def test_rotation_z_axis():
p = Point(0, 1, 0)
h_q = rotation_z(pi / 4)
h_f = rotation_z(pi / 2)
assert h_q * p == Point(-sqrt(2) / 2, sqrt(2) / 2, 0)
assert h_f * p == Point(-1, 0, 0)
def test_ray_position():
r = Ray(Point(2, 3, 4), Vector(1, 0, 0))
assert r.position(0) == Point(2, 3, 4)
assert r.position(1) == Point(3, 3, 4)
assert r.position(-1) == Point(1, 3, 4)
assert r.position(2.5) == Point(4.5, 3, 4)
def test_rotation_y_axis():
p = Point(0, 0, 1)
h_q = rotation_y(pi / 4)
h_f = rotation_y(pi / 2)
assert h_q * p == Point(sqrt(2) / 2, 0, sqrt(2) / 2)
assert h_f * p == Point(1, 0, 0)
def test_rotation_x_axis():
p = Point(0, 1, 0)
h_q = rotation_x(pi / 4)
f_q = rotation_x(pi / 2)
assert h_q * p == Point(0, sqrt(2) / 2, sqrt(2) / 2)
assert f_q * p == Point(0, 0, 1)
def test_transformation_chain():
p = Point(1, 0, 1)
A = rotation_x(pi / 2)
B = scaling(5, 5, 5)
C = translation(10, 5, 7)
T = C @ B @ A
assert T * p == Point(15, 0, 7)
def test_lightning_eye_angle():
m = DefaultMaterial()
position = Point(0, 0, 0)
eyev = Vector(0, sqrt(2) / 2, -sqrt(2) / 2)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
result = m.lighting(light, position, eyev, normalv)
assert result == Color(1.0, 1.0, 1.0)
def test_lightning_light_behind():
m = DefaultMaterial()
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 = m.lighting(light, position, eyev, normalv)
assert result == Color(0.1, 0.1, 0.1)
def test_lighting_direct():
m = DefaultMaterial()
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 = m.lighting(light, position, eyev, normalv)
assert result == Color(1.9, 1.9, 1.9)
def test_lightning_light_angle():
m = DefaultMaterial()
position = Point(0, 0, 0)
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 10, -10), Color(1, 1, 1))
result = m.lighting(light, position, eyev, normalv)
assert result == Color(0.7363961030678927, 0.7363961030678927,
0.7363961030678927)
def test_ray_init():
origin = Point(1, 2, 3)
direct = Vector(4, 5, 6)
r = Ray(origin, direct)
assert r.origin == origin
assert r.direction == direct
def test_ray_intersect_from_middle():
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
s = Sphere()
x = r.intersects(s)
assert len(x) == 2
assert x[0].t == -1
assert x[1].t == 1
def test_ray_intersects_sphere_object():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
x = r.intersects(s)
assert len(x) == 2
assert x[0].object == s
assert x[1].object == s
def test_sphere_intersection_scaled():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
s.set_transform(scaling(2, 2, 2))
x = r.intersects(s)
assert len(x) == 2
assert x[0].t == 3
assert x[1].t == 7
def test_ray_intersect_sphere_tangent():
r = Ray(Point(0, 1, -5), Vector(0, 0, 1))
s = Sphere()
x = r.intersects(s)
assert len(x) == 2
assert x[0].t == 5
assert x[1].t == 5
def test_ray_intersect_from_behind():
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
s = Sphere()
x = r.intersects(s)
assert len(x) == 2
assert x[0].t == -6
assert x[1].t == -4
def intersects(self, s):
transformed_ray = self.transform(s.transform.inv)
obj_to_ray = transformed_ray.origin - Point(0, 0, 0)
a = transformed_ray.direction.dot(transformed_ray.direction)
b = 2 * transformed_ray.direction.dot(obj_to_ray)
c = obj_to_ray.dot(obj_to_ray) - 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(s, t1)
i2 = Intersection(s, t2)
if t1 > t2:
return Intersections(i2, i1)
else:
return Intersections(i1, i2)
def test_sphere_normal_at_arbitrary():
s = Sphere()
n = s.normal_at(Point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
assert n == Vector(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3)
def test_sphere_normal_at_z():
s = Sphere()
n = s.normal_at(Point(0, 0, 1))
assert n == Vector(0, 0, 1)
def test_sphere_normal_at_x():
s = Sphere()
n = s.normal_at(Point(1, 0, 0))
assert n == Vector(1, 0, 0)
def test_sphere_intersection_translate():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
s.set_transform(translation(5, 0, 0))
x = r.intersects(s)
assert len(x) == 0
def test_shearing_x_y():
t = shearing(1, 0, 0, 0, 0, 0)
p = Point(2, 3, 4)
assert t * p == Point(5, 3, 4)
def test_sphere_normal_at_scaled():
s = Sphere()
s.set_transform(scaling(1, 0.5, 1))
n = s.normal_at(Point(0, sqrt(2) / 2, -sqrt(2) / 2))
assert n == Vector(0, 0.9701425001453319, -0.24253562503633297)
def test_rotation_x_axis_inverse():
p = Point(0, 1, 0)
h_q = rotation_x(pi / 4)
inv = h_q.inv
assert inv * p == Point(0, sqrt(2) / 2, -sqrt(2) / 2)
def test_ray_intersect_sphere_no_intersection():
r = Ray(Point(0, 2, -5), Vector(0, 0, 1))
s = Sphere()
x = r.intersects(s)
assert len(x) == 0
def test_sphere_normal_normalized():
s = Sphere()
n = s.normal_at(Point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
assert n == n.normalize()
def test_translate():
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = translation(3, 4, 5)
r2 = r.transform(m)
assert r2.origin == Point(4, 6, 8)
assert r2.direction == Vector(0, 1, 0)
def test_sphere_normal_at_translate():
s = Sphere()
s.set_transform(translation(0, 1, 0))
n = s.normal_at(Point(0, 1.70711, -0.70711))
assert n == Vector(0, 0.7071067811865475, -0.7071067811865476)
def test_scale():
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = scaling(2, 3, 4)
r2 = r.transform(m)
assert r2.origin == Point(2, 6, 12)
assert r2.direction == Vector(0, 3, 0)
from src.canvas import Canvas
from src.color import Color
from src.tupl import Vector, Point
def tick(p, v):
p += v
v += Vector(0, -0.1, 0) + Vector(-0.01, 0, 0)
return p, v
c = Canvas(900, 550)
col = Color(255, 255, 255)
if __name__ == '__main__':
p = Point(0, 1, 0)
v = Vector(1, 1.8, 0).normalize() * 11.25
for i in range(100):
X = int(p.x)
Y = int(p.y)
if p.y <= 0:
break
if (0 <= X < c.width) and (0 <= c.height - Y < c.height):
c.write_pixel(X, c.height - Y, col)
p, v = tick(p, v)
c.to_ppm('trajectory.ppm')
def test_shearing_x_z():
t = shearing(0, 1, 0, 0, 0, 0)
p = Point(2, 3, 4)
assert t * p == Point(6, 3, 4)
