions) if flux != None: rayb.set_energy(N.pi*(radius**2.-radius_in**2.)/num_rays*flux*N.ones(num_rays)) return rayb
class TestHomogenizer(unittest.TestCase):
def setUp(self):
"""A homogenizer transforms a bundle correctly"""
hmg = rect_homogenizer(5., 3., 10., 0.9)
self.engine = TracerEngine(hmg)
self.bund = RayBundle()
# 4 rays starting somewhat above (+z) the homogenizer
pos = N.zeros((3,4))
pos[2] = N.r_[11, 11, 11, 11]
self.bund.set_vertices(pos)
# One ray going to each wall:
dir = N.c_[[1, 0, -1], [-1, 0, -1], [0, 1, -1], [0, -1, -1]]/N.sqrt(2)
self.bund.set_directions(dir)
# Laborious setup details:
self.bund.set_energy(N.ones(4)*4.)
self.bund.set_ref_index(N.ones(4))
def test_first_hits(self):
"""Test bundle enters homogenizer correctly"""
v, d = self.engine.ray_tracer(self.bund, 1, 0.05)
out_dirs = N.c_[[-1, 0, -1], [1, 0, -1], [0, -1, -1], [0, 1, -1]]/N.sqrt(2)
N.testing.assert_array_almost_equal(d, out_dirs)
out_hits = N.c_[
[2.5, 0, 8.5],
[-2.5, 0, 8.5],
[0, 1.5, 9.5],
[0, -1.5, 9.5]]
N.testing.assert_array_almost_equal(v, out_hits)
def test_up_down(self):
"""Rays coming from below are absorbed, from above reflected"""
going_down = N.c_[[1, 1, -1], [-1, 1, -1], [-1, -1, -1], [1, -1, -1]] / N.sqrt(3)
going_up = going_down.copy()
going_up[2] = 1 / N.sqrt(3)
pos_up = N.c_[[0,0,1], [1,-1,1], [1,1,1], [-1,1,1]]
pos_down = pos_up.copy()
pos_down[2] = -1
bund = RayBundle()
bund.set_directions(N.hstack((going_down, going_up)))
bund.set_vertices(N.hstack((pos_up, pos_down)))
bund.set_energy(N.tile(100, 8))
bund.set_ref_index(N.tile(1, 8))
gm = FlatGeometryManager()
prm = gm.find_intersections(N.eye(4), bund)
absref = optics_callables.AbsorberReflector(0.)
selector = N.arange(8)
gm.select_rays(selector)
outg = absref(gm, bund, selector)
e = outg.get_energy()
N.testing.assert_array_equal(e[:4], 100)
N.testing.assert_array_equal(e[4:], 0)
def oblique_solar_rect_bundle(num_rays,
center,
source_direction,
rays_direction,
x,
y,
ang_range,
flux=None,
procs=1):
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(rays_direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
xs = random.uniform(low=-x / 2., high=x / 2., size=num_rays)
ys = random.uniform(low=-y / 2., high=y / 2., size=num_rays)
if (source_direction == N.array([0, 0, -1])).all():
xs, ys = ys, xs
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((ys, xs, N.zeros(num_rays)))
perp_rot = rotation_to_z(source_direction)
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
cosangle = 2. * N.sin(
N.sqrt(N.sum((rays_direction - source_direction)**2)) / 2.)
rayb.set_energy(x * y / num_rays * flux * N.ones(num_rays) *
N.cos(cosangle))
else:
rayb.set_energy(N.ones(num_rays) / float(num_rays) / procs)
return rayb
def test_up_down(self):
"""Rays coming from below are absorbed, from above reflected"""
going_down = N.c_[[1, 1, -1], [-1, 1, -1], [-1, -1, -1], [1, -1, -1]] / N.sqrt(3)
going_up = going_down.copy()
going_up[2] = 1 / N.sqrt(3)
pos_up = N.c_[[0,0,1], [1,-1,1], [1,1,1], [-1,1,1]]
pos_down = pos_up.copy()
pos_down[2] = -1
bund = RayBundle()
bund.set_directions(N.hstack((going_down, going_up)))
bund.set_vertices(N.hstack((pos_up, pos_down)))
bund.set_energy(N.tile(100, 8))
bund.set_ref_index(N.tile(1, 8))
gm = FlatGeometryManager()
prm = gm.find_intersections(N.eye(4), bund)
absref = optics_callables.AbsorberReflector(0.)
selector = N.arange(8)
gm.select_rays(selector)
outg = absref(gm, bund, selector)
e = outg.get_energy()
N.testing.assert_array_equal(e[:4], 100)
N.testing.assert_array_equal(e[4:], 0)
class TestHomogenizer(unittest.TestCase):
def setUp(self):
"""A homogenizer transforms a bundle correctly"""
hmg = rect_homogenizer(5., 3., 10., 0.9)
self.engine = TracerEngine(hmg)
self.bund = RayBundle()
# 4 rays starting somewhat above (+z) the homogenizer
pos = N.zeros((3, 4))
pos[2] = N.r_[11, 11, 11, 11]
self.bund.set_vertices(pos)
# One ray going to each wall:
dir = N.c_[[1, 0, -1], [-1, 0, -1], [0, 1, -1],
[0, -1, -1]] / N.sqrt(2)
self.bund.set_directions(dir)
# Laborious setup details:
self.bund.set_energy(N.ones(4) * 4.)
self.bund.set_ref_index(N.ones(4))
def test_first_hits(self):
"""Test bundle enters homogenizer correctly"""
v, d = self.engine.ray_tracer(self.bund, 1, 0.05)
out_dirs = N.c_[[-1, 0, -1], [1, 0, -1], [0, -1, -1],
[0, 1, -1]] / N.sqrt(2)
N.testing.assert_array_almost_equal(d, out_dirs)
out_hits = N.c_[[2.5, 0, 8.5], [-2.5, 0, 8.5], [0, 1.5, 9.5],
[0, -1.5, 9.5]]
N.testing.assert_array_almost_equal(v, out_hits)
def edge_rays_bundle(num_rays,
center,
direction,
radius,
ang_range,
flux=None,
radius_in=0.):
radius = float(radius)
radius_in = float(radius_in)
a = edge_rays_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
# Locations:
# See [1]
xi1 = random.uniform(size=num_rays)
thetas = random.uniform(high=2. * N.pi, size=num_rays)
rs = N.sqrt(radius_in**2. + xi1 * (radius**2. - radius_in**2.))
xs = rs * N.cos(thetas)
ys = rs * N.sin(thetas)
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(N.pi * (radius**2. - radius_in**2.) / num_rays * flux *
N.ones(num_rays))
return rayb
class TestTraceProtocol6(unittest.TestCase):
"""
Tests a spherical surface
"""
def setUp(self):
surface1 = Surface(HemisphereGM(2.), opt.perfect_mirror,
rotation=general_axis_rotation(N.r_[1,0,0], N.pi/2.))
surface2 = Surface(HemisphereGM(2.), opt.perfect_mirror,
location=N.array([0,-2,0]),
rotation=general_axis_rotation(N.r_[1,0,0], -N.pi/2.))
self._bund = RayBundle()
self._bund.set_directions(N.c_[[0,1,0]])
self._bund.set_vertices(N.c_[[0,-1,0]])
self._bund.set_energy(N.r_[[1]])
self._bund.set_ref_index(N.r_[[1]])
assembly = Assembly()
object1 = AssembledObject()
object2 = AssembledObject()
object1.add_surface(surface1)
object2.add_surface(surface2)
assembly.add_object(object1)
assembly.add_object(object2)
self.engine = TracerEngine(assembly)
def test_ray_tracers1(self):
params = self.engine.ray_tracer(self._bund, 1, .05)[0]
correct_params = N.c_[[0,2,0]]
N.testing.assert_array_almost_equal(params,correct_params)
def rect_ray_bundle(num_rays,
center,
direction,
x,
y,
sunshape,
ang_rang,
flux=None,
BUIE=None):
'''
generate a rectancular ray bundle for different sunshape options
Arguments:
num_rays - number of rays to generate
center - a column 3-array with the 3D coordinate of the ray bundle's center
direction - a 1D 3-array with the unit average direction vector for the bundle.
x - width of the rectangular ray bundle
y - height of the rectangular ray bundle
sunshape - str, 'pillbox', 'Gaussian','Buie' or 'collimated'
ang_rang - the angular width of the solar disk (pillbox), sigma (gaussian) or CSR (Buie sunshape)
flux - if not None, the ray bundle's energy is set such that each ray has
an equal amount of energy, and the total energy is flux*pi*radius**2
Returns:
A RayBundle object with the above characteristics set.
'''
if sunshape == 'pillbox':
a = pillbox_sunshape_directions(num_rays, ang_rang)
elif sunshape == 'gaussian':
a = gaussian_sunshape_directions(num_rays, ang_rang)
elif sunshape == 'buie':
a = buie_sunshape_directions(num_rays, BUIE.sample, BUIE.FI)
elif sunshape == 'collimated':
a = collimated_directions(num_rays)
# making sure the rect bundle can cover the whole region of interest
x *= 1.2
y *= 1.2
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
# Locations:
# See [1]
xs = N.random.uniform(low=-x / 2., high=x / 2., size=num_rays)
ys = N.random.uniform(low=-y / 2., high=y / 2., size=num_rays)
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(x * y / num_rays * flux * N.ones(num_rays))
return rayb
class TestObjectBuilding1(unittest.TestCase):
"""Tests an object composed of sphere surfaces"""
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(HemisphereGM(3.), optics_callables.perfect_mirror,
location=N.array([0,0,-1.]),
rotation=general_axis_rotation(N.r_[1,0,0], N.pi))
surface2 = Surface(HemisphereGM(3.), optics_callables.perfect_mirror,
location=N.array([0,0,1.]))
self.object = AssembledObject()
self.object.add_surface(surface1)
self.object.add_surface(surface2)
self.assembly.add_object(self.object)
dir = N.c_[[0,0,1.],[0,0,1.]]
position = N.c_[[0,0,-3.],[0,0,-1.]]
self._bund = RayBundle(position, dir, energy=N.ones(2))
def test_object(self):
"""Tests that the assembly heirarchy works at a basic level"""
self.engine = TracerEngine(self.assembly)
inters = self.engine.ray_tracer(self._bund,1,.05)[0]
correct_inters = N.c_[[0,0,2],[0,0,-2]]
N.testing.assert_array_almost_equal(inters, correct_inters)
def test_translation(self):
"""Tests an assembly that has been translated"""
trans = N.array([[1,0,0,0],[0,1,0,0],[0,0,1,1],[0,0,0,1]])
self.assembly.transform_children(trans)
self.engine = TracerEngine(self.assembly)
params = self.engine.ray_tracer(self._bund,1,.05)[0]
correct_params = N.c_[[0,0,3],[0,0,-1]]
N.testing.assert_array_almost_equal(params, correct_params)
def test_rotation_and_translation(self):
"""Tests an assembly that has been translated and rotated"""
self._bund = RayBundle()
self._bund.set_vertices(N.c_[[0,-5,1],[0,5,1]])
self._bund.set_directions(N.c_[[0,1,0],[0,1,0]])
self._bund.set_energy(N.r_[[1,1]])
self._bund.set_ref_index(N.r_[[1,1]])
trans = generate_transform(N.r_[[1,0,0]], N.pi/2, N.c_[[0,0,1]])
self.assembly.transform_children(trans)
self.engine = TracerEngine(self.assembly)
params = self.engine.ray_tracer(self._bund,1,.05)[0]
correct_params = N.c_[[0,-2,1]]
N.testing.assert_array_almost_equal(params, correct_params)
def triangular_bundle(num_rays,
A,
AB,
AC,
direction,
ang_range=N.pi / 2.,
flux=None,
procs=1):
"""
Triangular ray-casting surface anchored on the point A.
Arguments:
- num_rays: the number of rays
- A: The first summit of the triangle and its anchor point.
- AB and AC the vertices of the sides of the triangle in its plane of reference.
- direction: The direction at which the source is pointing
- ang_range: the angular range of the rays emitted by the source
Returns:
- A ray bundle object for tracing
"""
# Triangle ray vertices:
# Declare random numbers:
r1 = N.vstack(N.random.uniform(size=num_rays))
r2 = N.vstack(N.random.uniform(size=num_rays))
# Define points in a local referential where A is at [0,0] on a z=0 plane.
sqrtr1 = N.sqrt(r1)
Plocs = sqrtr1 * (1. -
r2) * AB + r2 * sqrtr1 * AC # Triangle point picking
vertices_local = N.array([Plocs[:, 0], Plocs[:, 1], N.zeros(num_rays)])
# Bring everything back to the global referential:
rot = rotation_to_z(direction)
vertices_global = N.dot(rot, vertices_local) + N.vstack(A)
# Local referential directions:
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
directions = N.sum(rot[..., None] * a[None, ...], axis=1)
rayb = RayBundle()
rayb.set_vertices(vertices_global)
rayb.set_directions(directions)
l1 = N.sqrt(N.sum(AB**2))
l2 = N.sqrt(N.sum(AC**2))
l3 = N.sqrt(N.sum((-AB + AC)**2))
s = (l1 + l2 + l3) / 2.
area = N.sqrt(s * (s - l1) * (s - l2) * (s - l3))
if flux != None:
rayb.set_energy(N.ones(num_rays) * flux * area / float(num_rays))
else:
rayb.set_energy(N.ones(num_rays) / float(num_rays) / procs)
return rayb
def pillbox_rect_bundle(num_rays,
center,
direction,
x,
y,
ang_rang,
flux=None):
'''
generate a rectancular ray bundle for pillbox sunshape
Arguments:
num_rays - number of rays to generate
center - a column 3-array with the 3D coordinate of the ray bundle's center
direction - a 1D 3-array with the unit average direction vector for the bundle.
x - width of the rectangular ray bundle
y - height of the rectangular ray bundle
ang_rang - the angular width of the solar disk
flux - if not None, the ray bundle's energy is set such that each ray has
an equal amount of energy, and the total energy is flux*pi*radius**2
Returns:
A RayBundle object with the above characteristics set.
'''
a = pillbox_sunshape_directions(num_rays, ang_rang)
x *= 1.2
y *= 1.2
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
# Locations:
# See [1]
xs = N.random.uniform(low=-x / 2., high=x / 2., size=num_rays)
ys = N.random.uniform(low=-y / 2., high=y / 2., size=num_rays)
#if (direction == N.array([0,0,-1])).all():
# xs, ys = ys, xs
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
#dirct=N.vstack((-N.ones(num_rays)*direction[0],-N.ones(num_rays)*direction[1],-N.ones(num_rays)*direction[2]))
#vertices_global=vertices_local+dirct*100.
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(x * y / num_rays * flux * N.ones(num_rays))
return rayb
def pillbox_effective_rays(num_rays, X, Y, Z, hits, direction, A_source,
ang_rang, DNI):
'''
Generate a ray bundle according to Buie et al.: "Sunshape distributions for terrestrial simulations." Solar Energy 74 (2003) 113-122 (DOI: 10.1016/S0038-092X(03)00125-7).
*the ray source just cover each individule mirror
Arguments:
num_rays - number of rays over one heliostat, therefore total num of rays is num_rays*num_helios
direction - (1,3)direction of the normal to the source disc.
vertices - (3,n) array vertices of each ray
energy - float - energy of each ray , W
DNI - Direct normal irradiantion W/m2
Returns:
A raybundle object with the above characteristics set.
'''
total_rays = num_rays * N.sum(hits)
a = pillbox_sunshape_directions(total_rays, ang_rang)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
Xs = N.array([])
Ys = N.array([])
Zs = N.array([])
#X,Y=N.meshgrid(X,Y)
for i in xrange(len(hits)):
for j in xrange(len(hits[i])):
if hits[i, j] == 1:
xs = N.random.uniform(low=X[i], high=X[i + 1], size=num_rays)
ys = N.random.uniform(low=Y[j], high=Y[j + 1], size=num_rays)
zs = Z * N.ones(num_rays)
Xs = N.append(Xs, xs)
Ys = N.append(Ys, ys)
Zs = N.append(Zs, zs)
vertices = N.vstack((Xs, Ys, Zs))
energy = N.ones(total_rays) * DNI * A_source / float(total_rays)
rayb = RayBundle(vertices=vertices, directions=directions)
if DNI != None:
rayb.set_energy(energy)
print total_rays
return rayb
def solar_disk_bundle(num_rays, center, direction, radius, ang_range, flux=None, radius_in=0., angular_span=[0.,2.*N.pi], procs=1):
"""
Generates a ray bundle emanating from a disk, with each surface element of
the disk having the same ray density. The rays all point at directions uniformly
distributed between a given angle range from a given direction.
Setting of the bundle's energy is left to the caller.
Arguments:
num_rays - number of rays to generate.
center - a column 3-array with the 3D coordinate of the disk's center
direction - a 1D 3-array with the unit average direction vector for the
bundle.
radius - of the disk.
ang_range - in radians, the maximum deviation from <direction>.
flux - if not None, the ray bundle's energy is set such that each ray has
an equal amount of energy, and the total energy is flux*pi*radius**2
radius_in - Inner radius if the disc is pierced
angular_span - wedge of the disc to consider
Returns:
A RayBundle object with the above characteristics set.
"""
# FIXME why should 'center' be a column vector... that's just annoying.
radius = float(radius)
radius_in = float(radius_in)
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[...,None] * a[None,...], axis=1)
# Locations:
# See [1]
xi1 = random.uniform(size=num_rays)
thetas = random.uniform(low=angular_span[0], high=angular_span[1], size=num_rays)
rs = N.sqrt(radius_in**2.+xi1*(radius**2.-radius_in**2.))
xs = rs * N.cos(thetas)
ys = rs * N.sin(thetas)
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(N.pi*(radius**2.-radius_in**2.)/num_rays*flux*N.ones(num_rays))
else:
rayb.set_energy(N.ones(num_rays)/num_rays/procs)
return rayb
def test_paraxial_ray(self):
"""A paraxial ray in reflected correctly"""
bund = RayBundle()
bund.set_vertices(N.c_[[0.01, 0., 2.]])
bund.set_directions(N.c_[[0., 0., -1.]])
bund.set_energy(N.r_[100.])
bund.set_ref_index(N.r_[1])
self.engine.ray_tracer(bund, 15, 10.)
non_degenerate = self.engine.tree[-1].get_energy() > 10
v = self.engine.tree[-1].get_vertices()[:,non_degenerate]
d = self.engine.tree[-1].get_directions()[:,non_degenerate]
# Not high equality demanded, because of spherical aberration.
N.testing.assert_array_almost_equal(v, N.c_[[-0.01, 0., 1.5]], 2)
N.testing.assert_array_almost_equal(d, N.c_[[0., 0., 1.]], 2)
def test_paraxial_ray(self):
"""A paraxial ray in reflected correctly"""
bund = RayBundle()
bund.set_vertices(N.c_[[0.01, 0., 2.]])
bund.set_directions(N.c_[[0., 0., -1.]])
bund.set_energy(N.r_[100.])
bund.set_ref_index(N.r_[1])
self.engine.ray_tracer(bund, 15, 10.)
non_degenerate = self.engine.tree[-1].get_energy() > 10
v = self.engine.tree[-1].get_vertices()[:, non_degenerate]
d = self.engine.tree[-1].get_directions()[:, non_degenerate]
# Not high equality demanded, because of spherical aberration.
N.testing.assert_array_almost_equal(v, N.c_[[-0.01, 0., 1.5]], 2)
N.testing.assert_array_almost_equal(d, N.c_[[0., 0., 1.]], 2)
def triangular_bundle(num_rays, A, AB, AC, direction, ang_range=N.pi/2., flux=None, procs=1): """ Triangular ray-casting surface anchored on the point A. Arguments: - num_rays: the number of rays - A: The first summit of the triangle and its anchor point. - AB and AC the vertices of the sides of the triangle in its plane of reference. - direction: The direction at which the source is pointing - ang_range: the angular range of the rays emitted by the source Returns: - A ray bundle object for tracing """ # Triangle ray vertices: # Declare random numbers: r1 = N.vstack(N.random.uniform(size=num_rays)) r2 = N.vstack(N.random.uniform(size=num_rays)) # Define points in a local referential where A is at [0,0] on a z=0 plane. sqrtr1 = N.sqrt(r1) Plocs = sqrtr1*(1.-r2)*AB+r2*sqrtr1*AC # Triangle point picking vertices_local = N.array([Plocs[:,0], Plocs[:,1], N.zeros(num_rays)]) # Bring everything back to the global referential: rot = rotation_to_z(direction) vertices_global = N.dot(rot, vertices_local)+N.vstack(A) # Local referential directions: a = pillbox_sunshape_directions(num_rays, ang_range) # Rotate to a frame in which <direction> is Z: directions = N.sum(rot[...,None] * a[None,...], axis=1) rayb = RayBundle() rayb.set_vertices(vertices_global) rayb.set_directions(directions) l1 = N.sqrt(N.sum(AB**2)) l2 = N.sqrt(N.sum(AC**2)) l3 = N.sqrt(N.sum((-AB+AC)**2)) s = (l1+l2+l3)/2. area = N.sqrt(s*(s-l1)*(s-l2)*(s-l3)) if flux != None: rayb.set_energy(N.ones(num_rays)*flux*area/float(num_rays)) else: rayb.set_energy(N.ones(num_rays)/float(num_rays)/procs) return rayb
class TestRectOneSided(unittest.TestCase):
def setUp(self):
self.mirror = rect_one_sided_mirror(1.5, 1.5, 0.9)
pos = N.zeros((3, 8))
pos[0] = N.tile(N.r_[0, 0.5, 2, -2], 2)
pos[2] = N.repeat(N.r_[1, -1], 4)
dir = N.zeros((3, 8))
dir[2] = N.repeat(N.r_[-1, 1], 4)
self.bund = RayBundle()
self.bund.set_vertices(pos)
self.bund.set_directions(dir)
self.bund.set_energy(N.ones(8) * 1000)
self.bund.set_ref_index(N.ones(8))
def test_regular(self):
"""One-sided plate without rotation"""
e = TracerEngine(Assembly(objects=[self.mirror]))
e.ray_tracer(self.bund, 1, 0.05)
outg = e.tree[-1]
correct_verts = N.zeros((3, 2))
correct_verts[0] = N.r_[0, 0.5]
N.testing.assert_array_equal(
outg.get_vertices()[:, outg.get_energy() > 0], correct_verts)
N.testing.assert_array_almost_equal(outg.get_energy(), N.r_[100., 100.,
0, 0])
def test_rotated(self):
"""One-sided plate with rotation"""
rot = sp.roty(N.pi / 4.)
self.mirror.set_transform(rot)
e = TracerEngine(Assembly(objects=[self.mirror]))
e.ray_tracer(self.bund, 1, 0.05)
outg = e.tree[-1]
correct_verts = N.array([[0., 0.5], [0., 0.], [0., -0.5]])
N.testing.assert_array_almost_equal(
outg.get_vertices()[:, outg.get_energy() > 0], correct_verts)
N.testing.assert_array_almost_equal(outg.get_energy(), N.r_[100., 100.,
0, 0])
def single_ray_source(position, direction, flux=None):
'''
Establishes a single ray source originating from a definned point on a defined exact
direction for the purpose of testing single ray behviours.
Arguments:
position - column 3-array with the ray's starting position.
direction - a 1D 3-array with the unit average direction vector for the
bundle.
flux - if not None, the energy transported by the ray.
Returns:
A Raybundle object with the corresponding characteristics.
'''
directions = N.tile(direction[:, None], 1)
directions /= N.sqrt(N.sum(directions**2, axis=0))
singray = RayBundle(vertices=position, directions=directions)
singray.set_energy(flux * N.ones(1))
return singray
def single_ray_source(position, direction, flux=None): ''' Establishes a single ray source originating from a definned point on a defined exact direction for the purpose of testing single ray behviours. Arguments: position - column 3-array with the ray's starting position. direction - a 1D 3-array with the unit average direction vector for the bundle. flux - if not None, the energy transported by the ray. Returns: A Raybundle object with the corresponding characteristics. ''' directions = N.tile(direction[:,None],1) directions /= N.sqrt(N.sum(directions**2, axis=0)) singray = RayBundle(vertices = position, directions = directions) singray.set_energy(flux*N.ones(1)) return singray
class TestRectOneSided(unittest.TestCase):
def setUp(self):
self.mirror = rect_one_sided_mirror(1.5, 1.5, 0.9)
pos = N.zeros((3,8))
pos[0] = N.tile(N.r_[0, 0.5, 2, -2], 2)
pos[2] = N.repeat(N.r_[1, -1], 4)
dir = N.zeros((3,8))
dir[2] = N.repeat(N.r_[-1, 1], 4)
self.bund = RayBundle()
self.bund.set_vertices(pos)
self.bund.set_directions(dir)
self.bund.set_energy(N.ones(8)*1000)
self.bund.set_ref_index(N.ones(8))
def test_regular(self):
"""One-sided plate without rotation"""
e = TracerEngine(Assembly(objects=[self.mirror]))
e.ray_tracer(self.bund, 1, 0.05)
outg = e.tree[-1]
correct_verts = N.zeros((3,2))
correct_verts[0] = N.r_[0, 0.5]
N.testing.assert_array_equal(
outg.get_vertices()[:,outg.get_energy() > 0], correct_verts)
N.testing.assert_array_almost_equal(
outg.get_energy(), N.r_[100., 100., 0, 0])
def test_rotated(self):
"""One-sided plate with rotation"""
rot = sp.roty(N.pi/4.)
self.mirror.set_transform(rot)
e = TracerEngine(Assembly(objects=[self.mirror]))
e.ray_tracer(self.bund, 1, 0.05)
outg = e.tree[-1]
correct_verts = N.array([[0., 0.5], [0., 0.], [0., -0.5]])
N.testing.assert_array_almost_equal(
outg.get_vertices()[:,outg.get_energy() > 0], correct_verts)
N.testing.assert_array_almost_equal(
outg.get_energy(), N.r_[100., 100., 0, 0])
def solar_rect_bundle(num_rays, center, direction, x, y, ang_range, flux=None):
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
xs = random.uniform(low=-x / 2., high=x / 2., size=num_rays)
ys = random.uniform(low=-y / 2., high=y / 2., size=num_rays)
if (direction == N.array([0, 0, -1])).all():
xs, ys = ys, xs
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(x * y / num_rays * flux * N.ones(num_rays))
return rayb
def solar_rect_bundle(num_rays, center, direction, x, y, ang_range, flux=None):
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
perp_rot = rotation_to_z(direction)
directions = N.sum(perp_rot[...,None] * a[None,...], axis=1)
xs = random.uniform(low=-x/2., high=x/2., size=num_rays)
ys = random.uniform(low=-y/2., high=y/2., size=num_rays)
if (direction == N.array([0,0,-1])).all():
xs, ys = ys, xs
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((ys, xs, N.zeros(num_rays)))
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
rayb.set_energy(x*y/num_rays*flux*N.ones(num_rays))
return rayb
class TestTraceProtocol6(unittest.TestCase):
"""
Tests a spherical surface
"""
def setUp(self):
surface1 = Surface(HemisphereGM(2.),
opt.perfect_mirror,
rotation=general_axis_rotation(
N.r_[1, 0, 0], N.pi / 2.))
surface2 = Surface(HemisphereGM(2.),
opt.perfect_mirror,
location=N.array([0, -2, 0]),
rotation=general_axis_rotation(
N.r_[1, 0, 0], -N.pi / 2.))
self._bund = RayBundle()
self._bund.set_directions(N.c_[[0, 1, 0]])
self._bund.set_vertices(N.c_[[0, -1, 0]])
self._bund.set_energy(N.r_[[1]])
self._bund.set_ref_index(N.r_[[1]])
assembly = Assembly()
object1 = AssembledObject()
object2 = AssembledObject()
object1.add_surface(surface1)
object2.add_surface(surface2)
assembly.add_object(object1)
assembly.add_object(object2)
self.engine = TracerEngine(assembly)
def test_ray_tracers1(self):
params = self.engine.ray_tracer(self._bund, 1, .05)[0]
correct_params = N.c_[[0, 2, 0]]
N.testing.assert_array_almost_equal(params, correct_params)
def oblique_solar_rect_bundle(num_rays, center, source_direction, rays_direction, x, y, ang_range, flux=None, procs=1): a = pillbox_sunshape_directions(num_rays, ang_range) # Rotate to a frame in which <direction> is Z: perp_rot = rotation_to_z(rays_direction) directions = N.sum(perp_rot[...,None] * a[None,...], axis=1) xs = random.uniform(low=-x/2., high=x/2., size=num_rays) ys = random.uniform(low=-y/2., high=y/2., size=num_rays) if (source_direction == N.array([0,0,-1])).all(): xs, ys = ys, xs # Rotate locations to the plane defined by <direction>: vertices_local = N.vstack((ys, xs, N.zeros(num_rays))) perp_rot = rotation_to_z(source_direction) vertices_global = N.dot(perp_rot, vertices_local) rayb = RayBundle(vertices=vertices_global + center, directions=directions) if flux != None: cosangle = 2.*N.sin(N.sqrt(N.sum((rays_direction-source_direction)**2))/2.) rayb.set_energy(x*y/num_rays*flux*N.ones(num_rays)*N.cos(cosangle)) else: rayb.set_energy(N.ones(num_rays)/float(num_rays)/procs) return rayb
class TestObjectBuilding1(unittest.TestCase):
"""Tests an object composed of sphere surfaces"""
def setUp(self):
self.assembly = Assembly()
surface1 = Surface(HemisphereGM(3.),
optics_callables.perfect_mirror,
location=N.array([0, 0, -1.]),
rotation=general_axis_rotation(N.r_[1, 0, 0], N.pi))
surface2 = Surface(HemisphereGM(3.),
optics_callables.perfect_mirror,
location=N.array([0, 0, 1.]))
self.object = AssembledObject()
self.object.add_surface(surface1)
self.object.add_surface(surface2)
self.assembly.add_object(self.object)
dir = N.c_[[0, 0, 1.], [0, 0, 1.]]
position = N.c_[[0, 0, -3.], [0, 0, -1.]]
self._bund = RayBundle(position, dir, energy=N.ones(2))
def test_object(self):
"""Tests that the assembly heirarchy works at a basic level"""
self.engine = TracerEngine(self.assembly)
inters = self.engine.ray_tracer(self._bund, 1, .05)[0]
correct_inters = N.c_[[0, 0, 2], [0, 0, -2]]
N.testing.assert_array_almost_equal(inters, correct_inters)
def test_translation(self):
"""Tests an assembly that has been translated"""
trans = N.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 1],
[0, 0, 0, 1]])
self.assembly.transform_children(trans)
self.engine = TracerEngine(self.assembly)
params = self.engine.ray_tracer(self._bund, 1, .05)[0]
correct_params = N.c_[[0, 0, 3], [0, 0, -1]]
N.testing.assert_array_almost_equal(params, correct_params)
def test_rotation_and_translation(self):
"""Tests an assembly that has been translated and rotated"""
self._bund = RayBundle()
self._bund.set_vertices(N.c_[[0, -5, 1], [0, 5, 1]])
self._bund.set_directions(N.c_[[0, 1, 0], [0, 1, 0]])
self._bund.set_energy(N.r_[[1, 1]])
self._bund.set_ref_index(N.r_[[1, 1]])
trans = generate_transform(N.r_[[1, 0, 0]], N.pi / 2, N.c_[[0, 0, 1]])
self.assembly.transform_children(trans)
self.engine = TracerEngine(self.assembly)
params = self.engine.ray_tracer(self._bund, 1, .05)[0]
correct_params = N.c_[[0, -2, 1]]
N.testing.assert_array_almost_equal(params, correct_params)
def solar_disk_bundle(num_rays,
center,
direction,
radius,
ang_range,
flux=None,
radius_in=0.,
angular_span=[0., 2. * N.pi],
x_cut=None,
procs=1,
rays_direction=None):
"""
Generates a ray bundle emanating from a disk, with each surface element of
the disk having the same ray density. The rays all point at directions uniformly
distributed between a given angle range from a given direction.
Setting of the bundle's energy is left to the caller.
Arguments:
num_rays - number of rays to generate.
center - a column 3-array with the 3D coordinate of the disk's center
direction - a 1D 3-array with the unit average direction vector for the
bundle.
radius - of the disk.
ang_range - in radians, the maximum deviation from <direction>.
flux - if not None, the ray bundle's energy is set such that each ray has
an equal amount of energy, and the total energy is flux*pi*radius**2
radius_in - Inner radius if the disc is pierced
angular_span - wedge of the disc to consider
Returns:
A RayBundle object with the above characteristics set.
"""
radius = float(radius)
radius_in = float(radius_in)
a = pillbox_sunshape_directions(num_rays, ang_range)
# Rotate to a frame in which <direction> is Z:
if rays_direction == None:
rays_direction = direction
perp_rot = rotation_to_z(rays_direction)
directions = N.sum(perp_rot[..., None] * a[None, ...], axis=1)
# Locations:
# See [1]
xi1 = random.uniform(size=num_rays)
thetas = random.uniform(low=angular_span[0],
high=angular_span[1],
size=num_rays)
rs = N.sqrt(radius_in**2. + xi1 * (radius**2. - radius_in**2.))
xs = rs * N.cos(thetas)
ys = rs * N.sin(thetas)
# Rotate locations to the plane defined by <direction>:
vertices_local = N.vstack((xs, ys, N.zeros(num_rays)))
if x_cut != None:
vertices_local = vertices_local[:, xs < x_cut]
missing_rays = num_rays - vertices_local.shape[1]
while missing_rays > 0:
xi1 = random.uniform(size=2 * missing_rays)
thetas = random.uniform(low=angular_span[0],
high=angular_span[1],
size=2 * missing_rays)
rs = N.sqrt(radius_in**2. + xi1 * (radius**2. - radius_in**2.))
xs = rs * N.cos(thetas)
ys = rs * N.sin(thetas)
vertices_local = N.concatenate(
(vertices_local, N.vstack(
(xs, ys, N.zeros(2 * missing_rays)))),
axis=1)
vertices_local = vertices_local[:, vertices_local[0] < x_cut]
missing_rays = num_rays - vertices_local.shape[1]
if missing_rays < 0:
vertices_local = vertices_local[:, :num_rays]
vertices_global = N.dot(perp_rot, vertices_local)
rayb = RayBundle(vertices=vertices_global + center, directions=directions)
if flux != None:
cosangle = 2. * N.sin(
N.sqrt(N.sum((rays_direction - direction)**2)) / 2.)
rayb.set_energy(N.pi * (radius**2. - radius_in**2.) / num_rays * flux *
N.ones(num_rays) * N.cos(cosangle))
else:
rayb.set_energy(N.ones(num_rays) / float(num_rays) / procs)
return rayb
def triangular_bundle(num_rays,
A,
B,
C,
direction=None,
ang_range=N.pi / 2.,
flux=None,
procs=1):
"""
Triangular ray-casting surface. A, B and C are 3D coordinates of the vertices. Right hand rule determines the normal vector direction.
Arguments:
- num_rays: the number of rays
- A: The first summit of the triangle and its anchor point.
- AB and AC the vertices of the sides of the triangle in its plane of reference.
- direction: The direction around which rays are escaping the source. If None, the direction is the normal.
- ang_range: the angular range of the rays emitted by the source
Returns:
- A ray bundle object for tracing
"""
# Triangle ray vertices:
# Declare random numbers:
r1 = N.vstack(N.random.uniform(size=num_rays))
r2 = N.vstack(N.random.uniform(size=num_rays))
AB = B - A
AC = C - A
sqrtr1 = N.sqrt(r1)
vertices = (A + sqrtr1 * (1. - r2) * AB +
r2 * sqrtr1 * AC).T # Triangle point picking
# Local referential directions:
a = pillbox_sunshape_directions(num_rays, ang_range)
# Normal vector:
normal = N.cross(AB, AC)
normal = normal / N.sqrt(N.sum(normal**2))
if direction is None:
direction = normal
# Rotate to a frame in which <direction> is direction:
rot = rotation_to_z(direction)
directions = N.sum(rot[..., None] * a[None, ...], axis=1)
rayb = RayBundle()
rayb.set_vertices(vertices)
rayb.set_directions(directions)
# Heron's formula for triangle surface area
l1 = N.sqrt(N.sum(AB**2))
l2 = N.sqrt(N.sum(AC**2))
l3 = N.sqrt(N.sum((-AB + AC)**2))
s = (l1 + l2 + l3) / 2.
area = N.sqrt(s * (s - l1) * (s - l2) * (s - l3))
if flux != None:
cosangle = 2. * N.arcsin(0.5 * N.sqrt(N.sum((direction - normal)**2)))
rayb.set_energy(area / num_rays * flux * N.ones(num_rays) *
N.cos(cosangle))
else:
rayb.set_energy(N.ones(num_rays) / float(num_rays) / procs)
return rayb
