def test_make_rotation_x():
a = Matrix4()
b = sqrt(3) / 2
c = Matrix4().set(1, 0, 0, 0, 0, b, -0.5, 0, 0, 0.5, b, 0, 0, 0, 0, 1)
a.make_rotation_x(pi / 6)
assert matrix_equals(a, c)
def test_make_translation():
a = Matrix4()
b = Vector3(2, 3, 4)
c = Matrix4().set(1, 0, 0, 2, 0, 1, 0, 3, 0, 0, 1, 4, 0, 0, 0, 1)
a.make_translation(b.x, b.y, b.z)
assert matrix_equals(a, c)
def test_make_rotation_axis():
axis = Vector3(1.5, 0.0, 1.0).normalize()
rads = radians(45)
a = Matrix4().make_rotation_axis(axis, rads)
expected = Matrix4().set(
0.9098790095958609,
-0.39223227027636803,
0.13518148560620882,
0,
0.39223227027636803,
0.7071067811865476,
-0.588348405414552,
0,
0.13518148560620882,
0.588348405414552,
0.7972277715906868,
0,
0,
0,
0,
1,
)
assert matrix_equals(a, expected), "Check numeric result"
def test_make_orthographic():
a = Matrix4().make_orthographic(-1, 1, -1, 1, 1, 100)
expected = Matrix4().set(
1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2 / 99, -101 / 99, 0, 0, 0, 1
)
assert matrix_equals(a, expected), "Check result"
def test_scale():
a = Matrix4().set(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
b = Vector3(2, 3, 4)
c = Matrix4().set(2, 6, 12, 4, 10, 18, 28, 8, 18, 30, 44, 12, 26, 42, 60, 16)
a.scale(b)
assert matrix_equals(a, c)
def test_set_position():
a = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
b = Vector3(-1, -2, -3)
c = Matrix4().set(0, 1, 2, -1, 4, 5, 6, -2, 8, 9, 10, -3, 12, 13, 14, 15)
a.set_position(b)
assert matrix_equals(a, c)
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_copy_position():
a = Matrix4().set(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
b = Matrix4().set(1, 2, 3, 0, 5, 6, 7, 0, 9, 10, 11, 0, 13, 14, 15, 16)
assert not matrix_equals(a, b), "a and b initially not equal"
b.copy_position(a)
assert matrix_equals(a, b), "a and b equal after copy_position()"
def test_copy():
a = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
b = Matrix4().copy(a)
assert matrix_equals(a, b)
# ensure that it is a True copy
a.elements[0] = 2
assert not matrix_equals(a, b)
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_transpose():
a = Matrix4()
b = a.clone().transpose()
assert matrix_equals(a, b)
b = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
c = b.clone().transpose()
assert not matrix_equals(b, c)
c.transpose()
assert matrix_equals(b, c)
def test_equals():
a = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
b = Matrix4().set(0, -1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
assert not a.equals(b), "Check that a does not equal b"
assert not b.equals(a), "Check that b does not equal a"
a.copy(b)
assert a.equals(b), "Check that a equals b after copy()"
assert b.equals(a), "Check that b equals a after copy()"
def test_set_from_rotation_matrix():
# contrived examples purely to please the god of code coverage...
# match conditions in various 'else [if]' blocks
a = Quaternion()
q = Quaternion(-9, -2, 3, -4).normalize()
m = Matrix4().make_rotation_from_quaternion(q)
expected = Vector4(
0.8581163303210332,
0.19069251784911848,
-0.2860387767736777,
0.38138503569823695,
)
a.set_from_rotation_matrix(m)
assert abs(a.x - expected.x) <= eps, "m11 > m22 && m11 > m33: check x"
assert abs(a.y - expected.y) <= eps, "m11 > m22 && m11 > m33: check y"
assert abs(a.z - expected.z) <= eps, "m11 > m22 && m11 > m33: check z"
assert abs(a.w - expected.w) <= eps, "m11 > m22 && m11 > m33: check w"
q = Quaternion(-1, -2, 1, -1).normalize()
m.make_rotation_from_quaternion(q)
expected = Vector4(
0.37796447300922714,
0.7559289460184544,
-0.37796447300922714,
0.37796447300922714,
)
a.set_from_rotation_matrix(m)
assert abs(a.x - expected.x) <= eps, "m22 > m33: check x"
assert abs(a.y - expected.y) <= eps, "m22 > m33: check y"
assert abs(a.z - expected.z) <= eps, "m22 > m33: check z"
assert abs(a.w - expected.w) <= eps, "m22 > m33: check w"
def test_set_from_matrix_position():
a = Vector3()
m = Matrix4().set(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53)
a.set_from_matrix_position(m)
assert a.x == 7, "Check x"
assert a.y == 19, "Check y"
assert a.z == 37, "Check z"
def test_set_from_euler_set_from_rotation_matrix():
# ensure euler conversion for Quaternion matches that of Matrix4
for i in range(len(orders)):
q = Quaternion().set_from_euler(
change_euler_order(euler_angles, orders[i]))
m = Matrix4().make_rotation_from_euler(
change_euler_order(euler_angles, orders[i]))
q2 = Quaternion().set_from_rotation_matrix(m)
assert q_sub(q, q2).length() < 0.001
def test_transform_direction():
a = Vector3(x, y, z)
m = Matrix4()
transformed = Vector3(0.3713906763541037, 0.5570860145311556,
0.7427813527082074)
a.transform_direction(m)
assert abs(a.x - transformed.x) <= eps, "Check x"
assert abs(a.y - transformed.y) <= eps, "Check y"
assert abs(a.z - transformed.z) <= eps, "Check z"
def test_set_from_matrix_scale():
a = Vector3()
m = Matrix4().set(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53)
expected = Vector3(25.573423705088842, 31.921779399024736,
35.70714214271425)
a.set_from_matrix_scale(m)
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_multiply_matrices():
# Reference:
#
# #!/usr/bin/env python
# from __future__ import print_function
# import numpy as np
# print(
# np.dot(
# np.reshape([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53], (4, 4)),
# np.reshape([59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131], (4, 4))
# )
# )
#
# [[ 1585 1655 1787 1861]
# [ 5318 5562 5980 6246]
# [10514 11006 11840 12378]
# [15894 16634 17888 18710]]
lhs = Matrix4().set(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53)
rhs = Matrix4().set(
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131
)
ans = Matrix4()
ans.multiply_matrices(lhs, rhs)
assert ans.elements[0] == 1585
assert ans.elements[1] == 5318
assert ans.elements[2] == 10514
assert ans.elements[3] == 15894
assert ans.elements[4] == 1655
assert ans.elements[5] == 5562
assert ans.elements[6] == 11006
assert ans.elements[7] == 16634
assert ans.elements[8] == 1787
assert ans.elements[9] == 5980
assert ans.elements[10] == 11840
assert ans.elements[11] == 17888
assert ans.elements[12] == 1861
assert ans.elements[13] == 6246
assert ans.elements[14] == 12378
assert ans.elements[15] == 18710
def test_determinant():
a = Matrix4()
assert a.determinant() == 1
a.elements[0] = 2
assert a.determinant() == 2
a.elements[0] = 0
assert a.determinant() == 0
# calculated via http://www.euclideanspace.com/maths/algebra/matrix/functions/determinant/fourD/index.htm
a.set(2, 3, 4, 5, -1, -21, -3, -4, 6, 7, 8, 10, -8, -9, -10, -12)
assert a.determinant() == 76
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_set_from_matrix_column():
a = Vector3()
m = Matrix4().set(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53)
a.set_from_matrix_column(m, 0)
assert a.x == 2, "Index 0: check x"
assert a.y == 11, "Index 0: check y"
assert a.z == 23, "Index 0: check z"
a.set_from_matrix_column(m, 2)
assert a.x == 5, "Index 2: check x"
assert a.y == 17, "Index 2: check y"
assert a.z == 31, "Index 2: check z"
def test_instancing():
a = Matrix4()
assert a.determinant() == 1
b = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
assert b.elements[0] == 0
assert b.elements[1] == 4
assert b.elements[2] == 8
assert b.elements[3] == 12
assert b.elements[4] == 1
assert b.elements[5] == 5
assert b.elements[6] == 9
assert b.elements[7] == 13
assert b.elements[8] == 2
assert b.elements[9] == 6
assert b.elements[10] == 10
assert b.elements[11] == 14
assert b.elements[12] == 3
assert b.elements[13] == 7
assert b.elements[14] == 11
assert b.elements[15] == 15
assert not matrix_equals(a, b)
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_apply_matrix4():
a = Vector3(x, y, z)
b = Vector4(x, y, z, 1)
m = Matrix4().make_rotation_x(pi)
a.apply_matrix4(m)
b.apply_matrix4(m)
assert a.x == b.x / b.w
assert a.y == b.y / b.w
assert a.z == b.z / b.w
m = Matrix4().make_translation(3, 2, 1)
a.apply_matrix4(m)
b.apply_matrix4(m)
assert a.x == b.x / b.w
assert a.y == b.y / b.w
assert a.z == b.z / b.w
m = Matrix4().set(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0)
a.apply_matrix4(m)
b.apply_matrix4(m)
assert a.x == b.x / b.w
assert a.y == b.y / b.w
assert a.z == b.z / b.w
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_identity():
b = Matrix4().set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
assert b.elements[0] == 0
assert b.elements[1] == 4
assert b.elements[2] == 8
assert b.elements[3] == 12
assert b.elements[4] == 1
assert b.elements[5] == 5
assert b.elements[6] == 9
assert b.elements[7] == 13
assert b.elements[8] == 2
assert b.elements[9] == 6
assert b.elements[10] == 10
assert b.elements[11] == 14
assert b.elements[12] == 3
assert b.elements[13] == 7
assert b.elements[14] == 11
assert b.elements[15] == 15
a = Matrix4()
assert not matrix_equals(a, b)
b.identity()
assert matrix_equals(a, b)
def test_to_array():
a = Matrix4().set(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
no_offset = [1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 8, 12, 16]
with_offset = [None, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 8, 12, 16]
array = a.to_array()
assert array == no_offset, "No array, no offset"
array = []
a.to_array(array)
assert array == no_offset, "With array, no offset"
array = []
a.to_array(array, 1)
assert array == with_offset, "With array, with offset"
def test_make_basisextract_basis():
identity_basis = [Vector3(1, 0, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)]
a = Matrix4().make_basis(identity_basis[0], identity_basis[1], identity_basis[2])
identity = Matrix4()
assert matrix_equals(a, identity)
test_bases = [[Vector3(0, 1, 0), Vector3(-1, 0, 0), Vector3(0, 0, 1)]]
for i in range(len(test_bases)):
test_basis = test_bases[i]
b = Matrix4().make_basis(test_basis[0], test_basis[1], test_basis[2])
out_basis = [Vector3(), Vector3(), Vector3()]
b.extract_basis(out_basis[0], out_basis[1], out_basis[2])
# check what goes in, is what comes out.
for j in range(len(out_basis)):
assert out_basis[j].equals(test_basis[j])
# get the basis out the hard war
for j in range(len(identity_basis)):
out_basis[j].copy(identity_basis[j])
out_basis[j].apply_matrix4(b)
# did the multiply method of basis extraction work?
for j in range(len(out_basis)):
assert out_basis[j].equals(test_basis[j])
def test_premultiply():
lhs = Matrix4().set(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53)
rhs = Matrix4().set(
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131
)
rhs.premultiply(lhs)
assert rhs.elements[0] == 1585
assert rhs.elements[1] == 5318
assert rhs.elements[2] == 10514
assert rhs.elements[3] == 15894
assert rhs.elements[4] == 1655
assert rhs.elements[5] == 5562
assert rhs.elements[6] == 11006
assert rhs.elements[7] == 16634
assert rhs.elements[8] == 1787
assert rhs.elements[9] == 5980
assert rhs.elements[10] == 11840
assert rhs.elements[11] == 17888
assert rhs.elements[12] == 1861
assert rhs.elements[13] == 6246
assert rhs.elements[14] == 12378
assert rhs.elements[15] == 18710
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