def test_rotate_point_around_z_axis(self):
p = Point(0, 1, 0)
half_quarter = rotation_z(math.pi / 4)
full_quarter = rotation_z(math.pi / 2)
assert half_quarter * p == Point(-math.sqrt(2) / 2,
math.sqrt(2) / 2, 0)
assert full_quarter * p == Point(-1, 0, 0)
def test_chained_transformations_are_in_reverse_order(self):
p = Point(1, 0, 1)
a = rotation_x(math.pi / 2)
b = scaling(5, 5, 5)
c = translation(10, 5, 7)
t = c * b * a * p
assert t == Point(15, 0, 7)
def test_hit_when_intersection_occurs_on_inside(self):
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
shape = Sphere()
i = Intersection(1, shape)
comps = i.prepare_computations(r)
assert comps.point == Point(0, 0, 1)
assert comps.eyev == Vector(0, 0, -1)
assert comps.inside
assert comps.normalv == Vector(0, 0, -1)
def test_render_world_with_camera(self, default_world):
w = default_world
c = Camera(11, 11, pi / 2)
_from = Point(0, 0, -5)
to = Point(0, 0, 0)
up = Vector(0, 2, 0)
c.transformation = view_transform(_from, to, up)
image = c.render(w)
assert image.pixel_at(5, 5) == Color(0.38066, 0.47583, 0.2855)
def test_shading_intersection_from_inside(self, default_world):
w = default_world
w.light_source = PointLight(Point(0, 0.25, 0), Color.white())
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
shape = w.objects[1]
i = Intersection(0.5, shape)
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
assert c == Color(0.90498, 0.90498, 0.90498)
def test_arbitrary_view_transformation(self):
_from = Point(1, 3, 2)
to = Point(4, -2, 8)
up = Vector(1, 1, 0)
t = view_transform(_from, to, up)
assert t == Matrix([[-0.50709, 0.50709, 0.67612, -2.36643],
[0.76772, 0.60609, 0.12122, -2.82843],
[-0.35857, 0.59761, -0.71714, 0.0],
[0.0, 0.0, 0.0, 1.0]])
def test_precomputing_state_of_intersection(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
i = Intersection(4, shape)
comps = i.prepare_computations(r)
assert comps.t == i.t
assert comps.object == i.object
assert comps.point == Point(0, 0, -1)
assert comps.eyev == Vector(0, 0, -1)
assert comps.normalv == Vector(0, 0, -1)
def test_individual_transformations_in_sequence(self):
p = Point(1, 0, 1)
a = rotation_x(math.pi / 2)
b = scaling(5, 5, 5)
c = translation(10, 5, 7)
p2 = a * p
assert p2 == Point(1, -1, 0)
p3 = b * p2
assert p3 == Point(5, -5, 0)
p4 = c * p3
assert p4 == Point(15, 0, 7)
def test_shade_hit_is_given_an_intersection_in_shadow(self):
w = World()
w.light_source = PointLight(Point(0, 0, -10), Color.white())
s1 = Sphere()
s2 = Sphere()
s2.transformation = translation(0, 0, 10)
w.add(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 c == Color(0.1, 0.1, 0.1)
def test_lighting_with_pattern_applied(self):
m = Material()
m.pattern = StripePattern(Color.white(), Color.black())
m.ambient = 1
m.diffuse = 0
m.specular = 0
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color.white())
c1 = m.lighting(Sphere(), light, Point(0.9, 0, 0), eyev, normalv, False)
c2 = m.lighting(Sphere(), light, Point(1.1, 0, 0), eyev, normalv, False)
assert c1 == Color.white()
assert c2 == Color.black()
def test_color_at_with_mutually_reflective_surfaces(self):
w = World()
w.light_source = PointLight(Point(0, 0, 0), Color.white())
lower = Plane()
lower.material.reflective = 1
lower.transformation = translation(0, -1, 0)
upper = Plane()
upper.material.reflective = 1
upper.transformation = translation(0, 1, 0)
w.add(lower, upper)
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
# Avoid Infinite Recursion
w.color_at(r)
assert True
def test_pattern_with_both_object_and_pattern_transformation(self):
obj = Sphere()
obj.transformation = scaling(2, 2, 2)
pattern = test_pattern()
pattern.transformation = translation(0.5, 1, 1.5)
c = pattern.pattern_at_shape(obj, Point(2.5, 3, 3.5))
assert c == Color(0.75, 0.5, 0.25)
def test_lighting_with_surface_in_shadow(self, background):
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
in_shadow = True
result = background['m'].lighting(Sphere(), light, background['position'], eyev, normalv, in_shadow)
assert result == Color(0.1, 0.1, 0.1)
def test_shading_intersection(self, default_world):
w = default_world
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = w.objects[0]
i = Intersection(4, shape)
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
assert c == Color(0.38066, 0.47583, 0.2855)
def test_schlick_approximation_with_perpendicular_viewing_angle(
self, glass_sphere):
shape = glass_sphere()
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
xs = Intersections(Intersection(-1, shape), Intersection(1, shape))
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
assert reflectance == pytest.approx(0.04)
def test_refracted_color_with_opaque_surface(self, default_world):
w = default_world
shape = w.objects[0]
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = Intersections(Intersection(4, shape), Intersection(6, shape))
comps = xs[0].prepare_computations(r, xs)
c = w.refracted_color(comps, 5)
assert c == Color.black()
def test_schlick_approximation_with_small_angle_and_n2_greater_than_n1(
self, glass_sphere):
shape = glass_sphere()
r = Ray(Point(0, 0.99, -2), Vector(0, 0, 1))
xs = Intersections(Intersection(1.8589, shape))
comps = xs[0].prepare_computations(r, xs)
reflectance = comps.schlick()
assert reflectance == pytest.approx(0.48873, EPSILON)
def test_hit_should_offset_the_point(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.transformation = translation(0, 0, 1)
i = Intersection(5, shape)
comps = i.prepare_computations(r)
assert comps.over_point.z < -EPSILON / 2
assert comps.point.z > comps.over_point.z
def test_schlick_approximation_under_total_internal_reflection(
self, glass_sphere):
shape = glass_sphere()
r = Ray(Point(0, 0, sqrt(2) / 2), Vector(0, 1, 0))
xs = Intersections(Intersection(-sqrt(2) / 2, shape),
Intersection(sqrt(2) / 2, shape))
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
assert reflectance == 1.0
def test_reflected_color_for_nonreflective_material(self, default_world):
w = default_world
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
shape = w.objects[1]
shape.material.ambient = 1
i = Intersection(1, shape)
comps = i.prepare_computations(r)
color = w.reflected_color(comps)
assert color == Color.black()
def test_intersect_world_with_ray(self, default_world):
w = default_world
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = w.intersect(r)
assert xs.count == 4
assert xs[0].t == 4
assert xs[1].t == 4.5
assert xs[2].t == 5.5
assert xs[3].t == 6
def test_under_point_is_offset_below_the_surface(self, glass_sphere):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = glass_sphere()
shape.transformation = translation(0, 0, 1)
i = Intersection(5, shape)
xs = Intersections(i)
comps = i.prepare_computations(r, xs)
assert comps.under_point.z > EPSILON / 2
assert comps.point.z < comps.under_point.z
def test_color_with_intersection_behind_ray(self, default_world):
w = default_world
outer = w.objects[0]
outer.material.ambient = 1
inner = w.objects[1]
inner.material.ambient = 1
r = Ray(Point(0, 0, 0.75), Vector(0, 0, -1))
c = w.color_at(r)
assert c == inner.material.color
def test_refracted_color_at_max_recursive_depth(self, default_world):
w = default_world
shape = w.objects[0]
shape.material.transparency = 1.0
shape.material.refractive_index = 1.5
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = Intersections(Intersection(4, shape), Intersection(6, shape))
comps = xs[0].prepare_computations(r, xs)
c = w.refracted_color(comps, 0)
assert c == Color.black()
def test_shade_hit_with_reflective_material(self, default_world):
w = default_world
shape = Plane()
shape.material.reflective = 0.5
shape.transformation = translation(0, -1, 0)
w.add(shape)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
color = w.shade_hit(comps)
assert color == Color(0.87676, 0.92434, 0.82917)
def test_reflected_color_for_reflective_material(self, default_world):
w = default_world
shape = Plane()
shape.material.reflective = 0.5
shape.transformation = translation(0, -1, 0)
w.add(shape)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
color = w.reflected_color(comps)
assert color == Color(0.19033, 0.23791, 0.14274)
def default_world():
w = World()
w.light_source = PointLight(Point(-10, 10, -10), Color.white())
s1 = Sphere()
s1.material.color = Color(0.8, 1.0, 0.6)
s1.material.diffuse = 0.7
s1.material.specular = 0.2
s2 = Sphere()
s2.transformation = scaling(0.5, 0.5, 0.5)
w.add(s1, s2)
return w
def test_reflected_color_at_max_recursive_depth(self, default_world):
w = default_world
shape = Plane()
shape.material.reflective = 0.5
shape.transformation = translation(0, -1, 0)
w.add(shape)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
color = w.reflected_color(comps, 0)
assert color == Color.black()
def test_refracted_color_under_total_internal_reflection(self, default_world):
w = default_world
shape = w.objects[0]
shape.material.transparency = 1.0
shape.material.refractive_index = 1.5
r = Ray(Point(0, 0, sqrt(2) / 2), Vector(0, 1, 0))
xs = Intersections(Intersection(-sqrt(2) / 2, shape), Intersection(sqrt(2) / 2, shape))
# NOTE: this time you're inside the sphere, so you need
# to look at the second intersection, xs[1], not xs[0]
comps = xs[1].prepare_computations(r, xs)
c = w.refracted_color(comps, 5)
assert c == Color.black()
def test_stripe_pattern_alternates_in_x(self):
pattern = StripePattern(Color.white(), Color.black())
assert pattern.pattern_at(Point(0, 0, 0)) == Color.white()
assert pattern.pattern_at(Point(0.9, 0, 0)) == Color.white()
assert pattern.pattern_at(Point(1, 0, 0)) == Color.black()
assert pattern.pattern_at(Point(-0.1, 0, 0)) == Color.black()
assert pattern.pattern_at(Point(-1, 0, 0)) == Color.black()
assert pattern.pattern_at(Point(-1.1, 0, 0)) == Color.white()
