def test_cross_scalar_multiply(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
for k in utils.ALL_SCALARS:
vec1 = vector_ops.cross(k * v1, v2)
vec2 = vector_ops.cross(v1, k * v2)
vec3 = k * vector_ops.cross(v1, v2)
for a, b in itertools.combinations([vec1, vec2, vec3], 2):
utils.assert_vectors_almost_equal(a, b)
def test_cross_parallelepiped_volume(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
for v3 in utils.ALL_VECTORS:
f1 = v1 @ vector_ops.cross(v2, v3)
f2 = v2 @ vector_ops.cross(v3, v1)
f3 = v3 @ vector_ops.cross(v1, v2)
for a, b in itertools.combinations([f1, f2, f3], 2):
self.assertAlmostEqual(a, b, PRECISION)
def test_cross_angle_equality(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
if v1.norm > 0 and v2.norm > 0:
theta = vector_ops.angle_between(v1, v2)
f1 = vector_ops.cross(v1, v2).norm
f2 = v1.norm * v2.norm * abs(math.sin(theta))
self.assertAlmostEqual(f1, f2, PRECISION)
def test_cross_jacobi_identity(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
for v3 in utils.ALL_VECTORS:
vec1 = vector_ops.cross(v1, vector_ops.cross(v2, v3))
vec2 = vector_ops.cross(v2, vector_ops.cross(v3, v1))
vec3 = vector_ops.cross(v3, vector_ops.cross(v1, v2))
utils.assert_vectors_almost_equal(vec1 + vec2 + vec3,
Vector.make_zero(3))
def test_cross_dot_relationship(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
for v3 in utils.ALL_VECTORS:
vec1 = vector_ops.cross(v1, vector_ops.cross(v2, v3))
vec2 = ((v1 @ v3) * v2) - ((v1 @ v2) * v3)
utils.assert_vectors_almost_equal(vec1, vec2)
def test_cross_distributive(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
for v3 in utils.ALL_VECTORS:
vec1 = vector_ops.cross(v1, v2 + v3)
vec2 = vector_ops.cross(v1, v2) + vector_ops.cross(v1, v3)
utils.assert_vectors_almost_equal(vec1, vec2)
def test_cross_anticommutative(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
vec1 = vector_ops.cross(v1, v2)
vec2 = vector_ops.cross(v2, v1)
utils.assert_vectors_almost_equal(vec1, -vec2)
def test_cross_self(self):
for v1, v2 in itertools.product(utils.ALL_VECTORS, utils.ALL_VECTORS):
if v1 == v2:
vec = vector_ops.cross(v1, v2)
utils.assert_vectors_almost_equal(vec, Vector.make_zero(3))
def test_cross_orthogonal(self):
v1 = Vector([0, 1, 0])
v2 = Vector([1, 0, 0])
utils.assert_vectors_almost_equal(vector_ops.cross(v1, v2),
Vector([0, 0, -1]))
def test_cross_parallel(self):
v1 = Vector([1, 0, 0])
v2 = Vector([2, 0, 0])
utils.assert_vectors_almost_equal(vector_ops.cross(v1, v2),
Vector.make_zero(3))