def test_composedecompose():
t_values = [
Vector3(),
Vector3(3, 0, 0),
Vector3(0, 4, 0),
Vector3(0, 0, 5),
Vector3(-6, 0, 0),
Vector3(0, -7, 0),
Vector3(0, 0, -8),
Vector3(-2, 5, -9),
Vector3(-2, -5, -9),
]
s_values = [
Vector3(1, 1, 1),
Vector3(2, 2, 2),
Vector3(1, -1, 1),
Vector3(-1, 1, 1),
Vector3(1, 1, -1),
Vector3(2, -2, 1),
Vector3(-1, 2, -2),
Vector3(-1, -1, -1),
Vector3(-2, -2, -2),
]
r_values = [
Quaternion(),
Quaternion().set_from_euler(Euler(1, 1, 0)),
Quaternion().set_from_euler(Euler(1, -1, 1)),
Quaternion(0, 0.9238795292366128, 0, 0.38268342717215614),
]
for ti in range(len(t_values)):
for si in range(len(s_values)):
for ri in range(len(r_values)):
t = t_values[ti]
s = s_values[si]
r = r_values[ri]
m = Matrix4().compose(t, r, s)
t2 = Vector3()
r2 = Quaternion()
s2 = Vector3()
m.decompose(t2, r2, s2)
m2 = Matrix4().compose(t2, r2, s2)
##
# debug code
# matrixIsSame = matrix_equals( m, m2 )
# if ( ! matrixIsSame ) {
# console.log( t, s, r )
# console.log( t2, s2, r2 )
# console.log( m, m2 )
# }
##
assert matrix_equals(m, m2)
def test_angle_to():
a = Quaternion()
b = Quaternion().set_from_euler(Euler(0, pi, 0))
c = Quaternion().set_from_euler(Euler(0, pi * 2, 0))
assert a.angle_to(a) == 0
assert a.angle_to(b) == pi
assert a.angle_to(c) == 0
def test_set_from_euler_set_from_quaternion():
angles = [Vector3(1, 0, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)]
# ensure euler conversion to/from Quaternion matches.
for i in range(len(orders)):
for j in range(len(angles)):
eulers2 = Euler().set_from_quaternion(
Quaternion().set_from_euler(
Euler(angles[j].x, angles[j].y, angles[j].z, orders[i])),
orders[i],
)
new_angle = Vector3(eulers2.x, eulers2.y, eulers2.z)
assert new_angle.distance_to(angles[j]) < 0.001
def test_set_from_vector3_to_vector3():
a = Euler()
a.set(0, 1, 0, Euler.RotationOrders.ZYX)
assert a.equals(euler_azyx)
assert not a.equals(euler_axyz)
assert not a.equals(euler_zero)
vec = Vector3(0, 1, 0)
b = Euler().set_from_vector3(vec, Euler.RotationOrders.ZYX)
assert a.equals(b)
c = b.to_vector3()
assert c.equals(vec)
def test_multiply_vector3():
angles = [Euler(1, 0, 0), Euler(0, 1, 0), Euler(0, 0, 1)]
# ensure euler conversion for Quaternion matches that of Matrix4
for i in range(len(orders)):
for j in range(len(angles)):
q = Quaternion().set_from_euler(
change_euler_order(angles[j], orders[i]))
m = Matrix4().make_rotation_from_euler(
change_euler_order(angles[j], orders[i]))
v0 = Vector3(1, 0, 0)
qv = v0.clone().apply_quaternion(q)
mv = v0.clone().apply_matrix4(m)
assert qv.distance_to(mv) < 0.001
def test_quaternion_set_from_euler_euler_from_quaternion():
test_values = [euler_zero, euler_axyz, euler_azyx]
for i in range(len(test_values)):
v = test_values[i]
q = Quaternion().set_from_euler(v)
v2 = Euler().set_from_quaternion(q, v.order)
q2 = Quaternion().set_from_euler(v2)
assert quat_equals(q, q2)
def test_matrix4_set_from_euler_euler_from_rotation_matrix():
test_values = [euler_zero, euler_axyz, euler_azyx]
for i in range(len(test_values)):
v = test_values[i]
m = Matrix4().make_rotation_from_euler(v)
v2 = Euler().set_from_rotation_matrix(m, v.order)
m2 = Matrix4().make_rotation_from_euler(v2)
assert matrix_equals(m, m2, 0.0001)
def test_apply_euler():
a = Vector3(x, y, z)
euler = Euler(90, -45, 0)
expected = Vector3(-2.352970120501014, -4.7441750936226645,
0.9779234597246458)
a.apply_euler(euler)
assert abs(a.x - expected.x) <= eps, "Check x"
assert abs(a.y - expected.y) <= eps, "Check y"
assert abs(a.z - expected.z) <= eps, "Check z"
def test_update_matrix_world():
root = WorldObject()
root.position.set(-5, 8, 0)
root.rotation.set_from_euler(Euler(pi / 4, 0, 0))
root.update_matrix()
child1 = WorldObject()
child1.position.set(0, 0, 5)
root.add(child1)
child2 = WorldObject()
child2.rotation.set_from_euler(Euler(0, -pi / 4, 0))
child1.add(child2)
objs = [root, child1, child2]
assert all(obj.matrix_world_dirty for obj in objs)
# test both updating parents and children
child1.update_matrix_world(update_parents=True)
assert all(not obj.matrix_world_dirty for obj in objs)
p = Vector3(10, 10, 10)
p.apply_matrix4(child2.matrix)
p.apply_matrix4(child1.matrix)
p.apply_matrix4(root.matrix)
x = Vector3(10, 10, 10)
x.apply_matrix4(child2.matrix_world)
# if there is a difference it's a floating point error
assert Vector3().sub_vectors(p, x).length() < 0.00000000001
# reorganize such that child1 and 2 become siblings
child1.remove(child2)
root.add(child2)
assert not child1.matrix_world_dirty
# child2 should be flagged as dirty again now
assert child2.matrix_world_dirty
def test_gimbal_local_quat():
# known problematic quaternions
q1 = Quaternion(0.5207769385244341, -0.4783214164122354, 0.520776938524434,
0.47832141641223547)
# q2 = Quaternion(
# 0.11284905712620674,
# 0.6980437630368944,
# -0.11284905712620674,
# 0.6980437630368944,
# )
euler_order = Euler.RotationOrders.ZYX
# create Euler directly from a Quaternion
e_via_q1 = Euler().set_from_quaternion(
q1, euler_order) # there is likely a bug here
# create Euler from Quaternion via an intermediate Matrix4
m_via_q1 = Matrix4().make_rotation_from_quaternion(q1)
e_via_m_via_q1 = Euler().set_from_rotation_matrix(m_via_q1, euler_order)
# the results here are different
assert euler_equals(e_via_q1, e_via_m_via_q1) # this result is correcy
def test_update_matrix():
root = WorldObject()
root.position.set(3, 6, 8)
root.scale.set(1, 1.2, 1)
root.rotation.set_from_euler(Euler(pi / 2, 0, 0))
root.update_matrix()
t, r, s = Vector3(), Quaternion(), Vector3()
root.matrix.decompose(t, r, s)
assert t == root.position
# todo: do somehting like np.allclose
# assert r == root.rotation # close, but not quite the same
# assert s == root.scale
assert root.matrix_world_dirty
def test_from_array():
a = Euler()
array = [x, y, z]
a.from_array(array)
assert a.x == x, "No order: check x"
assert a.y == y, "No order: check y"
assert a.z == z, "No order: check z"
assert a.order == Euler.RotationOrders.XYZ, "No order: check order"
a = Euler()
array = [x, y, z, Euler.RotationOrders.ZXY]
a.from_array(array)
assert a.x == x, "With order: check x"
assert a.y == y, "With order: check y"
assert a.z == z, "With order: check z"
assert a.order == Euler.RotationOrders.ZXY, "With order: check order"
def test_multiply_quaternions_multiply():
angles = [Euler(1, 0, 0), Euler(0, 1, 0), Euler(0, 0, 1)]
q1 = Quaternion().set_from_euler(
change_euler_order(angles[0], Euler.RotationOrders.XYZ))
q2 = Quaternion().set_from_euler(
change_euler_order(angles[1], Euler.RotationOrders.XYZ))
q3 = Quaternion().set_from_euler(
change_euler_order(angles[2], Euler.RotationOrders.XYZ))
q = Quaternion().multiply_quaternions(q1, q2).multiply(q3)
m1 = Matrix4().make_rotation_from_euler(
change_euler_order(angles[0], Euler.RotationOrders.XYZ))
m2 = Matrix4().make_rotation_from_euler(
change_euler_order(angles[1], Euler.RotationOrders.XYZ))
m3 = Matrix4().make_rotation_from_euler(
change_euler_order(angles[2], Euler.RotationOrders.XYZ))
m = Matrix4().multiply_matrices(m1, m2).multiply(m3)
q_from_m = Quaternion().set_from_rotation_matrix(m)
assert q_sub(q, q_from_m).length() < 0.001
def test_rotate_towards():
a = Quaternion()
b = Quaternion().set_from_euler(Euler(0, pi, 0))
c = Quaternion()
half_pi = pi * 0.5
a.rotate_towards(b, 0)
assert a.equals(a) is True
a.rotate_towards(b, pi * 2)
# test overshoot
assert a.equals(b) is True
a.set(0, 0, 0, 1)
a.rotate_towards(b, half_pi)
assert a.angle_to(c) - half_pi <= eps
def test_look_at():
a = Matrix4()
expected = Matrix4().identity()
eye = Vector3(0, 0, 0)
target = Vector3(0, 1, -1)
up = Vector3(0, 1, 0)
a.look_at(eye, target, up)
rotation = Euler().set_from_rotation_matrix(a)
assert rotation.x * (180 / pi) == 45, "Check the rotation"
# eye and target are in the same position
eye.copy(target)
a.look_at(eye, target, up)
assert matrix_equals(a, expected), "Check the result for eye == target"
# up and z are parallel
eye.set(0, 1, 0)
target.set(0, 0, 0)
a.look_at(eye, target, up)
expected.set(1, 0, 0, 0, 0, 0.0001, 1, 0, 0, -1, 0.0001, 0, 0, 0, 0, 1)
assert matrix_equals(a, expected), "Check the result for when up and z are parallel"
def test_make_rotation_from_eulerextract_rotation():
test_values = [
Euler(0, 0, 0, Euler.RotationOrders.XYZ),
Euler(1, 0, 0, Euler.RotationOrders.XYZ),
Euler(0, 1, 0, Euler.RotationOrders.ZYX),
Euler(0, 0, 0.5, Euler.RotationOrders.YZX),
Euler(0, 0, -0.5, Euler.RotationOrders.YZX),
]
for i in range(len(test_values)):
v = test_values[i]
m = Matrix4().make_rotation_from_euler(v)
v2 = Euler().set_from_rotation_matrix(m, v.order)
m2 = Matrix4().make_rotation_from_euler(v2)
assert matrix_equals(m, m2, eps), (
"make_rotation_from_euler #"
+ i
+ ": original and Euler-derived matrices are equal"
)
assert euler_equals(v, v2, eps), (
"make_rotation_from_euler #"
+ i
+ ": original and matrix-derived Eulers are equal"
)
m3 = Matrix4().extract_rotation(m2)
v3 = Euler().set_from_rotation_matrix(m3, v.order)
assert matrix_equals(m, m3, eps), (
"extract_rotation #" + i + ": original and extracted matrices are equal"
)
assert euler_equals(v, v3, eps), (
"extract_rotation #" + i + ": original and extracted Eulers are equal"
)
def test_to_array():
order = Euler.RotationOrders.YXZ
a = Euler(x, y, z, order)
array = a.to_array()
assert array[0] == x, "No array, no offset: check x"
assert array[1] == y, "No array, no offset: check y"
assert array[2] == z, "No array, no offset: check z"
assert array[3] == order, "No array, no offset: check order"
array = []
a.to_array(array)
assert array[0] == x, "With array, no offset: check x"
assert array[1] == y, "With array, no offset: check y"
assert array[2] == z, "With array, no offset: check z"
assert array[3] == order, "With array, no offset: check order"
array = []
a.to_array(array, 1)
assert array[0] is None, "With array and offset: check [0]"
assert array[1] == x, "With array and offset: check x"
assert array[2] == y, "With array and offset: check y"
assert array[3] == z, "With array and offset: check z"
assert array[4] == order, "With array and offset: check order"
def test_order():
a = Euler()
assert a.order == Euler.DefaultOrder
a = Euler(1, 2, 3)
assert a.order == Euler.DefaultOrder
a = Euler(4, 5, 6, Euler.RotationOrders.YZX)
assert a.order == Euler.RotationOrders.YZX
a = Euler(7, 8, 9, Euler.RotationOrders.YZX)
a.order = Euler.RotationOrders.ZXY
assert a.order == Euler.RotationOrders.ZXY
a = Euler(11, 12, 13, Euler.RotationOrders.YZX)
a.order = Euler.RotationOrders.ZXY
assert a.order == Euler.RotationOrders.ZXY
def test_z():
a = Euler()
assert a.z == 0
a = Euler(1, 2, 3)
assert a.z == 3
a = Euler(4, 5, 6, Euler.RotationOrders.XYZ)
assert a.z == 6
a = Euler(7, 8, 9, Euler.RotationOrders.XYZ)
a.z = 10
assert a.z == 10
a = Euler(11, 12, 13, Euler.RotationOrders.XYZ)
a.z = 14
assert a.z == 14
def test_y():
a = Euler()
assert a.y == 0
a = Euler(1, 2, 3)
assert a.y == 2
a = Euler(4, 5, 6, Euler.RotationOrders.XYZ)
assert a.y == 5
a = Euler(7, 8, 9, Euler.RotationOrders.XYZ)
a.y = 10
assert a.y == 10
a = Euler(11, 12, 13, Euler.RotationOrders.XYZ)
a.y = 14
assert a.y == 14
def test_x():
a = Euler()
assert a.x == 0
a = Euler(1, 2, 3)
assert a.x == 1
a = Euler(4, 5, 6, Euler.RotationOrders.XYZ)
assert a.x == 4
a = Euler(7, 8, 9, Euler.RotationOrders.XYZ)
a.x = 10
assert a.x == 10
a = Euler(11, 12, 13, Euler.RotationOrders.XYZ)
a.x = 14
assert a.x == 14
def test_instancing():
a = Euler()
assert a.equals(euler_zero)
assert not a.equals(euler_axyz)
assert not a.equals(euler_azyx)
)
x = 2
y = 3
z = 4
w = 5
eps = 0.0001
orders = [
Euler.RotationOrders.XYZ,
Euler.RotationOrders.YXZ,
Euler.RotationOrders.ZXY,
Euler.RotationOrders.ZYX,
Euler.RotationOrders.YZX,
Euler.RotationOrders.XZY,
]
euler_angles = Euler(0.1, -0.3, 0.25)
def q_sub(a, b):
result = a.clone()
result.x -= b.x
result.y -= b.y
result.z -= b.z
result.w -= b.w
return result
def change_euler_order(euler, order):
return Euler(euler.x, euler.y, euler.z, order)
from pygfx.linalg import (
Vector3,
Euler,
Matrix4,
Quaternion,
)
from utils import matrix_equals, euler_equals, quat_equals
x = 2
y = 3
z = 4
w = 5
euler_zero = Euler(0, 0, 0, Euler.RotationOrders.XYZ)
euler_axyz = Euler(1, 0, 0, Euler.RotationOrders.XYZ)
euler_azyx = Euler(0, 1, 0, Euler.RotationOrders.ZYX)
# INSTANCING
def test_instancing():
a = Euler()
assert a.equals(euler_zero)
assert not a.equals(euler_axyz)
assert not a.equals(euler_azyx)
# PROPERTIES STUFF
def test_x():
a = Euler()
assert a.x == 0
def change_euler_order(euler, order):
return Euler(euler.x, euler.y, euler.z, order)