def test_findinf_n1_n2_at_various_intersections(self):
a = GlassSphere()
a.transform = Transformations.scaling(2, 2, 2)
a.material.refractive_index = 1.5
b = GlassSphere()
b.transform = Transformations.translation(0, 0, -0.25)
b.material.refractive_index = 2.0
c = GlassSphere()
c.transform = Transformations.translation(0, 0, 0.25)
c.material.refractive_index = 2.5
r = Ray(Point(0, 0, -4), Vector(0, 0, 1))
xs = Intersection.intersections(Intersection(2, a), Intersection(2.75, b), Intersection(3.25, c), Intersection(4.75, b), Intersection(5.25, c), Intersection(6, a))
RefractiveIndices = namedtuple("RefractiveIndices", ["n1", "n2"])
refractive_indices_list = [
RefractiveIndices(1.0, 1.5),
RefractiveIndices(1.5, 2.0),
RefractiveIndices(2.0, 2.5),
RefractiveIndices(2.5, 2.5),
RefractiveIndices(2.5, 1.5),
RefractiveIndices(1.5, 1.0)
]
for index, refractive_index in enumerate(refractive_indices_list):
comps = Computations.prepare_computations(xs[index], r, xs)
print(comps.n1)
print(comps.n2)
self.assertEqual(comps.n1, refractive_index.n1)
self.assertEqual(comps.n2, refractive_index.n2)
def test_subdivide_csg_subdivide_children(self):
s1 = Sphere()
s1.transform = Transformations.translation(-1.5, 0, 0)
s2 = Sphere()
s2.transform = Transformations.translation(1.5, 0, 0)
left = Group()
left.add_child(s1)
left.add_child(s2)
s3 = Sphere()
s3.transform = Transformations.translation(0, 0, -1.5)
s4 = Sphere()
s4.transform = Transformations.translation(0, 0, 1.5)
right = Group()
right.add_child(s3)
right.add_child(s4)
shape = CSG("difference", left, right)
shape.divide(1)
self.assertIsInstance(left.members[0], Group)
self.assertEqual(left.members[0].members, [s1])
self.assertIsInstance(left.members[1], Group)
self.assertEqual(left.members[1].members, [s2])
self.assertIsInstance(right.members[0], Group)
self.assertEqual(right.members[0].members, [s3])
self.assertIsInstance(right.members[1], Group)
self.assertEqual(right.members[1].members, [s4])
def test_color_at_with_mutually_reflective_surfaces(self):
w = World()
w.light = PointLight(Point(0, 0, 0), Color(1, 1, 1))
lower = Plane()
lower.material.reflective = 1
lower.transform = Transformations.translation(0, -1, 0)
w.objects.append(lower)
upper = Plane()
upper.material.reflective = 1
upper.transform = Transformations.translation(0, 1, 0)
w.objects.append(upper)
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
self.assertIsNotNone(World.color_at(w, r))
def test_partitioning_group_children(self):
s1 = Sphere()
s1.transform = Transformations.translation(-2, 0, 0)
s2 = Sphere()
s2.transform = Transformations.translation(2, 0, 0)
s3 = Sphere()
g = Group()
g.add_child(s1)
g.add_child(s2)
g.add_child(s3)
(left, right) = g.partition_children()
self.assertEqual(g.members, [s3])
self.assertEqual(left, [s1])
self.assertEqual(right, [s2])
def test_group_bounding_box_contains_children(self):
s = Sphere()
s.transform = Transformations.translation(2, 5, -3).dot(
Transformations.scaling(2, 2, 2))
c = Cylinder()
c.minimum = -2
c.maximum = 2
c.transform = Transformations.translation(-4, -1, 4).dot(
Transformations.scaling(0.5, 1, 0.5))
shape = Group()
shape.add_child(s)
shape.add_child(c)
box = shape.bounds_of()
self.assertEqual(box.min, Point(-4.5, -3, -5))
self.assertEqual(box.max, Point(4, 7, 4.5))
def test_pattern_object_and_pattern_transformation(self):
shape = Sphere()
shape.transform = Transformations.scaling(2, 2, 2)
pattern = Pattern.test_pattern()
pattern.transform = Transformations.translation(0.5, 1, 1.5)
c = pattern.pattern_at_shape(shape, Point(2.5, 3, 3.5))
self.assertEqual(c, Color(0.75, 0.5, 0.25))
def test_chained_transformations(self):
p = Point(1, 0, 1)
a = Transformations.rotation_x(math.pi / 2)
b = Transformations.scaling(5, 5, 5)
c = Transformations.translation(10, 5, 7)
t = c.dot(b.dot(a))
self.assertEqual(Matrix.multiply_tuple(t, p), Point(15, 0, 7))
def test_intersect_translated_shape_with_ray(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Shape.test_shape()
s.transform = Transformations.translation(5, 0, 0)
xs = s.intersect(r)
self.assertEqual(s.saved_ray.origin, Point(-5, 0, -5))
self.assertEqual(s.saved_ray.direction, Vector(0, 0, 1))
def test_transformation_move_world(self):
from_point = Point(0, 0, 8)
to = Point(0, 0, 0)
up = Vector(0, 1, 0)
t = World.view_transform(from_point, to, up)
self.assertTrue(
np.array_equal(t, Transformations.translation(0, 0, -8)))
def test_hit_offset_point(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.transform = Transformations.translation(0, 0, 1)
i = Intersection(5, shape)
comps = Computations.prepare_computations(i, r)
self.assertLess(comps.over_point.z, -Constants.epsilon / 2)
self.assertGreater(comps.point.z, comps.over_point.z)
def test_csg_bounding_box(self):
left = Sphere()
right = Sphere()
right.transform = Transformations.translation(2, 3, 4)
shape = CSG("difference", left, right)
box = shape.bounds_of()
self.assertEqual(box.min, Point(-1, -1, -1))
self.assertEqual(box.max, Point(3, 4, 5))
def test_intersecting_ray_with_nonempty_group(self):
g = Group()
s1 = Sphere()
s2 = Sphere()
s2.transform = Transformations.translation(0, 0, -3)
s3 = Sphere()
s3.transform = Transformations.translation(5, 0, 0)
g.add_child(s1)
g.add_child(s2)
g.add_child(s3)
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = g.local_intersect(r)
self.assertEqual(len(xs), 4)
self.assertEqual(xs[0].object, s2)
self.assertEqual(xs[1].object, s2)
self.assertEqual(xs[2].object, s1)
self.assertEqual(xs[3].object, s1)
def test_ray_camera_transformed(self):
c = Camera(201, 101, math.pi / 2)
c.transform = Transformations.rotation_y(math.pi / 4).dot(
Transformations.translation(0, -2, 5))
r = Camera.ray_for_pixel(c, 100, 50)
self.assertEqual(r.origin, Point(0, 2, -5))
self.assertEqual(r.direction,
Vector(math.sqrt(2) / 2, 0, -math.sqrt(2) / 2))
def test_group_partitions_children(self):
s1 = Sphere()
s1.transform = Transformations.translation(-2, -2, 0)
s2 = Sphere()
s2.transform = Transformations.translation(-2, 2, 0)
s3 = Sphere()
s3.transform = Transformations.scaling(4, 4, 4)
g = Group()
g.add_child(s1)
g.add_child(s2)
g.add_child(s3)
g.divide(1)
self.assertEqual(g.members[0], s3)
subgroup = g.members[1]
self.assertIsInstance(subgroup, Group)
self.assertEqual(len(subgroup.members), 2)
self.assertEqual(subgroup.members[0].members, [s1])
self.assertEqual(subgroup.members[1].members, [s2])
def test_intersecting_transformed_group(self):
g = Group()
g.transform = Transformations.scaling(2, 2, 2)
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
g.add_child(s)
r = Ray(Point(10, 0, -10), Vector(0, 0, 1))
xs = g.intersect(r)
self.assertEqual(len(xs), 2)
def test_under_point_offset_below_surface(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = GlassSphere()
shape.transform = Transformations.translation(0, 0, 1)
i = Intersection(5, shape)
xs = Intersection.intersections(i)
comps = Computations.prepare_computations(i, r, xs)
self.assertGreater(comps.under_point.z, Constants.epsilon / 2)
self.assertLess(comps.point.z, comps.under_point.z)
def test_shade_hit_with_transparent_material(self):
w = World.default_world()
floor = Plane()
floor.transform = Transformations.translation(0, -1, 0)
floor.material.transparency = 0.5
floor.material.refractive_index = 1.5
w.objects.append(floor)
ball = Sphere()
ball.material.color = Color(1, 0, 0)
ball.material.ambient = 0.5
ball.transform = Transformations.translation(0, -3.5, -0.5)
w.objects.append(ball)
r = Ray(Point(0, 0, -3), Vector(0, -math.sqrt(2) / 2,
math.sqrt(2) / 2))
xs = Intersection.intersections(Intersection(math.sqrt(2), floor))
comps = Computations.prepare_computations(xs[0], r, xs)
color = World.shade_hit(w, comps, 5)
self.assertEqual(color, Color(0.93642, 0.68642, 0.68642))
def test_converting_normal_from_object_to_world_space(self):
g1 = Group()
g1.transform = Transformations.rotation_y(math.pi / 2)
g2 = Group()
g2.transform = Transformations.scaling(1, 2, 3)
g1.add_child(g2)
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
g2.add_child(s)
n = s.normal_to_world(Vector(math.sqrt(3) /3, math.sqrt(3) / 3, math.sqrt(3) / 3))
self.assertEqual(n, Vector(0.2857, 0.4286, -0.8571))
def test_converting_point_from_world_to_object_space(self):
g1 = Group()
g1.transform = Transformations.rotation_y(math.pi / 2)
g2 = Group()
g2.transform = Transformations.scaling(2, 2, 2)
g1.add_child(g2)
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
g2.add_child(s)
p = s.world_to_object(Point(-2, 0, -10))
self.assertEqual(p, Point(0, 0, -1))
def test_finding_normal_on_child_object(self):
g1 = Group()
g1.transform = Transformations.rotation_y(math.pi / 2)
g2 = Group()
g2.transform = Transformations.scaling(1, 2, 3)
g1.add_child(g2)
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
g2.add_child(s)
n = s.normal_at(Point(1.7321, 1.1547, -5.5774))
self.assertEqual(n, Vector(0.2857, 0.4286, -0.8571))
def test_ray_hits_csg_object(self):
s1 = Sphere()
s2 = Sphere()
s2.transform = Transformations.translation(0, 0, 0.5)
c = CSG("union", s1, s2)
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = c.local_intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, 4)
self.assertEqual(xs[0].object, s1)
self.assertEqual(xs[1].t, 6.5)
self.assertEqual(xs[1].object, s2)
def test_reflected_color_at_maximum_recursive_depth(self):
w = World.default_world()
shape = Plane()
shape.material.reflective = 0.5
shape.transform = Transformations.translation(0, -1, 0)
w.objects.append(shape)
r = Ray(Point(0, 0, -3), Vector(0, -math.sqrt(2) / 2,
math.sqrt(2) / 2))
i = Intersection(math.sqrt(2), shape)
comps = Computations.prepare_computations(i, r)
color = World.reflected_color(w, comps, 0)
self.assertEqual(color, Color(0, 0, 0))
def test_subdividing_group_too_few_children(self):
s1 = Sphere()
s1.transform = Transformations.translation(-2, 0, 0)
s2 = Sphere()
s2.transform = Transformations.translation(2, 1, 0)
s3 = Sphere()
s3.transform = Transformations.translation(2, -1, 0)
subgroup = Group()
subgroup.add_child(s1)
subgroup.add_child(s2)
subgroup.add_child(s3)
s4 = Sphere()
g = Group()
g.add_child(subgroup)
g.add_child(s4)
g.divide(3)
self.assertEqual(g.members[0], subgroup)
self.assertEqual(g.members[1], s4)
self.assertEqual(len(subgroup.members), 2)
self.assertEqual(subgroup.members[0].members, [s1])
self.assertEqual(subgroup.members[1].members, [s2, s3])
def test_shade_hit_reflective_material(self):
w = World.default_world()
shape = Plane()
shape.material.reflective = 0.5
shape.transform = Transformations.translation(0, -1, 0)
w.objects.append(shape)
r = Ray(Point(0, 0, -3), Vector(0, -math.sqrt(2) / 2,
math.sqrt(2) / 2))
i = Intersection(math.sqrt(2), shape)
comps = Computations.prepare_computations(i, r)
color = World.shade_hit(w, comps)
self.assertEqual(color, Color(0.87677, 0.92436, 0.82918))
def test_shade_hit_intersection_in_shadow(self):
w = World()
w.light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
s1 = Sphere()
w.objects.append(s1)
s2 = Sphere()
s2.transform = Transformations.translation(0, 0, 10)
w.objects.append(s2)
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
i = Intersection(4, s2)
comps = Computations.prepare_computations(i, r)
c = World.shade_hit(w, comps)
self.assertEqual(c, Color(0.1, 0.1, 0.1))
def test_individual_transformations(self):
p = Point(1, 0, 1)
a = Transformations.rotation_x(math.pi / 2)
b = Transformations.scaling(5, 5, 5)
c = Transformations.translation(10, 5, 7)
# rotate first
p2 = Matrix.multiply_tuple(a, p)
self.assertEqual(p2, Point(1, -1, 0))
# apply scaling
p3 = Matrix.multiply_tuple(b, p2)
self.assertEqual(p3, Point(5, -5, 0))
# apply translation
p4 = Matrix.multiply_tuple(c, p3)
self.assertEqual(p4, Point(15, 0, 7))
class Clock:
if __name__ == '__main__':
canvas_size = 300
canvas = Canvas(canvas_size, canvas_size)
color = Color(1, 1, 1)
radius = canvas_size * 3 / 8
scale = Transformations.scaling(radius, radius, 0)
origin = Point(0, 0, 0)
center_translation = Transformations.translation(
canvas_size / 2, canvas_size / 2, 0)
center = Matrix.multiply_tuple(center_translation, origin)
hour = Point(0, 1, 0) # twelve
for _ in range(12):
scaled_hour = Matrix.multiply_tuple(scale, hour)
positioned_hour = scaled_hour + center
canvas.write_pixel(round(positioned_hour.x),
round(canvas.height - positioned_hour.y), color)
hour_rotation = Transformations.rotation_z(math.pi / 6)
hour = Matrix.multiply_tuple(hour_rotation, hour)
canvas.canvas_to_ppm()
from sphere import Sphere
from transformations import Transformations
from tuple import Point, Vector
from world import World
if __name__ == '__main__':
# The floor is an extremely flattened sphere with a matte texture
floor = Sphere()
floor.transform = Transformations.scaling(10, 0.1, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
# The wall on the left has the same scale and color as the floor, but is also rotated and translated into place
left_wall = Sphere()
left_wall.transform = Transformations.translation(0, 0, 5)
left_wall.transform = left_wall.transform.dot(
Transformations.rotation_y(-math.pi / 4))
left_wall.transform = left_wall.transform.dot(
Transformations.rotation_x(math.pi / 2))
left_wall.transform = left_wall.transform.dot(
Transformations.scaling(10, 0.1, 10))
left_wall.material = floor.material
# The wall on the right is identical to the left wall, but is rotated the opposite direction in y
right_wall = Sphere()
right_wall.transform = Transformations.translation(0, 0, 5)
right_wall.transform = right_wall.transform.dot(
Transformations.rotation_y(math.pi / 4))
right_wall.transform = right_wall.transform.dot(
Transformations.rotation_x(math.pi / 2))
def test_intersect_translated_sphere(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
xs = s.intersect(r)
self.assertEqual(len(xs), 0)
def test_normal_translated_sphere(self):
s = Sphere()
s.transform = Transformations.translation(0, 1, 0)
n = s.normal_at(Point(0, 1.70711, -0.70711))
self.assertEqual(n, Vector(0, 0.70711, -0.70711))