def test_intersecting_a_translated_sphere_with_a_ray():
sphere = Sphere(transformation=transformations.translation(5, 0, 0))
ray = Ray(point(0, 0, -5), vector(0, 0, 1))
xs = sphere.intersect(ray)
assert(len(xs) == 0)
def test_hit_should_offset_the_point():
r = Ray(point(0, 0, -5), vector(0, 0, 1))
shape = Sphere(transformation=translation(0, 0, 1))
i = Intersection(5, shape)
comps = i.prepare_computations(r)
assert(comps.point[2] < -EPSILON/2)
def test_constructing_a_ray_when_the_camera_is_transformed():
c = Camera(201, 101, math.pi/2,
transform=concat(rotation_y(math.pi/4), translation(0, -2, 5)))
r = c.ray_for_pixel(100, 50)
assert(np.allclose(point(0, 2, -5), r.origin))
assert(np.allclose(vector(math.sqrt(2)/2, 0, -math.sqrt(2)/2), r.direction))
def test_chained_transofrmations_must_be_applied_in_reverse_order():
p = point(1, 0, 1)
A = transformations.rotation_x(math.pi / 2)
B = transformations.scaling(5, 5, 5)
C = transformations.translation(10, 5, 7)
CBA = transformations.concat(C, B, A)
assert (np.allclose(point(15, 0, 7), CBA(p)))
def test_translating_a_ray():
origin = point(1, 2, 3)
direction = vector(0, 1, 0)
r = Ray(origin, direction)
m = transformations.translation(3, 4, 5)
translated_ray = r.transform(m)
assert (np.allclose(point(4, 6, 8), translated_ray.origin))
assert (np.allclose(vector(0, 1, 0), translated_ray.direction))
def test_shade_hit_is_given_an_intersection_in_shadow():
light = PointLight(point(0, 0, -10), color(1, 1, 1))
s1 = Sphere()
s2 = Sphere(transformation=translation(0, 0, 10))
w = World(light, s1, s2)
r = Ray(point(0, 0, 5), vector(0, 0, 1))
i = Intersection(4, s2)
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
assert(np.allclose(color(0.1, 0.1, 0.1), c))
def test_the_view_transformation_moves_the_world():
from_ = point(0, 0, 8)
to = point(0, 0, 0)
up = vector(0, 1, 0)
t = view_transformation(from_, to, up)
actual_transform_matrix = t(identity_matrix())
expected_transform_matrix = translation(0, 0, -8)(identity_matrix())
assert (np.allclose(actual_transform_matrix, expected_transform_matrix))
def test_individual_transformations_are_applied_in_sequence():
p = point(1, 0, 1)
A = transformations.rotation_x(math.pi / 2)
B = transformations.scaling(5, 5, 5)
C = transformations.translation(10, 5, 7)
p2 = A(p)
assert (np.allclose(point(1, -1, 0), p2))
p3 = B(p2)
assert (np.allclose(point(5, -5, 0), p3))
p4 = C(p3)
assert (np.allclose(point(15, 0, 7), p4))
def test_computing_the_normal_on_a_translated_sphere():
sphere = Sphere(transformations.translation(0, 1, 0))
n = sphere.normal_at(point(0, 1.70711, -0.70711))
assert(np.allclose(vector(0, 0.70711, -0.70711), n))
def test_multiplying_by_a_translation_matrix():
transform = transformations.translation(5, -3, 2)
p = point(-3, 4, 5)
assert ((point(2, 1, 7) == transform(p)).all())
def test_translation_does_not_affect_vectors():
transform = transformations.translation(5, -3, 2)
v = vector(-3, 4, 5)
assert ((v == transform(v)).all())
def test_multiplying_by_the_inverse_of_a_translation_matrix():
transform = transformations.translation(5, -3, 2)
transform = transformations.invert(transform)
p = point(-3, 4, 5)
assert ((point(-8, 7, 3) == transform(p)).all())
from pytracer.spheres import Sphere
from pytracer.transformations import scaling, rotation_y, rotation_x, translation, concat, view_transformation
from pytracer.materials import Material
from pytracer.colors import color
from pytracer.camera import Camera
from pytracer.tuples import point, vector
from pytracer.lights import PointLight
from pytracer.world import World
import math
floor_material = Material(color=color(1, 0.9, 0.9), specular=0)
floor = Sphere(transformation=scaling(10, 0.01, 10), material=floor_material)
left_wall_transformation = concat(translation(0, 0,
5), rotation_y(-math.pi / 4),
rotation_x(math.pi / 2),
scaling(10, 0.01, 10))
left_wall = Sphere(transformation=left_wall_transformation,
material=floor_material)
right_wall_transform = concat(translation(0, 0, 5), rotation_y(math.pi / 4),
rotation_x(math.pi / 2), scaling(10, 0.01, 10))
right_wall = Sphere(transformation=right_wall_transform,
material=floor_material)
middle_transform = translation(-0.5, 1, 0.5)
middle_material = Material(color=color(0.1, 1, 0.5), diffuse=0.7, specular=0.3)
middle = Sphere(material=middle_material, transformation=middle_transform)
right_transform = concat(translation(1.5, 0.5, -0.5), scaling(0.5, 0.5, 0.5))
right_material = Material(color=color(0.5, 1, 0.1), diffuse=0.7, specular=0.3)
