def test_scaling(self):
transform = scaling(2, 3, 4)
p = point(-4, 6, 8)
p_out = point(-8, 18, 32)
self.assertEqual(transform * p, p_out, 'The scaling of point fail')
def test_reflection(self):
transform = scaling(-1, 1, 1)
p = point(2, 3, 4)
p_out = point(-2, 3, 4)
self.assertEqual(transform * p, p_out, 'The reflection failed')
def test_translation(self):
transform = translation(5, -3, 2)
p = point(-3, 4, 5)
p_out = point(2, 1, 7)
self.assertEqual(transform * p, p_out, 'The translation failed')
def test_position(self):
r = ray(point(2, 3, 4), vector(1, 0, 0))
self.assertEqual(position(r, 0), point(2, 3, 4), 'Ray position failed')
self.assertEqual(position(r, 1), point(3, 3, 4), 'Ray position failed')
self.assertEqual(position(r, -1), point(1, 3, 4),
'Ray position failed')
self.assertEqual(position(r, 2.5), point(4.5, 3, 4),
'Ray position failed')
def test_shearing_zy(self):
transform = shearing(zy=1)
p = point(2, 3, 4)
p_out = point(2, 3, 7)
self.assertEqual(transform * p, p_out,
'Shearing in zy direction failed')
def test_shearing_yz(self):
transform = shearing(yz=1)
p = point(2, 3, 4)
p_out = point(2, 7, 4)
self.assertEqual(transform * p, p_out,
'Shearing in yz direction failed')
def test_shearing_xy(self):
transform = shearing(xy=1)
p = point(2, 3, 4)
p_out = point(5, 3, 4)
self.assertEqual(transform * p, p_out,
'shearing in xy direction failed')
def test_inv_translation(self):
transform = translation(5, -3, 2)
inv = inverse(transform)
p = point(-3, 4, 5)
p_out = point(-8, 7, 3)
self.assertEqual(inv * p, p_out, 'The inverse translation failed')
def test_rotation_z(self):
p = point(0, 1, 0)
half_quarter = rotation_z(pi / 4)
full_quarter = rotation_z(pi / 2)
p_out_half = point(-sqrt(2) / 2, sqrt(2) / 2, 0)
p_out_full = point(-1, 0, 0)
self.assertEqual(half_quarter * p, p_out_half, 'z rotation failed')
self.assertEqual(full_quarter * p, p_out_full, 'z rotation failed')
def test_rotation_x(self):
p = point(0, 1, 0)
half_quarter = rotation_x(pi / 4)
full_quarter = rotation_x(pi / 2)
half_quarter_inv = inverse(half_quarter)
p_out_half = point(0, sqrt(2) / 2, sqrt(2) / 2)
p_out_full = point(0, 0, 1)
p_out_inv = point(0, sqrt(2) / 2, -sqrt(2) / 2)
self.assertEqual(half_quarter * p, p_out_half, 'x rotation failed')
self.assertEqual(full_quarter * p, p_out_full, 'x rotation failed')
self.assertEqual(half_quarter_inv * p, p_out_inv,
'x inverse rotation failed')
def test_sphere_z(self):
"""Test sphere normal in z direction"""
s_var = sphere()
n_var = normal_at(s_var, point(0, 0, 1))
self.assertEqual(n_var, vector(0, 0, 1),
"Sphere normal in z direction failed.")
def test_sphere_nonaxial(self):
"""Test sphere normal in nonaxial direction"""
s_var = sphere()
n_var = normal_at(s_var, point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
self.assertEqual(n_var, vector(sqrt(3)/3, sqrt(3)/3, sqrt(3)/3),\
"Sphere normal in z direction failed.")
def test_sphere_normal_vector_is_normal(self):
"""Tests if the normal vector is normal in a sphere"""
s_var = sphere()
n_var = normal_at(s_var, point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
self.assertEqual(n_var, normalize(n_var),
'Normal in a sphere is not normalized.')
def test_sphere_miss(self):
r = ray(point(0, 2, -5), vector(0, 0, 1))
s = sphere()
xs = intersect(s, r)
self.assertEqual(len(xs), 0, 'There should be no intersections ')
def test_sphere_transformed2(self):
r = ray(point(0, 0, -5), vector(0, 0, 1))
s = sphere()
s.set_transform(translation(5, 0, 0))
xs = intersect(s, r)
self.assertEqual(len(xs), 0, 'There sould be no intersection')
def test_sphere_translated(self):
"""Tests a sphere normal vector under translation"""
s_var = sphere()
s_var.set_transform(translation(0, 1, 0))
n_var = normal_at(s_var, point(0, 1.70711, -0.70711))
self.assertEqual(n_var, vector(0, 0.70711, -0.70711),\
'The normal in the translated sphere is wrong.')
def test_ray(self):
origin = point(1, 2, 3)
direction = vector(4, 5, 6)
r = ray(origin, direction)
self.assertEqual(r.origin, origin, 'The origin of ray failed')
self.assertEqual(r.direction, direction, 'The direction of ray failed')
def test_lightning4(self):
"""Lighting with the light and the eye 45 degrees from the suface line"""
eyev = vector(0, -sqrt(2) / 2, -sqrt(2) / 2)
normalv = vector(0, 0, -1)
light = PointLight(point(0, 10, -10), color(1, 1, 1))
result = lighting(self.m_var, light, self.position, eyev, normalv)
self.assertEqual(result, color(1.6364, 1.6364, 1.6364), \
'The lighting function failed.')
def test_lightning1(self):
"""Lighting with the eye between the light and the surface."""
eyev = vector(0, 0, -1)
normalv = vector(0, 0, -1)
light = PointLight(point(0, 0, -10), color(1, 1, 1))
result = lighting(self.m_var, light, self.position, eyev, normalv)
self.assertEqual(result, color(1.9, 1.9, 1.9), \
'The lighting function failed.')
def test_sphere_intersect_group(self):
r = ray(point(0, 0, -5), vector(0, 0, 1))
s = sphere()
xs = intersect(s, r)
self.assertEqual(len(xs), 2, 'There should be 2 intersections')
self.assertEqual(xs[0].object, s, 'The intersection object failed')
self.assertEqual(xs[1].object, s, 'The intersection object failed')
def test_lightning5(self):
"""Lighting with the light hidden behind the surfice"""
eyev = vector(0, 0, -1)
normalv = vector(0, 0, -1)
light = PointLight(point(0, 0, 10), color(1, 1, 1))
result = lighting(self.m_var, light, self.position, eyev, normalv)
self.assertEqual(result, color(0.1, 0.1, 0.1), \
'The lighting function failed.')
def test_sphere(self):
r = ray(point(0, 0, -5), vector(0, 0, 1))
s = sphere()
xs = intersect(s, r)
self.assertEqual(len(xs), 2, 'There should be 2 intersections')
self.assertEqual(xs[0].t, 4.0, 't=4 should intersect')
self.assertEqual(xs[1].t, 6.0, 't=6 should intersect')
def test_transformation(self):
r = ray(point(1, 2, 3), vector(0, 1, 0))
m = translation(3, 4, 5)
r2 = transform(r, m)
self.assertEqual(r2.origin, point(4, 6, 8),
'The ray translation failed')
self.assertEqual(r2.direction, vector(0, 1, 0),
'The ray translation failed')
m2 = scaling(2, 3, 4)
r3 = transform(r, m2)
self.assertEqual(r3.origin, point(2, 6, 12), 'The ray scaling failed')
self.assertEqual(r3.direction, vector(0, 3, 0),
'The ray scaling failed')
def test_sphere_transformed(self):
"Tests the sphere normal vector under a transformation"
s_var = sphere()
m_var = scaling(1, 0.5, 1) * rotation_z(pi / 5)
s_var.set_transform(m_var)
n_var = normal_at(s_var, point(0, sqrt(2) / 2, -sqrt(2) / 2))
self.assertEqual(n_var, vector(0, 0.97014, -0.24254),\
'The normal of an sphere transformed is wrong.')
def test_sphere_inner(self):
r = ray(point(0, 0, 0), vector(0, 0, 1))
s = sphere()
xs = intersect(s, r)
self.assertEqual(len(xs), 2,
'There should be 2 intersections (virtual)')
self.assertEqual(xs[0].t, -1.0, 't=-1 should be an intersection time')
self.assertEqual(xs[1].t, 1.0, 't=1 should be an intersection time')
def test_chain_transform1(self):
p = point(1, 0, 1)
A = rotation_x(pi / 2)
B = scaling(5, 5, 5)
C = translation(10, 5, 7)
p2 = point(1, -1, 0)
self.assertEqual(A * p, p2, 'The rotation failed')
p3 = point(5, -5, 0)
self.assertEqual(B * p2, p3, 'The chain scaling failed')
p4 = point(15, 0, 7)
self.assertEqual(C * p3, p4, 'The chain translation failed')
self.assertEqual(C * B * A * p, p4, 'The chain transformations failed')
def test_sphere_behind(self):
r = ray(point(0, 0, 5), vector(0, 0, 1))
s = sphere()
xs = intersect(s, r)
self.assertEqual(len(xs), 2,
'There should be 2 intersections (virtual)')
self.assertEqual(xs[0].t, -6.0, 't=-6 should be an intersection time')
self.assertEqual(xs[1].t, -4.0, 't=-4 should be an intersection time')
def test_tuple_general(self):
ap = point(1.1, 4.5, 4.6)
av = vector(0, 2.1, 3.3)
ap2 = point(1.1, 6.6, 7.9)
av2 = vector(1, 2, 3)
av3 = vector(1, -0.1, -0.3)
ap3 = point(-1.1, -4.5, -4.6)
self.assertEqual(av + av3, av2, 'These shoud be equal')
self.assertEqual(ap + av, ap2, 'These shoud be equal')
self.assertEqual(ap2 - ap, av, 'These should be equal')
self.assertEqual(ap2 - av, ap, 'These should be equal')
self.assertEqual(av2 - av, av3, 'These should be equal')
self.assertEqual(-ap, ap3, 'These should be equal')
#multiplication and division
ascalar = 3.5
ascalar2 = 0.5
scalar3 = 2
ap = point(1, 2, 4.4)
ap2 = point(3.5, 7, 15.4)
ap3 = point(0.5, 1, 2.2)
self.assertEqual(ascalar * ap, ap2,
'This multiplication should be equal')
self.assertEqual(ascalar2 * ap, ap3,
'This multiplication should be equal')
self.assertEqual(ap / scalar3, ap3, 'This division shouldbe equal')
def test_pointlight(self):
"""
Tests the creation of a light source.
"""
intensity = color(1, 1, 1)
position = point(0, 0, 0)
light = PointLight(position, intensity)
self.assertEqual(light.position, position, "Light position is wrong.")
self.assertEqual(light.intensity, intensity,
"Light intensity is wrong")
def test_sphere_transformed(self):
r = ray(point(0, 0, -5), vector(0, 0, 1))
s = sphere()
s.set_transform(scaling(2, 2, 2))
xs = intersect(s, r)
self.assertEqual(len(xs), 2, 'There should have been 2 intersections')
self.assertEqual(xs[0].t, 3, 't=3 should have been present')
self.assertEqual(xs[1].t, 7, 't=4 should have been present')
