def test_multiplication(self):
m1 = Transformation(
m=[
[1.0, 2.0, 3.0, 4.0],
[5.0, 6.0, 7.0, 8.0],
[9.0, 9.0, 8.0, 7.0],
[6.0, 5.0, 4.0, 1.0],
],
invm=[
[-3.75, 2.75, -1, 0],
[4.375, -3.875, 2.0, -0.5],
[0.5, 0.5, -1.0, 1.0],
[-1.375, 0.875, 0.0, -0.5],
],
)
assert m1.is_consistent()
m2 = Transformation(
m=[
[3.0, 5.0, 2.0, 4.0],
[4.0, 1.0, 0.0, 5.0],
[6.0, 3.0, 2.0, 0.0],
[1.0, 4.0, 2.0, 1.0],
],
invm=[
[0.4, -0.2, 0.2, -0.6],
[2.9, -1.7, 0.2, -3.1],
[-5.55, 3.15, -0.4, 6.45],
[-0.9, 0.7, -0.2, 1.1],
],
)
assert m2.is_consistent()
expected = Transformation(
m=[
[33.0, 32.0, 16.0, 18.0],
[89.0, 84.0, 40.0, 58.0],
[118.0, 106.0, 48.0, 88.0],
[63.0, 51.0, 22.0, 50.0],
],
invm=[
[-1.45, 1.45, -1.0, 0.6],
[-13.95, 11.95, -6.5, 2.6],
[25.525, -22.025, 12.25, -5.2],
[4.825, -4.325, 2.5, -1.1],
],
)
assert expected.is_consistent()
assert expected.is_close(m1 * m2)
def test_vec_point_multiplication(self):
m = Transformation(
m=[
[1.0, 2.0, 3.0, 4.0],
[5.0, 6.0, 7.0, 8.0],
[9.0, 9.0, 8.0, 7.0],
[0.0, 0.0, 0.0, 1.0],
],
invm=[
[-3.75, 2.75, -1, 0],
[5.75, -4.75, 2.0, 1.0],
[-2.25, 2.25, -1.0, -2.0],
[0.0, 0.0, 0.0, 1.0],
],
)
assert m.is_consistent()
expected_v = Vec(14.0, 38.0, 51.0)
assert expected_v.is_close(m * Vec(1.0, 2.0, 3.0))
expected_p = Point(18.0, 46.0, 58.0)
assert expected_p.is_close(m * Point(1.0, 2.0, 3.0))
expected_n = Normal(-8.75, 7.75, -3.0)
assert expected_n.is_close(m * Normal(3.0, 2.0, 4.0))
def test_is_close(self):
m1 = Transformation(
m=[
[1.0, 2.0, 3.0, 4.0],
[5.0, 6.0, 7.0, 8.0],
[9.0, 9.0, 8.0, 7.0],
[6.0, 5.0, 4.0, 1.0],
],
invm=[
[-3.75, 2.75, -1, 0],
[4.375, -3.875, 2.0, -0.5],
[0.5, 0.5, -1.0, 1.0],
[-1.375, 0.875, 0.0, -0.5],
],
)
assert m1.is_consistent()
# Not using "deepcopy" here would make Python pass a pointer to the *same* matrices and vectors
m2 = Transformation(m=deepcopy(m1.m), invm=deepcopy(m1.invm))
assert m1.is_close(m2)
m3 = Transformation(m=deepcopy(m1.m), invm=deepcopy(m1.invm))
m3.m[2][
2] += 1.0 # Note: this makes "m3" not consistent (m3.is_consistent() == False)
assert not m1.is_close(m3)
m4 = Transformation(m=deepcopy(m1.m), invm=deepcopy(m1.invm))
m4.invm[2][
2] += 1.0 # Note: this makes "m4" not consistent (m4.is_consistent() == False)
assert not m1.is_close(m4)