def test_inverse_trans():
t = m3d.Transform()
t.pos.x = 1
t.orient.rotate_zb(np.pi / 2)
t.orient.rotate_yb(np.pi / 2)
v = m3d.Vector(2, 0, 0)
assert t * v == m3d.Vector(1, 2, 0)
def test_rotation_t():
t = m3d.Transform()
t.pos.x = 1
t.orient.rotate_zt(np.pi / 2)
t.orient.rotate_yt(np.pi / 2)
v = m3d.Vector(2, 0, 0)
assert t * v == m3d.Vector(1, 0, -2)
def test_transform():
t = m3d.Transform()
t.orient.rotate_zb(np.pi / 2)
t.pos.y = 2
v = m3d.Vector(1, 0, 0)
r = t * v
assert r == m3d.Vector(0, 3, 0)
def test_vect_div():
v1 = m3d.Vector(10, 10, 10)
const_val = 2
const_val_2 = -5
v_res = v1 / const_val
v_res_2 = v1 / const_val_2
assert v_res == m3d.Vector(5, 5, 5)
assert v_res_2 == m3d.Vector(-2, -2, -2)
def test_vector_dot():
d1 = np.array([1, 2, -3])
d2 = np.array([2, 2, 2])
v1 = m3d.Vector(d1)
v2 = m3d.Vector(d2)
assert np.dot(d1, d2) == v1.dot(v2)
assert v1.dot(v2) == v1 @ v2
assert v1 @ v1 == v1.length**2
def test_vector_except():
with pytest.raises(ValueError):
o = m3d.Vector(np.identity(4))
with pytest.raises(ValueError):
o = m3d.Vector("whatever")
with pytest.raises(ValueError):
o = m3d.Vector([1, 2, 3, 4])
o = m3d.Vector([1, 2, 3])
def test_vect_mul():
v1 = m3d.Vector(10, 10, 10)
const_val = 2
const_val_2 = -5
v_res = v1 * const_val
v_res_2 = v1 * const_val_2
assert v_res == m3d.Vector(20, 20, 20)
assert v_res_2 == m3d.Vector(-50, -50, -50)
def test_multiplication_orient():
o = m3d.Orientation()
o.rotate_zb(np.pi / 2)
v = m3d.Vector(1, 0, 0)
r = o * v
assert r == m3d.Vector(0, 1, 0)
o.rotate_zb(-np.pi)
v = m3d.Vector(2, 0, 0)
r = o * v
assert r == m3d.Vector(0, -2, 0)
def test_unit_vectors():
assert m3d.vector.e0 == m3d.Vector(1, 0, 0)
assert m3d.vector.e1 == m3d.Vector(0, 1, 0)
assert m3d.vector.e2 == m3d.Vector(0, 0, 1)
t = m3d.Transform()
assert m3d.vector.ex == t.orient.vec_x
assert m3d.vector.ey == t.orient.vec_y
assert m3d.vector.ez == t.orient.vec_z
t.orient.rotate_zb(1)
assert m3d.vector.ex != t.orient.vec_x
assert m3d.vector.ey != t.orient.vec_y
assert m3d.vector.ez == t.orient.vec_z
def test_construct():
o = m3d.Orientation()
o.rotate_zb(1)
v = m3d.Vector()
v[0] = 1
v[2] = 2
t = m3d.Transform(o, v)
assert t.pos.x == 1
assert t.pos.z == 2
t.pos = m3d.Vector()
t.orient.rotate_zb(-1)
assert t == m3d.Transform()
t.orient = o
assert t != m3d.Transform()
def test_from_xz():
x = m3d.Vector(1, 0, 0)
z = m3d.Vector(0, 0, 1)
orient = m3d.Orientation.from_xz(x, z)
assert _are_equals(orient.data, np.identity(3))
x = m3d.Vector(2, 0, 0.1)
z = m3d.Vector(0.1, -0.1, 3)
o = m3d.Orientation()
o.rotate_yb(1)
o.rotate_zb(1)
x = o @ x
z = o @ z
orient = m3d.Orientation.from_xz(x, z)
assert _are_equals(o, orient, eps=0.1)
def test_vector_project():
v1 = m3d.Vector(1, 1, 1)
v2 = m3d.Vector(2, 2, 2)
vx = m3d.Vector(1, 0, 0)
vy = m3d.Vector(0, 1, 0)
vz = m3d.Vector(0, 0, 1)
assert v1.project(vx) == vx
assert v1.project(vy) == vy
assert v1.project(vz) == vz
assert v1.project(v2) == v1
assert v2.project(v1) == v2
def test_vector_angle():
v1 = m3d.Vector(1, 1, 1)
v2 = m3d.Vector(2, 2, 2)
vx = m3d.Vector(1, 0, 0)
vy = m3d.Vector(0, 1, 0)
vz = m3d.Vector(0, 0, 1)
assert vx.angle(vx) == 0
assert vx.angle(vy) == np.pi / 2
assert vx.angle(vz) == np.pi / 2
assert v1.angle(v2) == 0
assert v2.angle(v1) == 0
def test_eq():
t = m3d.Transform()
t.orient.rotate_yb(1)
t.orient.rotate_zb(1)
t.pos.x = 1
v = m3d.Vector()
o = m3d.Orientation()
with pytest.raises(ValueError):
assert t != v
with pytest.raises(ValueError):
assert v != t
with pytest.raises(ValueError):
assert o != v
t2 = t.copy()
assert t == t2
assert t.pos == t2.pos
assert t.orient == t2.orient
t2.pos.y = 2
assert t != t2
assert t.pos != t2.pos
assert t.orient == t2.orient
t3 = t.copy()
t3.orient.rotate_xb(1)
assert t2.pos != t3.pos
assert t2.orient != t3.orient
assert t != t3
def test_transform_init_ref():
v = m3d.Vector(1, 2, 3)
o = m3d.Orientation()
o.rotate_zb(1)
t = m3d.Transform(o, v)
assert t.orient == o
o.rotate_xb(1)
assert t.orient != o
def test_from_axis_angle():
axis_tuple = (1, 2, 3)
axis_normalized = m3d.Vector(axis_tuple).normalized()
angle = 10
o1 = m3d.Orientation.from_axis_angle(axis_tuple, angle)
o2 = m3d.Orientation.from_axis_angle(axis_normalized, angle)
assert o1.similar(o2, CONVERTION_ERROR)
def test_rotation():
t = m3d.Transform()
t.pos.x = 1
t.orient.rotate_yb(1)
res = m3d.Transform(
m3d.Orientation([[0.54030228, 0, 0.84147096], [0., 1, 0.],
[-0.84147096, 0., 0.54030228]]), m3d.Vector(1, 0, 0))
assert _are_equals(res.data, t.data)
def test_inverse_orient():
o = m3d.Orientation()
o.rotate_xb(3)
o.rotate_yb(1)
o.rotate_xb(1)
v = m3d.Vector(-1, -2, -3)
assert o * v != v
assert o.inverse() * o * v == v
assert o * o.inverse() * v == v
assert o * o.inverse() * o == o
def test_init():
t = m3d.Transform()
assert t.pos.x == 0
assert t.pos.y == 0
t.pos.x = 2
assert t.pos.x == 2
i = t.inverse()
assert m3d.Vector(-2, 0, 0) == i.pos
assert m3d.Orientation() == i.orient
def test_inverse_2():
t = m3d.Transform()
t.pos.x = 1
t.pos.z = 3
t.orient.rotate_yb(1)
t.orient.rotate_zb(1)
v = m3d.Vector(2, 3, 4)
assert v != t * v
assert v == t.inverse() * t * v
assert v == t * t.inverse() * v
assert v != t @ v
assert v == t.inverse() @ t @ v
assert v == t @ t.inverse() @ v
def test_rotation_seq_2():
t = m3d.Transform()
t.pos.x = 1
t.pos.z = 3
t.orient.rotate_xb(1)
t.orient.rotate_yb(2)
t.orient.rotate_zb(3)
b = m3d.Transform()
b.orient.rotate_zb(-3)
b.orient.rotate_yb(-2)
b.orient.rotate_xb(-1)
b.pos = b.orient * m3d.Vector(1, 0, 3) * -1
assert _are_equals(t.inverse().data, b.data)
def test_transform_init():
v = m3d.Vector(1, 2, 3)
o = m3d.Orientation()
o.rotate_zb(1)
t = m3d.Transform(o, v)
assert t.pos == v
assert t.orient == o
t2 = m3d.Transform(o.data, v.data)
assert t2.pos == v
assert t2.orient == o
assert t == t2
with pytest.raises(ValueError):
m3d.Transform(np.array([1, 2, 3]), np.array([1, 2, 3]))
with pytest.raises(ValueError):
m3d.Transform(o.data, np.array([1, 2]))
def test_inverse():
t1 = m3d.Transform()
t1.orient.rotate_xb(np.pi / 3)
t1.pos.x = 1
t2 = m3d.Transform()
t2.orient.rotate_xb(-13 * np.pi / 6)
t2.pos.x = 2.3
v = m3d.Vector(0.1, -4.5, 3.0)
tr = m3d.Transform()
tr.orient.rotate_xb(np.pi)
tr.pos.x = 3
assert (t1 * t1.inverse()) == m3d.Transform(matrix=np.identity(4))
assert (t1 * t1.inverse()) == m3d.Transform()
assert (t2 * t2.inverse()) == m3d.Transform(matrix=np.identity(4))
assert (t2 * t2.inverse()) == m3d.Transform()
assert (t1 * t2 * t1.inverse() * t2.inverse()).similar(
m3d.Transform(matrix=np.identity(4)), CONVERTION_ERROR)
assert t1.inverse() * (t1 * v) == v
def test_mult_trans():
t1 = m3d.Transform()
t1.orient.rotate_xb(np.pi / 2)
t1.pos.x = 1
t2 = m3d.Transform()
t2.orient.rotate_xb(np.pi / 2)
t2.pos.x = 2
v = m3d.Vector(0, 0, 3)
tr = m3d.Transform()
tr.orient.rotate_xb(np.pi)
tr.pos.x = 3
tm = math3d.Transform()
tm.orient.rotate_xb(np.pi / 2)
tm.pos.x = 2
vm = math3d.Vector(0, 0, 3)
assert t1 * t2 * v == tr * v
assert t1 @ t2 @ v == tr @ v
assert _are_equals((t2 * v).data, (tm * vm)._data)
def test_vector_angle_perp():
v1 = m3d.Vector(1, 0, 0)
v2 = m3d.Vector(1, 1, 0)
v3 = m3d.Vector(1, -1, 0)
vx = m3d.Vector(1, 0, 0)
vy = m3d.Vector(0, 1, 0)
vz = m3d.Vector(0, 0, 1)
assert vx.angle(vx, vz) == 0
assert vx.angle(vy, vz) == np.pi / 2
assert vx.angle(vz, vy) == -np.pi / 2
# Flip nominal direction for perpendicular vector
assert vx.angle(vx, -vz) == 0
assert vx.angle(vy, -vz) == -np.pi / 2
assert vx.angle(vz, -vy) == np.pi / 2
assert v1.angle(v2, vz) == -v1.angle(v2, -vz)
assert v1.angle(v2, vz) == v1.angle(v3, -vz)
def test_dist():
v1 = m3d.Vector(1, 1, 1)
v2 = m3d.Vector(2, 2, 2)
v_res = v2.dist(v1)
assert v_res == m3d.Vector(1, 1, 1).length
def test_trans_init_except():
with pytest.raises(ValueError):
o = m3d.Vector(np.identity(5))
def test_norm():
v = m3d.Vector(1, 2, 3)
v.normalize()
assert abs(v.length - 1) <= m3d.float_eps
def test_from_xy():
x = m3d.Vector(1, 0, 0)
y = m3d.Vector(0.01, 2.1, 0)
orient = m3d.Orientation.from_xy(x, y)
assert _are_equals(orient.data, np.identity(3), eps=0.1)
def test_from_yz():
y = m3d.Vector(0, 1, 0)
z = m3d.Vector(0, 0.01, 0.1)
orient = m3d.Orientation.from_yz(y, z)
assert _are_equals(orient.data, np.identity(3), eps=0.1)
