def __init__(self):
# The energy bundle we'll use for now:
nrm = 1/(N.sqrt(2))
direct = N.c_[[0,-nrm, nrm],[0,0,-1]]
position = N.tile(N.c_[[0, self.source_y, self.source_z]], (1, 2))
self.bund = RayBundle(vertices=position, directions=direct, energy=N.r_[1, 1])
# The assembly for ray tracing:
rot1 = N.dot(G.rotx(N.pi/4)[:3,:3], G.roty(N.pi)[:3,:3])
surf1 = rect_one_sided_mirror(width=10, height=10)
surf1.set_rotation(rot1)
surf2 = rect_one_sided_mirror(width=10, height=10)
self.assembly = Assembly(objects=[surf1, surf2])
TracerScene.__init__(self, self.assembly, self.bund)
def test_tetrahedron(self):
"""Triangular mesh with oblique triangles"""
# Face set:
theta = np.arange(np.pi/2., np.pi*2, 2*np.pi/3)
base_verts = np.vstack(( np.cos(theta), np.sin(theta), np.ones(3) )).T
verts = np.vstack((np.zeros(3), base_verts))
faces = np.array([[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]])
fset = TriangulatedSurface(verts, faces, perfect_mirror)
# Flat floor:
floor = rect_one_sided_mirror(5., 5., 1.)
floor.set_location(np.r_[0., 0., 1.])
assembly = Assembly(objects=[fset, floor])
# Ray bundle of 3 rays starting at equal angles around the tetrahedron:
theta -= np.pi/3.
pos = np.vstack((np.cos(theta), np.sin(theta), np.ones(3)*0.2)) * 0.2
direct = np.vstack(( np.zeros((2,3)), np.ones(3) ))
rayb = RayBundle(pos, direct, energy=np.ones(6))
# Check that the points on the floor describe an isosceles.
engine = TracerEngine(assembly)
engine.ray_tracer(rayb, 2, .05)[0]
verts = engine.tree[-1].get_vertices()
sizes = np.sqrt(
np.sum((verts - np.roll(verts, 1, axis=1))**2, axis=0))
self.assertAlmostEqual(sizes[0], sizes[1])
self.assertAlmostEqual(sizes[2], sizes[1])
'''
def test_tetrahedron(self):
"""Triangular mesh with oblique triangles"""
# Face set:
theta = np.arange(np.pi / 2., np.pi * 2, 2 * np.pi / 3)
base_verts = np.vstack((np.cos(theta), np.sin(theta), np.ones(3))).T
verts = np.vstack((np.zeros(3), base_verts))
faces = np.array([[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]])
fset = TriangulatedSurface(verts, faces, perfect_mirror)
# Flat floor:
floor = rect_one_sided_mirror(5., 5., 1.)
floor.set_location(np.r_[0., 0., 1.])
assembly = Assembly(objects=[fset, floor])
# Ray bundle of 3 rays starting at equal angles around the tetrahedron:
theta -= np.pi / 3.
pos = np.vstack((np.cos(theta), np.sin(theta), np.ones(3) * 0.2)) * 0.2
direct = np.vstack((np.zeros((2, 3)), np.ones(3)))
rayb = RayBundle(pos, direct, energy=np.ones(6))
# Check that the points on the floor describe an isosceles.
engine = TracerEngine(assembly)
engine.ray_tracer(rayb, 2, .05)[0]
verts = engine.tree[-1].get_vertices()
sizes = np.sqrt(np.sum((verts - np.roll(verts, 1, axis=1))**2, axis=0))
self.assertAlmostEqual(sizes[0], sizes[1])
self.assertAlmostEqual(sizes[2], sizes[1])
def setUp(self):
"""
Prepare an assembly with two subassemblies: one assembly representing
a spherical lens behind a flat screen, and one asssembly representing a
perfect mirror.
The mirror will be placed at the two subassemblies' focus, so a paraxial
ray will come back on the other side of the optical axis.
Reference:
In [1], the lensmaker equation
"""
# focal length = 1, thickness = 1/6
R = 1./6.
back_surf = Surface(HemisphereGM(R), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -R/2.])
front_surf = Surface(HemisphereGM(R), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., R/2.], rotation=rotx(N.pi/2.)[:3,:3])
front_lens = AssembledObject(surfs=[back_surf, front_surf])
back_surf = Surface(FlatGeometryManager(), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -0.01])
front_surf = Surface(FlatGeometryManager(), opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., 0.01])
glass_screen = AssembledObject(surfs=[back_surf, front_surf],
transform=translate(0., 0., 0.5))
lens_assembly = Assembly(objects=[glass_screen, front_lens])
lens_assembly.set_transform(translate(0., 0., 1.))
full_assembly = Assembly(objects=[rect_one_sided_mirror(1., 1., 0.)],
subassemblies = [lens_assembly])
self.engine = TracerEngine(full_assembly)
def __init__(self):
# The energy bundle we'll use for now:
nrm = 1 / (N.sqrt(2))
direct = N.c_[[0, -nrm, nrm], [0, 0, -1]]
position = N.tile(N.c_[[0, self.source_y, self.source_z]], (1, 2))
self.bund = RayBundle(vertices=position,
directions=direct,
energy=N.r_[1, 1])
# The assembly for ray tracing:
rot1 = N.dot(G.rotx(N.pi / 4)[:3, :3], G.roty(N.pi)[:3, :3])
surf1 = rect_one_sided_mirror(width=10, height=10)
surf1.set_rotation(rot1)
surf2 = rect_one_sided_mirror(width=10, height=10)
self.assembly = Assembly(objects=[surf1, surf2])
TracerScene.__init__(self, self.assembly, self.bund)
def test_paraxial_ray(self):
"""A paraxial ray reaches the focus"""
rb = RayBundle(N.c_[[0., 0.001, 1.]], N.c_[[0., 0., -1.]],
energy=N.r_[1.], ref_index=N.r_[1.])
screen = rect_one_sided_mirror(5, 5)
f = self.lens.focal_length()
screen.set_transform(translate(0, 0, -f))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], 0, 4)
def test_paraxial_ray(self):
"""A paraxial ray reaches the focus of a planoconvex lens"""
rb = RayBundle(N.c_[[0., 0.001, 1.]], N.c_[[0., 0., -1.]],
energy=N.r_[1.], ref_index=N.r_[1.])
screen = rect_one_sided_mirror(5, 5)
f = self.lens.focal_length()
screen.set_transform(translate(0, 0, -f))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], 0, 4)
def test_image_size(self):
"""Image size of an object imaged by a biconcave lens matches theory"""
origin = N.c_[[0., 0.001, 1.]]
direct = -origin/N.linalg.norm(origin)
rb = RayBundle(origin, direct, energy=N.r_[1.], ref_index=N.r_[1.])
# Magnification, see [1] p. 26.
f = self.lens.focal_length()
m = f/(origin[2] + f)
# Image location, [ibid]:
loc = origin[2]*m
screen = rect_one_sided_mirror(5, 5)
screen.set_transform(translate(0, 0, -loc))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1,2], -m*origin[1], 4)
def test_image_size(self):
"""Image size of an object imaged by a biconcave lens matches theory"""
origin = N.c_[[0., 0.001, 1.]]
direct = -origin / N.linalg.norm(origin)
rb = RayBundle(origin, direct, energy=N.r_[1.], ref_index=N.r_[1.])
# Magnification, see [1] p. 26.
f = self.lens.focal_length()
m = f / (origin[2] + f)
# Image location, [ibid]:
loc = origin[2] * m
screen = rect_one_sided_mirror(5, 5)
screen.set_transform(translate(0, 0, -loc))
e = TracerEngine(Assembly([self.lens, screen]))
vert, _ = e.ray_tracer(rb, 3, 1e-6)
self.failUnlessAlmostEqual(vert[1, 2], -m * origin[1], 4)
def setUp(self):
"""
Prepare an assembly with two subassemblies: one assembly representing
a spherical lens behind a flat screen, and one asssembly representing a
perfect mirror.
The mirror will be placed at the two subassemblies' focus, so a paraxial
ray will come back on the other side of the optical axis.
Reference:
In [1], the lensmaker equation
"""
# focal length = 1, thickness = 1/6
R = 1. / 6.
back_surf = Surface(HemisphereGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -R / 2.])
front_surf = Surface(HemisphereGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., R / 2.],
rotation=rotx(N.pi / 2.)[:3, :3])
front_lens = AssembledObject(surfs=[back_surf, front_surf])
back_surf = Surface(RoundPlateGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., -0.01])
front_surf = Surface(RoundPlateGM(R),
opt.RefractiveHomogenous(1., 1.5),
location=N.r_[0., 0., 0.01])
glass_screen = AssembledObject(surfs=[back_surf, front_surf],
transform=translate(0., 0., 0.5))
lens_assembly = Assembly(objects=[glass_screen, front_lens])
lens_assembly.set_transform(translate(0., 0., 1.))
full_assembly = Assembly(objects=[rect_one_sided_mirror(1., 1., 0.)],
subassemblies=[lens_assembly])
self.engine = TracerEngine(full_assembly)
