def __eq__(self, other):
"""Overrides the default implementation"""
if not isinstance(other, Tuple):
return False
return all([
equal(self.x, other.x),
equal(self.y, other.y),
equal(self.z, other.z),
equal(self.w, other.w)
])
def test_calculating_the_inverse_of_a_matrix():
# Given
A = Matrix(-5, 2, 6, -8,
1, -5, 1, 8,
7, 7, -6, -7,
1, -3, 7, 4)
B = A.inverse()
# Then
assert A.determinant() == 532
assert A.cofactor(2, 3) == -160
assert equal(B.at(3, 2), -160/532)
assert A.cofactor(3, 2) == 105
assert equal(B.at(2, 3), 105/532)
assert B == Matrix(0.21805, 0.45113, 0.24060, -0.04511,
-0.80827, -1.45677, -0.44361, 0.52068,
-0.07895, -0.22368, -0.05263, 0.19737,
-0.52256, -0.81391, -0.30075, 0.30639)
def test_intersecting_a_cone_with_a_ray():
EXAMPLES = [
# origin direction t0 t1
(Point(0, 0, -5), Vector(0, 0, 1), 5, 5),
(Point(0, 0, -5), Vector(1, 1, 1), 8.66025, 8.66025),
(Point(1, 1, -5), Vector(-0.5, -1, 1), 4.55006, 49.44994),
]
for origin, direction, t0, t1 in EXAMPLES:
# Given
shape = Cone()
dir = direction.normalize()
r = Ray(origin, dir)
# When
xs = shape.local_intersect(r)
# Then
assert len(xs) == 2
assert equal(xs[0].t, t0)
assert equal(xs[1].t, t1)
def test_a_ray_strikes_a_cylinder():
EXAMPLES = [
# origin direction t0 t1
(Point(1, 0, -5), Vector(0, 0, 1), 5, 5),
(Point(0, 0, -5), Vector(0, 0, 1), 4, 6),
(Point(0.5, 0, -5), Vector(0.1, 1, 1), 6.80798, 7.08872),
]
for origin, direction, t0, t1 in EXAMPLES:
# Given
cyl = Cylinder()
dir = direction.normalize()
r = Ray(origin, dir)
# When
xs = cyl.local_intersect(r)
# Then
assert len(xs) == 2
assert equal(xs[0].t, t0)
assert equal(xs[1].t, t1)
def __eq__(self, other):
"""Overrides the default implementation"""
if not isinstance(other, Matrix):
return False
return all([
equal(self.at(r, c), other.at(r, c)) for r in range(self.size)
for c in range(self.size)
])
def test_intersecting_a_cone_with_a_ray_parallel_to_one_of_its_halves():
# Given
shape = Cone()
direction = Vector(0, 1, 1).normalize()
r = Ray(Point(0, 0, -1), direction)
# When
xs = shape.local_intersect(r)
# Then
assert len(xs) == 1
assert equal(xs[0].t, 0.35355)
def test_the_schlick_approximation_with_small_angle_and_n2_greater_than_n1():
# Given
shape = glass_sphere()
r = Ray(Point(0, 0.99, -2), Vector(0, 0, 1))
xs = Intersections(Intersection(1.8589, shape))
# When
comps = xs[0].prepare_computations(r, xs)
reflectance = comps.schlick()
# Then
assert equal(reflectance, 0.48873)
def test_the_schlick_approximation_with_a_perpendicular_viewing_angle():
# Given
shape = glass_sphere()
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
xs = Intersections(Intersection(-1, shape), Intersection(1, shape))
# When
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
# Then
assert equal(reflectance, 0.04)
def test_the_pixel_size_for_a_vertical_canvas():
# Given
c = Camera(125, 200, pi / 2)
# Then
assert equal(c.pixel_size, 0.01)
def test_the_pixel_size_for_a_horizontal_canvas():
# Given
c = Camera(200, 125, pi / 2)
# Then
assert equal(c.pixel_size, 0.01)
