def test_scaling_matrix_applied_to_vector(self):
transform = scaling(2, 3, 4)
vector = Coordinates.vector(-4, 6, 8)
result = transform * vector
assert result == Coordinates.vector(-8, 18, 32)
def test_multiply_by_inverse_of_scaling_matrix(self):
transform = scaling(2, 3, 4).inverse()
vector = Coordinates.vector(-4, 6, 8)
result = transform * vector
assert result == Coordinates.vector(-2, 2, 2)
def test_subtracting_vector_from_zero(self):
v1 = Coordinates.vector(0, 0, 0)
v2 = Coordinates.vector(1, -2, 3)
result = v1 - v2
assert result == Coordinates.vector(-1, 2, -3)
def test_dot_product(self):
v1 = Coordinates.vector(1, 2, 3)
v2 = Coordinates.vector(2, 3, 4)
result = v1.dot_product(v2)
assert result == 20
def test_subtract_vectors(self):
v1 = Coordinates.vector(3, 2, 1)
v2 = Coordinates.vector(5, 6, 7)
result = v1 - v2
assert result == Coordinates.vector(-2, -4, -6)
assert result.is_vector()
def test_cross_product(self):
v1 = Coordinates.vector(1, 2, 3)
v2 = Coordinates.vector(2, 3, 4)
result1 = v1.cross_product(v2)
result2 = v2.cross_product(v1)
assert result1 == Coordinates.vector(-1, 2, -1)
assert result2 == Coordinates.vector(1, -2, 1)
def test_translation_does_not_affect_vectors(self):
transform = translation(5, -3, 2)
vector = Coordinates.vector(-3, 4, 5)
result = transform * vector
assert result == vector
def test_subtract_vector_from_point(self):
point = Coordinates.point(3, 2, 1)
vector = Coordinates.vector(5, 6, 7)
result = point - vector
assert result == Coordinates.point(-2, -4, -6)
assert result.is_point()
def test_subtract_points(self):
p1 = Coordinates.point(x=3, y=2, z=1)
p2 = Coordinates.point(x=5, y=6, z=7)
result = p1 - p2
assert result == Coordinates.vector(x=-2, y=-4, z=-6)
assert result.is_vector()
def test_normalize_vector_1_2_3(self):
v = Coordinates.vector(1, 2, 3)
result = v.normalize()
assert round(result.x, 5) == 0.26726
assert round(result.y, 5) == 0.53452
assert round(result.z, 5) == 0.80178
from data_structures import Coordinates
from data_structures import Color
from drawing import Canvas
from drawing.formats import PPMFormat
# Challenge for end of chapter 1
projectile = {
"position": Coordinates.point(0, 1, 0),
"velocity": Coordinates.vector(1, 1.8, 0).normalize() * 11.25,
}
environment = {
"gravity": Coordinates.vector(0, -0.1, 0),
"wind": Coordinates.vector(-0.01, 0, 0),
}
def tick(projectile, environment):
position = projectile["position"] + projectile["velocity"]
velocity = projectile["velocity"] + environment["gravity"] + environment["wind"]
return {"position": position, "velocity": velocity}
projectiles = [projectile]
while projectile["position"].y > 0:
projectile = tick(projectile, environment)
projectiles.append(projectile)
red = Color(1, 0, 0)
def test_vector_conveniece_constructor(self):
coordinates = Coordinates.vector(1, 2, 3)
assert not coordinates.is_point()
assert coordinates.is_vector()
def test_magnitude_of_normalized_vector_is_1(self):
v = Coordinates.vector(1, 2, 3)
result = v.normalize().magnitude()
assert result == 1.0
def test_normalize_vector_4_0_0(self):
v = Coordinates.vector(4, 0, 0)
result = v.normalize()
assert result == Coordinates.vector(1, 0, 0)
def test_magnitude_of_vector_1_2_3(self):
v = Coordinates.vector(1, 2, 3)
result = v.magnitude()
assert result == sqrt(14)
def test_magnitude_of_vector_0_0_1(self):
v = Coordinates.vector(1, 0, 0)
result = v.magnitude()
assert result == 1.0