def test_reflect_angle(initial: Vector, normal: Vector):
"""Test angle-related properties of Vector.reflect:
* initial.reflect(normal) * normal == - initial * normal
* normal.angle(initial) == 180 - normal.angle(reflected)
"""
# Exclude initial vectors that are very small or very close to the surface.
assume(not angle_isclose(initial.angle(normal) % 180, 90, epsilon=10))
assume(initial.length > 1e-10)
reflected = initial.reflect(normal)
assert isclose((initial * normal), -(reflected * normal))
assert angle_isclose(normal.angle(initial), 180 - normal.angle(reflected))
def test_dot_rotational_invariance(x: Vector, y: Vector, angle: float):
"""Test that rotating vectors doesn't change their dot product."""
t = x.angle(y)
cos_t, _ = Vector._trig(t)
note(f"θ: {t}")
note(f"cos θ: {cos_t}")
# Exclude near-orthogonal test inputs
assume(abs(cos_t) > 1e-6)
assert isclose(x * y,
x.rotate(angle) * y.rotate(angle),
rel_to=(x, y),
rel_exp=2)
def test_dot_from_angle(x: Vector, y: Vector):
"""Test x · y == |x| · |y| · cos(θ)"""
t = x.angle(y)
cos_t, _ = Vector._trig(t)
# Dismiss near-othogonal test inputs
assume(abs(cos_t) > 1e-6)
min_len, max_len = sorted((x.length, y.length))
geometric = min_len * (max_len * cos_t)
note(f"θ: {t}")
note(f"cos θ: {cos_t}")
note(f"algebraic: {x * y}")
note(f"geometric: {geometric}")
assert isclose(x * y, geometric, rel_to=(x, y), rel_exp=2)
def test_angle_aligned(x: Vector, scalar: float):
"""x.angle(scalar * x) is 0 or 180, depending on whether scalar > 0"""
assume(scalar != 0)
y = scalar * x
assert angle_isclose(x.angle(y), 0 if scalar > 0 else 180)
def test_angle(left, right, expected):
left, right = Vector(left), Vector(right)
lr = left.angle(right)
rl = right.angle(left)
assert angle_isclose(lr, expected)
assert angle_isclose(rl, -expected)
