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_rotation_stability(angle, loops):
"""Rotating loops times by angle is equivalent to rotating by loops*angle."""
initial = Vector(1, 0)
fellswoop = initial.rotate(angle * loops)
note(f"One Fell Swoop: {fellswoop}")
stepwise = initial
for _ in range(loops):
stepwise = stepwise.rotate(angle)
note(f"Step-wise: {stepwise}")
assert fellswoop.isclose(stepwise, rel_tol=1e-8)
assert math.isclose(fellswoop.length, initial.length, rel_tol=1e-15)
def test_rotation_invariance(v: Vector, angle: float, n: int):
"""Check that rotating by angle and angle + n×360° have the same result."""
rot_once = v.rotate(angle)
rot_many = v.rotate(angle + 360 * n)
note(f"δ: {(rot_once - rot_many).length}")
assert rot_once.isclose(rot_many, rel_tol=n / 1e9)
