def test_hit3(self):
s = Sphere()
i1 = Intersection(-2, s)
i2 = Intersection(-1, s)
xs = Intersections([i1, i2])
i = xs.hit()
self.assertTrue(i == None)
def test_hit1(self):
s = Sphere()
i1 = Intersection(1, s)
i2 = Intersection(2, s)
xs = Intersections([i1, i2])
i = xs.hit()
self.assertTrue(i == i1)
def test_world3(self):
w = World()
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = w.objs[0]
i = Intersection(4, shape)
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
self.assertTrue(Color(0.38066, 0.47583, 0.2855).equals(c))
def test_offset1(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.transform = translate(0, 0, 1)
i = Intersection(5, shape)
comps = i.prepare_computations(r)
self.assertTrue(comps.over_point.z < -EPSILON / 2)
self.assertTrue(comps.point.z > comps.over_point.z)
def test_int2(self):
s = Sphere()
i1 = Intersection(1, s)
i2 = Intersection(2, s)
xs = Intersections([i1, i2])
self.assertEqual(xs.count, 2)
self.assertEqual(xs[0].t, 1)
self.assertEqual(xs[1].t, 2)
def test_reflective2(self):
shape = Plane()
r = Ray(Point(0, 1, -1), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
self.assertTrue(
Vector(0,
sqrt(2) / 2,
sqrt(2) / 2).equals(comps.reflectv))
def test_intersect5(self):
origin = Point(0, 0, 5)
direction = Vector(0, 0, 1)
r = Ray(origin, direction)
s = Sphere()
i1 = Intersection(-6, s)
i2 = Intersection(-4, s)
xs = Intersections([i1, i2])
self.assertTrue(s.intersect(r) == xs)
def test_hit4(self):
s = Sphere()
i1 = Intersection(5, s)
i2 = Intersection(7, s)
i3 = Intersection(-3, s)
i4 = Intersection(2, s)
xs = Intersections([i1, i2, i3, i4])
i = xs.hit()
self.assertTrue(i == i4)
def test_reflect1(self):
w = World()
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
shape = w.objs[1]
shape.material.abmient = 1
i = Intersection(1, shape)
comps = i.prepare_computations(r)
color = w.reflected_color(comps)
self.assertTrue(Color(0, 0, 0).equals(color))
def test_maximum_recursive_depth(self):
w = World()
shape = Plane()
shape.material.reflective = 0.5
shape.set_transform(translate(0, -1, 0))
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)
self.assertTrue(Color(0, 0, 0).equals(color))
def test_prepare3(self):
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
s = Sphere()
i = Intersection(1, s)
comps = i.prepare_computations(r)
self.assertTrue(comps.inside)
self.assertTrue(Point(0, 0, 1).equals(comps.point))
self.assertTrue(Vector(0, 0, -1).equals(comps.eyev))
self.assertTrue(Vector(0, 0, -1).equals(comps.normalv))
def test_prepare1(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
i = Intersection(4, s)
comps = i.prepare_computations(r)
self.assertEqual(i.t, comps.t)
self.assertTrue(i.obj == comps.obj)
self.assertTrue(Point(0, 0, -1).equals(comps.point))
self.assertTrue(Vector(0, 0, -1).equals(comps.eyev))
self.assertTrue(Vector(0, 0, -1).equals(comps.normalv))
def test_shade_hit(self):
w = World()
shape = Plane()
shape.material.reflective = 0.5
shape.set_transform(translate(0.0, -1.0, 0.0))
w.objs.append(shape)
r = Ray(Point(0.0, 0.0, -3.0), Vector(0.0, -sqrt(2)/2, sqrt(2)/2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
color = w.shade_hit(comps)
self.assertTrue(Color(0.87677, 0.92436, 0.82918).equals(color))
def local_intersect(self, ray):
xtmin, xtmax = self.check_axis(ray.origin.x, ray.direction.x)
ytmin, ytmax = self.check_axis(ray.origin.y, ray.direction.y)
ztmin, ztmax = self.check_axis(ray.origin.z, ray.direction.z)
tmin = max(xtmin, ytmin, ztmin)
tmax = min(xtmax, ytmax, ztmax)
if tmin > tmax:
return Intersections([])
ls = [Intersection(tmin, self), Intersection(tmax, self)]
xs = Intersections(ls)
return xs
def test_schlick_approximation_with_perpendicular_viewing_angle(self):
shape = GlassSphere()
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
ls = [
Intersection(-1, shape),
Intersection(1, shape)
]
xs = Intersections(ls)
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
self.assertTrue(equals(reflectance, 0.04))
def test_schlick_approximation_under_total_internal_reflection(self):
shape = GlassSphere()
r = Ray(Point(0, 0, sqrt(2)/2), Vector(0, 1, 0))
ls = [
Intersection(-sqrt(2)/2, shape),
Intersection(sqrt(2)/2, shape)
]
xs = Intersections(ls)
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
self.assertTrue(equals(reflectance, 1.0))
def test_refracted_color_opaque_surface(self):
w = World()
shape = w.objs[0]
r = Ray(Point(0, 0, -5), Vector(0, 0, -1))
ls = [
Intersection(4, shape),
Intersection(6, shape)
]
xs = Intersections(ls)
comps = xs[0].prepare_computations(r, xs)
c = w.refracted_color(comps, 5)
self.assertTrue(Color(0, 0, 0) == c)
def test_under_point1(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = GlassSphere()
shape.set_transform(translate(0, 0, 1))
i = Intersection(5, shape)
xs = Intersections([i])
comps = i.prepare_computations(r, xs)
# print(comps.normalv)
# print(comps.point)
# print(comps.under_point.z)
self.assertTrue(comps.under_point.z > EPSILON / 2)
self.assertTrue(comps.point.z < comps.under_point.z)
def test_reflect1(self):
w = World()
shape = Plane()
shape.material.reflective = 0.5
shape.set_transform(translate(0.0, -1.0, 0.0))
w.objs.append(shape)
r = Ray(Point(0.0, 0.0, -3.0), Vector(0.0, -sqrt(2)/2, sqrt(2)/2))
i = Intersection(sqrt(2), shape)
comps = i.prepare_computations(r)
color = w.reflected_color(comps)
# print(color)
self.assertTrue(Color(0.19032, 0.2379, 0.14274).equals(color))
def test_shadow5(self):
w = World()
light = Light(Point(0, 0, -10), Color(1, 1, 1))
w.light = light
s1 = Sphere()
s2 = Sphere()
s2.transform = translate(0, 0, 10)
w.objs = [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)
self.assertTrue(Color(0.1, 0.1, 0.1).equals(c))
def test_refracted_color_at_maximum_recursive_depth(self):
w = World()
shape = w.objs[0]
shape.material.transparency = 1.0
shape.material.refractive_index = 1.5
r = Ray(Point(0, 0, -5), Vector(0, 0, -1))
ls = [
Intersection(4, shape),
Intersection(6, shape)
]
xs = Intersections(ls)
comps = xs[0].prepare_computations(r, xs)
c = w.refracted_color(comps, 0)
self.assertTrue(Color(0, 0, 0) == c)
def local_intersect(self, ray):
if abs(ray.direction.y) < EPSILON:
return Intersections([])
else:
t1 = -ray.origin.y / ray.direction.y
i1 = Intersection(t1, self)
return Intersections([i1])
def local_intersect(self, ray):
# ray2 = self.transform.inverse() * ray
# ray = Ray(self.transform.inverse()*ray.origin, self.transform.inverse()*ray.direction)
sphere2ray = ray.origin - Point(0, 0, 0)
a = ray.direction.dot(ray.direction)
b = 2 * ray.direction.dot(sphere2ray)
c = sphere2ray.dot(sphere2ray) - 1
discriminant = b * b - 4 * a * c
if discriminant < 0:
return Intersections([])
else:
t1 = (-b - sqrt(discriminant)) / (2 * a)
t2 = (-b + sqrt(discriminant)) / (2 * a)
i1 = Intersection(t1, self)
i2 = Intersection(t2, self)
return Intersections([i1, i2])
def test_refracted_color_under_total_internal_reflection(self):
w = World()
shape = w.objs[0]
shape.material.transparency = 1.0
shape.material.refractive_index = 1.5
r = Ray(Point(0, 0, sqrt(2)/2), Vector(0, 1, 0))
ls = [
Intersection(-sqrt(2)/2, shape),
Intersection(sqrt(2)/2, shape)
]
xs = Intersections(ls)
comps = xs[1].prepare_computations(r, xs)
c = w.refracted_color(comps, 5)
self.assertTrue(c == Color(0, 0, 0))
def test_schlick_approximation_with_small_angle_and_n2_larger_than_n1(self):
shape = GlassSphere()
r = Ray(Point(0, 0.99, -2), Vector(0, 0, 1))
ls = [
Intersection(1.8589, shape),
]
xs = Intersections(ls)
comps = xs[0].prepare_computations(r, xs)
reflectance = comps.schlick()
self.assertTrue(equals(reflectance, 0.48873))
def test_refracted_color_with_refracted_ray(self):
# this test failed!
w = World()
A = w.objs[0]
A.material.ambient = 1
A.material.pattern = TestPattern()
B = w.objs[1]
B.material.transparency = 1.0
B.material.refractive_index = 1.5
r = Ray(Point(0, 0, 0.1), Vector(0, 1, 0))
ls = [
Intersection(-0.9899, A),
Intersection(-0.4899, B),
Intersection(0.4899, B),
Intersection(0.9899, A)
]
xs = Intersections(ls)
comps = xs[2].prepare_computations(r, xs)
c = w.refracted_color(comps, 5)
# the expected answer is color(0, 0.99888, 0.04725)
self.assertTrue(c == Color(0, 0.99888, 0.04721))
def test_refract1(self):
A = GlassSphere()
A.set_transform(scale(2, 2, 2))
A.material.refractive_index = 1.5
B = GlassSphere()
B.set_transform(translate(0, 0, -0.25))
B.material.refractive_index = 2.0
C = GlassSphere()
C.set_transform(translate(0, 0, 0.25))
C.material.refractive_index = 2.5
r = Ray(Point(0, 0, -4), Vector(0, 0, 1))
ls = [
Intersection(2, A),
Intersection(2.75, B),
Intersection(3.25, C),
Intersection(4.75, B),
Intersection(5.25, C),
Intersection(6, A)
]
xs = Intersections(ls)
comps0 = xs[0].prepare_computations(r, xs)
self.assertEqual(comps0.n1, 1.0)
self.assertEqual(comps0.n2, 1.5)
comps1 = xs[1].prepare_computations(r, xs)
self.assertEqual(comps1.n1, 1.5)
self.assertEqual(comps1.n2, 2.0)
comps2 = xs[2].prepare_computations(r, xs)
self.assertEqual(comps2.n1, 2.0)
self.assertEqual(comps2.n2, 2.5)
comps3 = xs[3].prepare_computations(r, xs)
self.assertEqual(comps3.n1, 2.5)
self.assertEqual(comps3.n2, 2.5)
comps4 = xs[4].prepare_computations(r, xs)
self.assertEqual(comps4.n1, 2.5)
self.assertEqual(comps4.n2, 1.5)
comps5 = xs[5].prepare_computations(r, xs)
self.assertEqual(comps5.n1, 1.5)
self.assertEqual(comps5.n2, 1.0)
def test_shade_hit_with_reflective_transparent_material(self):
w = World()
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2))
floor = Plane()
floor.set_transform(translate(0, -1, 0))
floor.material.reflective = 0.5
floor.material.transparency = 0.5
floor.material.refractive_index = 1.5
w.objs.append(floor)
ball = Sphere()
ball.material.color = Color(1, 0, 0)
ball.material.ambient = 0.5
ball.set_transform(translate(0, -3.5, -0.5))
w.objs.append(ball)
ls = [Intersection(sqrt(2), floor)]
xs = Intersections(ls)
comps = xs[0].prepare_computations(r, xs)
color = w.shade_hit(comps, 5)
# print(color)
self.assertTrue(Color(0.93391, 0.69643, 0.69243) == color)
def test_shade_hit_with_transparent_material(self):
w = World()
floor = Plane()
floor.set_transform(translate(0, -1, 0))
floor.material.transparency = 0.5
floor.material.refractive_index = 1.5
ball = Sphere()
ball.material.color = Color(1., 0., 0.)
ball.material.ambient = 0.5
ball.set_transform(translate(0, -3.5, -0.5))
w.objs = [floor, ball]
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2))
ls = [Intersection(sqrt(2), floor)]
xs = Intersections(ls)
comps = xs[0].prepare_computations(r, xs)
color = w.shade_hit(comps, 5)
self.assertTrue(Color(0.93642, 0.68642, 0.68642) == color)
def test_prepare2(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
i = Intersection(4, s)
comps = i.prepare_computations(r)
self.assertFalse(comps.inside)
