def test_light_directly_behind_surface_and_eye(self):
m = Material()
position = Point(0, 0, 0)
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, 10), Color(1, 1, 1))
result = lighting(m, light, position, eyev, normalv)
self.assertEqual(result, Color(0.1, 0.1, 0.1))
def test_light_and_eye_perpendicular(self):
m = Material()
position = Point(0, 0, 0)
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
result = lighting(m, light, position, eyev, normalv)
self.assertEqual(result, Color(1.9, 1.9, 1.9))
def test_light_perpendicular_and_eye_at_45(self):
r = math.sqrt(2) / 2
m = Material()
position = Point(0, 0, 0)
eyev = Vector(0, r, -r)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
result = lighting(m, light, position, eyev, normalv)
self.assertEqual(result, Color(1.0, 1.0, 1.0))
def test_scaling(self):
s = Matrix.scale(2, 3, 4)
p = Point(-4, 6, 8)
self.assertEqual(s * p, Point(-8, 18, 32))
v = Vector(-4, 6, 8)
self.assertEqual(s * v, Vector(-8, 18, 32))
self.assertEqual(s.inverse() * v, Vector(-2, 2, 2))
s = Matrix.scale(-1, 1, 1)
p = Point(2, 3, 4)
self.assertEqual(s * p, Point(-2, 3, 4))
def test_light_at_45_and_eye_at_neg_45(self):
r = math.sqrt(2) / 2
m = Material()
position = Point(0, 0, 0)
eyev = Vector(0, -r, -r)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 10, -10), Color(1, 1, 1))
result = lighting(m, light, position, eyev, normalv)
x = 1.6363961
self.assertColorEqual(result, Color(x, x, x))
def test_point_subtraction(self):
# subtracting two points results in a vector
p1 = Point(3, 2, 1)
p2 = Point(5, 6, 7)
self.assertEqual(p1 - p2, Vector(-2, -4, -6))
# subtracting a vector from a point results in a new point
p = Point(3, 2, 1)
v = Vector(5, 6, 7)
self.assertEqual(p - v, Point(-2, -4, -6))
def test_normal_with_transform(self):
s = Sphere()
s.transform = Matrix.translate(0, 5, 0)
n = s.normal(Point(1, 5, 0))
self.assertEqual(n, Vector(1, 0, 0))
s = Sphere()
s.transform = Matrix.scale(1, 0.5, 1)
r = math.sqrt(2) / 2
n = s.normal(Point(0, r, -r))
self.assertTupleEqual(n, Vector(0, 0.97014, -0.24254))
def test_reflection(self):
v = Vector(1, -1, 0)
n = Vector(0, 1, 0)
r = v.reflect(n)
self.assertEqual(r, Vector(1, 1, 0))
x = math.sqrt(2) / 2
v = Vector(0, -1, 0)
n = Vector(x, x, 0)
r = v.reflect(n)
self.assertTupleEqual(r, Vector(1, 0, 0))
def test_normal(self):
s = Sphere()
n = s.normal(Point(1, 0, 0))
self.assertEqual(n, Vector(1, 0, 0))
n = s.normal(Point(0, 1, 0))
self.assertEqual(n, Vector(0, 1, 0))
n = s.normal(Point(0, 0, 1))
self.assertEqual(n, Vector(0, 0, 1))
r = math.sqrt(3) / 3
n = s.normal(Point(r, r, r))
self.assertEqual(n, Vector(r, r, r))
self.assertEqual(n, n.norm())
def test_intersect(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].object, s)
self.assertEqual(xs[1].object, s)
def test_intersect_with_transform(self):
# intersect a scaled sphere
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
s.transform = Matrix.scale(2, 2, 2)
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, 3)
self.assertEqual(xs[1].t, 7)
# intersect a translated sphere
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
s.transform = Matrix.translate(5, 0, 0)
xs = s.intersect(r)
self.assertEqual(len(xs), 0)
def test_translation(self):
t = Matrix.translate(5, -3, 2)
p = Point(-3, 4, 5)
self.assertEqual(t * p, Point(2, 1, 7))
self.assertEqual(t.inverse() * p, Point(-8, 7, 3))
v = Vector(-3, 4, 5)
self.assertEqual(t * v, v)
self.assertEqual(t.inverse() * v, v)
def normal(self, point):
inv = self.transform.inverse()
# transform world point back to object space
obj_point = inv * point
obj_normal = obj_point - self.center
# transform the normal back to world space and normalize it
normal = (inv.transpose() * obj_normal).norm()
d = normal.x * normal.x + normal.y * normal.y + normal.z * normal.z
assert abs(d - 1.0) < 0.01
# the inverse transform can mess up the w-component so we ensure it is clear
return Vector(normal.x, normal.y, normal.z)
def test_intersect_sphere(self):
# through the center
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, 4)
self.assertEqual(xs[1].t, 6)
# at a tangent
r = Ray(Point(0, 1, -5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, 5)
self.assertEqual(xs[1].t, 5) # why two points?
# no intersection
r = Ray(Point(0, 2, -5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 0)
# starting inside the sphere
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, -1)
self.assertEqual(xs[1].t, 1)
# starting past the sphere
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
self.assertEqual(len(xs), 2)
self.assertEqual(xs[0].t, -6)
self.assertEqual(xs[1].t, -4)
def test_translation(self):
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = Matrix.translate(3, 4, 5)
r2 = m.transform(r)
self.assertEqual(r2.origin, Point(4, 6, 8))
self.assertEqual(r2.direction, Vector(0, 1, 0))
def test_dot_product(self):
a = Vector(1, 2, 3)
b = Vector(2, 3, 4)
self.assertEqual(20, a.dot(b))
def test_normalization(self):
self.assertEqual(Vector(1, 0, 0), Vector(4, 0, 0).norm())
x = math.sqrt(14)
self.assertEqual(Vector(1 / x, 2 / x, 3 / x), Vector(1, 2, 3).norm())
# the magnitude of a normalized vector should always be 1.0
self.assertEqual(1, Vector(1, 2, 3).norm().mag())
def test_vector(self):
v = Vector(4.3, -4.2, 3.1)
self.assertEqual(v.x, 4.3)
self.assertEqual(v.y, -4.2)
self.assertEqual(v.z, 3.1)
self.assertEqual(v.w, 0.0)
def __str__(self):
return "P={}, V={}".format(self.position, self.velocity)
class World(object):
def __init__(self, gravity, wind):
self.gravity = gravity
self.wind = wind
def tick(world, projectile):
p = projectile.position + projectile.velocity
v = projectile.velocity + world.gravity + world.wind
return Projectile(p, v)
W, H = 900, 550
im = Image.new('RGB', (W, H))
pix = im.load()
p = Projectile(Point(0, 1, 0), Vector(1, 1.8, 0).norm() * 11.25)
w = World(Vector(0, -0.1, 0), Vector(-0.01, 0, 0))
while p.position.y > 0:
pix[int(p.position.x), H - int(p.position.y)] = (255, 0, 0)
print(p)
p = tick(w, p)
im.show()
def test_cross_product(self):
a = Vector(1, 2, 3)
b = Vector(2, 3, 4)
self.assertEqual(Vector(-1, 2, -1), a.cross(b))
self.assertEqual(Vector(1, -2, 1), b.cross(a))
def test_scaling(self):
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = Matrix.scale(2, 3, 4)
r2 = m.transform(r)
self.assertEqual(r2.origin, Point(2, 6, 12))
self.assertEqual(r2.direction, Vector(0, 3, 0))
def test_magnitude(self):
self.assertEqual(1, Vector(1, 0, 0).mag())
self.assertEqual(1, Vector(0, 1, 0).mag())
self.assertEqual(1, Vector(0, 0, 1).mag())
self.assertEqual(math.sqrt(14), Vector(1, 2, 3).mag())
self.assertEqual(math.sqrt(14), Vector(-1, -2, -3).mag())
def test_vector_tuple_equality(self):
a = Vector(4, -4, 3)
t = Tuple(4, -4, 3, 0)
self.assertEqual(a, t)
def test_ray_position(self):
r = Ray(Point(2, 3, 4), Vector(1, 0, 0))
self.assertEqual(r.position(0.0), Point(2, 3, 4))
self.assertEqual(r.position(1.0), Point(3, 3, 4))
self.assertEqual(r.position(-1.0), Point(1, 3, 4))
self.assertEqual(r.position(2.5), Point(4.5, 3, 4))
def test_create_ray(self):
origin = Point(1, 2, 3)
direction = Vector(4, 5, 6)
r = Ray(origin, direction)
self.assertEqual(r.origin, origin)
self.assertEqual(r.direction, direction)
def test_vector_subtraction(self):
# subtracting two vectors results in a vector
v1 = Vector(3, 2, 1)
v2 = Vector(5, 6, 7)
self.assertEqual(v1 - v2, Vector(-2, -4, -6))