def local_intersect(self, local_ray: rays.Ray):
"""Return the t-value where the ray intersects with the plane, in local
units
"""
# If the y-direction of the ray is small it is approximately parallel to
#the plane, no intersections
if abs(local_ray.direction.y) < MIN_Y_FOR_PLANE_INTERSECT:
return intersections.Intersections()
t = -local_ray.origin.y / local_ray.direction.y
return intersections.Intersections(intersections.Intersection(self, t))
def test_reflective_transparent_material(self):
"""Test shade_hit with a reflective, transparent material"""
world = copy.deepcopy(self.default_scene)
floor = shapes.Plane(material=materials.Material(
reflective=0.5, transparency=0.5, refractive_index=1.5))
floor.set_transform(transforms.Translate(0, -1, 0))
ball = shapes.Sphere(material=materials.Material(
color=colors.Color(1, 0, 0), ambient=0.5))
ball.set_transform(transforms.Translate(0, -3.5, -0.5))
r = rays.Ray(points.Point(0, 0, -3),
vectors.Vector(0, -math.sqrt(2) / 2,
math.sqrt(2) / 2))
xs = intersections.Intersections(
intersections.Intersection(floor, math.sqrt(2)))
world.add_object(floor)
world.add_object(ball)
comps = xs.intersections[0].precompute(r, all_intersections=xs)
color, _ = world.shade_hit(comps, remaining=5)
self.assertEqual(color, colors.Color(0.93391, 0.69643, 0.69243))
def test_refraction__standard(self):
"""Test that we return the correct color under normal refraction"""
world = copy.deepcopy(self.default_scene)
# s1 = A
s1 = world.objects[1]
s1.material.ambient = 1.0
s1.material.pattern = patterns.TestPattern()
# s2 = B
s2 = world.objects[0]
s2.material.transparency = 1.0
s2.material.refractive_index = 1.5
r = rays.Ray(points.Point(0, 0, 0.1), vectors.Vector(0, 1, 0))
xs = intersections.Intersections(
intersections.Intersection(s1, -0.9899),
intersections.Intersection(s2, -0.4899),
intersections.Intersection(s2, 0.4899),
intersections.Intersection(s1, 0.9899))
# Intersections[2] because the first two are behind the camera
comps = xs.intersections[2].precompute(r, all_intersections=xs)
result, _ = world.refracted_color(comps, 5)
# Remember the test pattern returns the x, y, z coordinates of the
# input point as the color so we can inspect positions
self.assertEqual(result, colors.Color(0, 0.99888, 0.0475))
def test_refraction__total_internal_reflection(self):
"""Test that we return black if we hit total internal reflection"""
world = copy.deepcopy(self.default_scene)
s = world.objects[1]
s.material.transparency = 1.0
s.material.refractive_index = 1.5
r = rays.Ray(points.Point(0, 0,
math.sqrt(2) / 2), vectors.Vector(0, 1, 0))
xs = intersections.Intersections(
intersections.Intersection(s, -math.sqrt(2) / 2),
intersections.Intersection(s,
math.sqrt(2) / 2))
# n.b. the camera is inside the inner-sphere so use the second
# intersection
comps = xs.intersections[1].precompute(r, all_intersections=xs)
result, _ = world.refracted_color(comps, 5)
self.assertEqual(result, colors.Color(0, 0, 0))
def test_refractive_index_intersections(self):
"""Test we can calculate the refractive indices between intersections"""
# Set up a scene with three glass spheres. One at the origin with size
# 2 then inside of that 2 that are offset along z by different amounts
A = shapes.Sphere(material=materials.Material(refractive_index=1.5,
transparency=1.0))
B = shapes.Sphere(material=materials.Material(refractive_index=2.0,
transparency=1.0))
C = shapes.Sphere(material=materials.Material(refractive_index=2.5,
transparency=1.0))
A.set_transform(transforms.Scale(2, 2, 2))
B.set_transform(transforms.Translate(0, 0, -0.25))
C.set_transform(transforms.Translate(0, 0, 0.25))
r = rays.Ray(points.Point(0, 0, -4), vectors.Vector(0, 0, 1))
xs = intersections.Intersections(intersections.Intersection(A, 2),
intersections.Intersection(B, 2.75),
intersections.Intersection(C, 3.25),
intersections.Intersection(B, 4.75),
intersections.Intersection(C, 5.25),
intersections.Intersection(A, 6))
expected_results = [
{
"n1": 1.0,
"n2": 1.5
},
{
"n1": 1.5,
"n2": 2.0
},
{
"n1": 2.0,
"n2": 2.5
},
{
"n1": 2.5,
"n2": 2.5
},
{
"n1": 2.5,
"n2": 1.5
},
{
"n1": 1.5,
"n2": 1.0
},
]
for index, expected in enumerate(expected_results):
comps = xs.intersections[index].precompute(r, all_intersections=xs)
self.assertDictEqual(expected, {"n1": comps.n1, "n2": comps.n2})
def test_hits__all_negative(self):
"""Test we get no hits for all negative intersections"""
shape = shapes.Sphere()
i1 = intersections.Intersection(shape, -1)
i2 = intersections.Intersection(shape, -2)
isections = intersections.Intersections(i1, i2)
self.assertIsNone(isections.hit())
def test_hits__some_negative(self):
"""Test we get the correct hit for some negative intersections"""
shape = shapes.Sphere()
i1 = intersections.Intersection(shape, -1)
i2 = intersections.Intersection(shape, 1)
isections = intersections.Intersections(i1, i2)
self.assertEqual(isections.hit(), i2)
def test_hits__positive(self):
"""Test we get the correct hit for multiple positive intersections"""
shape = shapes.Sphere()
i1 = intersections.Intersection(shape, 2)
i2 = intersections.Intersection(shape, 1)
isections = intersections.Intersections(i1, i2)
self.assertEqual(isections.hit(), i2)
def local_intersect(self, local_ray: rays.Ray):
"""Return to t values for where the ray intersects the shape. All in
local coordinates for the shape
"""
sphere_to_ray = local_ray.origin - points.Point(0, 0, 0)
a = local_ray.direction.dot(local_ray.direction)
b = 2 * local_ray.direction.dot(sphere_to_ray)
c = sphere_to_ray.dot(sphere_to_ray) - 1
discriminant = b**2 - 4 * a * c
if discriminant < 0:
return intersections.Intersections()
else:
t1 = (-b - math.sqrt(discriminant)) / (2 * a)
t2 = (-b + math.sqrt(discriminant)) / (2 * a)
return intersections.Intersections(
intersections.Intersection(self, t1),
intersections.Intersection(self, t2))
def test_schlick__small_angle(self):
"""Test that we calculate the reflectance at a small angle
"""
r = rays.Ray(points.Point(0, 0.99, -2), vectors.Vector(0, 0, 1))
xs = intersections.Intersections(
intersections.Intersection(self.glass_sphere, 1.8589), )
comps = xs.intersections[0].precompute(r, all_intersections=xs)
self.assertAlmostEqual(comps.schlick, 0.48873081)
def test_hits__multiple(self):
"""Test we get the correct hit for some negative intersections"""
shape = shapes.Sphere()
i1 = intersections.Intersection(shape, -1)
i2 = intersections.Intersection(shape, 7)
i3 = intersections.Intersection(shape, -5)
i4 = intersections.Intersection(shape, 2)
i5 = intersections.Intersection(shape, 3)
isections = intersections.Intersections(i1, i2, i3, i4, i5)
self.assertEqual(isections.hit(), i4)
def test_schlick__perpendicular(self):
"""Test that we calculate the reflectance for a perpendicular ray
"""
r = rays.Ray(points.Point(0, 0, 0), vectors.Vector(0, 1, 0))
xs = intersections.Intersections(
intersections.Intersection(self.glass_sphere, -1),
intersections.Intersection(self.glass_sphere, 1))
comps = xs.intersections[1].precompute(r, all_intersections=xs)
self.assertAlmostEqual(comps.schlick, 0.04)
def test_initialization(self):
shape = shapes.Sphere()
t1 = 3.5
t2 = -3.5
i1 = intersections.Intersection(shape, t1)
self.assertEqual(i1.t, 3.5)
self.assertEqual(i1.shape, shape)
i2 = intersections.Intersection(shape, t2)
self.assertEqual(i2.t, -3.5)
i = intersections.Intersections(i1, i2)
self.assertEqual(i.intersections, [i2, i1])
def test_schlick__total_internal_reflection(self):
"""Test that we calculate the reflectance under total internal
reflection
"""
r = rays.Ray(points.Point(0, 0,
math.sqrt(2) / 2), vectors.Vector(0, 1, 0))
xs = intersections.Intersections(
intersections.Intersection(self.glass_sphere, -math.sqrt(2) / 2),
intersections.Intersection(self.glass_sphere,
math.sqrt(2) / 2))
comps = xs.intersections[1].precompute(r, all_intersections=xs)
self.assertEqual(comps.schlick, 1)
def test_refraction__opaque(self):
"""Test the refraction color of an opaque material is black"""
world = copy.deepcopy(self.default_scene)
s = world.objects[1]
r = rays.Ray(points.Point(0, 0, -5), vectors.Vector(0, 0, 1))
xs = intersections.Intersections(intersections.Intersection(s, 4),
intersections.Intersection(s, 6))
comps = xs.intersections[0].precompute(r, all_intersections=xs)
result, _ = world.refracted_color(comps, 5)
self.assertEqual(result, colors.Color(0, 0, 0))
def test_refraction__recursion_limit(self):
"""Test that we return black if we hit the refraction limit"""
world = copy.deepcopy(self.default_scene)
s = world.objects[1]
s.material.transparency = 1.0
s.material.refractive_index = 1.5
r = rays.Ray(points.Point(0, 0, -5), vectors.Vector(0, 0, 1))
xs = intersections.Intersections(intersections.Intersection(s, 4),
intersections.Intersection(s, 6))
comps = xs.intersections[0].precompute(r, all_intersections=xs)
result, _ = world.refracted_color(comps, 0)
self.assertEqual(result, colors.Color(0, 0, 0))