def test_scale_from_matrix():
factor = random.random() * 10 - 5
origin = np.random.random(3) - 0.5
direct = np.random.random(3) - 0.5
S0 = t.scale_matrix(factor, origin)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
S0 = t.scale_matrix(factor, origin, direct)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
def test_scale_from_matrix():
factor = random.random() * 10 - 5
origin = np.random.random(3) - 0.5
direct = np.random.random(3) - 0.5
S0 = t.scale_matrix(factor, origin)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
S0 = t.scale_matrix(factor, origin, direct)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
def test_scale_from_matrix():
factor = 7
origin = np.array([0.2, 0.2, 0.2]) # arbitrary values
direct = np.array([0.4, 0.4, 0.4])
S0 = t.scale_matrix(factor, origin)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
S0 = t.scale_matrix(factor, origin, direct)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
def test_scale_from_matrix():
factor = 7
origin = np.array([0.2, 0.2, 0.2]) # arbitrary values
direct = np.array([0.4, 0.4, 0.4])
S0 = t.scale_matrix(factor, origin)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
S0 = t.scale_matrix(factor, origin, direct)
factor, origin, direction = t.scale_from_matrix(S0)
S1 = t.scale_matrix(factor, origin, direction)
assert_equal(t.is_same_transform(S0, S1), True)
def test_rotation_matrix(self):
R = self.f(np.pi/2.0, [0, 0, 1], [1, 0, 0])
assert_allclose(np.dot(R, [0, 0, 0, 1]), [ 1., -1., 0., 1.])
angle = (random.random() - 0.5) * (2*np.pi)
direc = np.random.random(3) - 0.5
point = np.random.random(3) - 0.5
R0 = self.f(angle, direc, point)
R1 = self.f(angle-2*np.pi, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
R0 = self.f(angle, direc, point)
R1 = self.f(-angle, -direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
I = np.identity(4, np.float64)
assert_allclose(I, self.f(np.pi*2, direc), atol=_ATOL)
assert_allclose(2., np.trace(self.f(np.pi/2, direc, point)))
def test_rotation_matrix(f):
R = f(np.pi / 2.0, [0, 0, 1], [1, 0, 0])
assert_allclose(np.dot(R, [0, 0, 0, 1]), [1., -1., 0., 1.])
angle = 0.2 * 2 * np.pi # arbitrary value
direc = np.array([0.2, 0.2, 0.2])
point = np.array([0.4, 0.4, 0.4])
R0 = f(angle, direc, point)
R1 = f(angle - 2 * np.pi, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
R0 = f(angle, direc, point)
R1 = f(-angle, -direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
I = np.identity(4, np.float64)
assert_allclose(I, f(np.pi * 2, direc), atol=_ATOL)
assert_allclose(2., np.trace(f(np.pi / 2, direc, point)))
def test_rotation_matrix(self):
R = self.f(np.pi / 2.0, [0, 0, 1], [1, 0, 0])
assert_allclose(np.dot(R, [0, 0, 0, 1]), [1., -1., 0., 1.])
angle = 0.2 * 2 * np.pi # arbitrary value
direc = np.array([0.2, 0.2, 0.2])
point = np.array([0.4, 0.4, 0.4])
R0 = self.f(angle, direc, point)
R1 = self.f(angle - 2 * np.pi, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
R0 = self.f(angle, direc, point)
R1 = self.f(-angle, -direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
I = np.identity(4, np.float64)
assert_allclose(I, self.f(np.pi * 2, direc), atol=_ATOL)
assert_allclose(2., np.trace(self.f(np.pi / 2, direc, point)))
def test_rotation_matrix(self):
R = self.f(np.pi / 2.0, [0, 0, 1], [1, 0, 0])
assert_allclose(np.dot(R, [0, 0, 0, 1]), [1., -1., 0., 1.])
angle = (random.random() - 0.5) * (2 * np.pi)
direc = np.random.random(3) - 0.5
point = np.random.random(3) - 0.5
R0 = self.f(angle, direc, point)
R1 = self.f(angle - 2 * np.pi, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
R0 = self.f(angle, direc, point)
R1 = self.f(-angle, -direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
I = np.identity(4, np.float64)
assert_allclose(I, self.f(np.pi * 2, direc), atol=_ATOL)
assert_allclose(2., np.trace(self.f(np.pi / 2, direc, point)))
def test_reflection_from_matrix():
v0 = np.array([0.2, 0.2, 0.2]) # arbitrary values
v1 = np.array([0.4, 0.4, 0.4])
M0 = t.reflection_matrix(v0, v1)
point, normal = t.reflection_from_matrix(M0)
M1 = t.reflection_matrix(point, normal)
assert_equal(t.is_same_transform(M0, M1), True)
def test_reflection_from_matrix():
v0 = np.array([0.2, 0.2, 0.2]) # arbitrary values
v1 = np.array([0.4, 0.4, 0.4])
M0 = t.reflection_matrix(v0, v1)
point, normal = t.reflection_from_matrix(M0)
M1 = t.reflection_matrix(point, normal)
assert_equal(t.is_same_transform(M0, M1), True)
def test_reflection_from_matrix():
v0 = np.random.random(3) - 0.5
v1 = np.random.random(3) - 0.5
M0 = t.reflection_matrix(v0, v1)
point, normal = t.reflection_from_matrix(M0)
M1 = t.reflection_matrix(point, normal)
assert_equal(t.is_same_transform(M0, M1), True)
def test_projection_from_matrix_4(self, data):
point, normal, direct, persp = data
P0 = t.projection_matrix(
point, normal, perspective=persp, pseudo=True)
result = t.projection_from_matrix(P0, pseudo=True)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_reflection_from_matrix():
v0 = np.random.random(3) - 0.5
v1 = np.random.random(3) - 0.5
M0 = t.reflection_matrix(v0, v1)
point, normal = t.reflection_from_matrix(M0)
M1 = t.reflection_matrix(point, normal)
assert_equal(t.is_same_transform(M0, M1), True)
def test_projection_from_matrix_4(self, data):
point, normal, direct, persp = data
P0 = t.projection_matrix(
point, normal, perspective=persp, pseudo=True)
result = t.projection_from_matrix(P0, pseudo=True)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_rotation_from_matrix():
angle = 0.2 * 2 * np.pi # arbitrary values
direc = np.array([0.2, 0.2, 0.2])
point = np.array([0.4, 0.4, 0.4])
R0 = t.rotation_matrix(angle, direc, point)
angle, direc, point = t.rotation_from_matrix(R0)
R1 = t.rotation_matrix(angle, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
def test_rotation_from_matrix():
angle = 0.2 * 2 * np.pi # arbitrary values
direc = np.array([0.2, 0.2, 0.2])
point = np.array([0.4, 0.4, 0.4])
R0 = t.rotation_matrix(angle, direc, point)
angle, direc, point = t.rotation_from_matrix(R0)
R1 = t.rotation_matrix(angle, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
def test_rotation_from_matrix():
angle = (random.random() - 0.5) * (2*np.pi)
direc = np.random.random(3) - 0.5
point = np.random.random(3) - 0.5
R0 = t.rotation_matrix(angle, direc, point)
angle, direc, point = t.rotation_from_matrix(R0)
R1 = t.rotation_matrix(angle, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
def test_projection_from_matrix_4(self):
P0 = t.projection_matrix(self.point,
self.normal,
perspective=self.persp,
pseudo=True)
result = t.projection_from_matrix(P0, pseudo=True)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_rotation_from_matrix():
angle = (random.random() - 0.5) * (2 * np.pi)
direc = np.random.random(3) - 0.5
point = np.random.random(3) - 0.5
R0 = t.rotation_matrix(angle, direc, point)
angle, direc, point = t.rotation_from_matrix(R0)
R1 = t.rotation_matrix(angle, direc, point)
assert_equal(t.is_same_transform(R0, R1), True)
def test_projection_matrix_2(self):
point = np.random.random(3) - 0.5
normal = np.random.random(3) - 0.5
direct = np.random.random(3) - 0.5
persp = np.random.random(3) - 0.5
P0 = self.f(point, normal)
P1 = self.f(point, normal, direction=direct)
P2 = self.f(point, normal, perspective=persp)
P3 = self.f(point, normal, perspective=persp, pseudo=True)
assert_equal(t.is_same_transform(P2, np.dot(P0, P3)), True)
def test_projection_matrix_2(self):
point = np.random.random(3) - 0.5
normal = np.random.random(3) - 0.5
direct = np.random.random(3) - 0.5
persp = np.random.random(3) - 0.5
P0 = self.f(point, normal)
P1 = self.f(point, normal, direction=direct)
P2 = self.f(point, normal, perspective=persp)
P3 = self.f(point, normal, perspective=persp, pseudo=True)
assert_equal(t.is_same_transform(P2, np.dot(P0, P3)), True)
def test_compose_matrix():
scale = np.random.random(3) - 0.5
shear = np.random.random(3) - 0.5
angles = (np.random.random(3) - 0.5) * (2 * math.pi)
trans = np.random.random(3) - 0.5
persp = np.random.random(4) - 0.5
M0 = t.compose_matrix(scale, shear, angles, trans, persp)
result = t.decompose_matrix(M0)
M1 = t.compose_matrix(*result)
assert_equal(t.is_same_transform(M0, M1), True)
def test_compose_matrix():
scale = np.random.random(3) - 0.5
shear = np.random.random(3) - 0.5
angles = (np.random.random(3) - 0.5) * (2*math.pi)
trans = np.random.random(3) - 0.5
persp = np.random.random(4) - 0.5
M0 = t.compose_matrix(scale, shear, angles, trans, persp)
result = t.decompose_matrix(M0)
M1 = t.compose_matrix(*result)
assert_equal(t.is_same_transform(M0, M1), True)
def test_compose_matrix():
scale = np.array([0.2, 0.2, 0.2]) # arbitrary values
shear = np.array([0.4, 0.4, 0.4])
angles = np.array([0.6, 0.6, 0.6]) * 2 * np.pi
trans = np.array([0.8, 0.8, 0.8])
persp = np.array([0.9, 0.9, 0.9, 0.9])
M0 = t.compose_matrix(scale, shear, angles, trans, persp)
result = t.decompose_matrix(M0)
M1 = t.compose_matrix(*result)
assert_equal(t.is_same_transform(M0, M1), True)
def test_compose_matrix():
scale = np.array([0.2, 0.2, 0.2]) # arbitrary values
shear = np.array([0.4, 0.4, 0.4])
angles = np.array([0.6, 0.6, 0.6]) * 2 * np.pi
trans = np.array([0.8, 0.8, 0.8])
persp = np.array([0.9, 0.9, 0.9, 0.9])
M0 = t.compose_matrix(scale, shear, angles, trans, persp)
result = t.decompose_matrix(M0)
M1 = t.compose_matrix(*result)
assert_equal(t.is_same_transform(M0, M1), True)
def test_projection_matrix_2(self):
point = np.array([0.2, 0.2, 0.2]) # arbitrary values
normal = np.array([0.4, 0.4, 0.4])
direct = np.array([0.6, 0.6, 0.6])
persp = np.array([0.8, 0.8, 0.8])
P0 = self.f(point, normal)
# TODO: why isn't this used anymore?
P1 = self.f(point, normal, direction=direct)
P2 = self.f(point, normal, perspective=persp)
P3 = self.f(point, normal, perspective=persp, pseudo=True)
assert_equal(t.is_same_transform(P2, np.dot(P0, P3)), True)
def test_projection_matrix_2(self, f):
point = np.array([0.2, 0.2, 0.2]) # arbitrary values
normal = np.array([0.4, 0.4, 0.4])
direct = np.array([0.6, 0.6, 0.6])
persp = np.array([0.8, 0.8, 0.8])
P0 = f(point, normal)
# TODO: why isn't this used anymore?
P1 = f(point, normal, direction=direct)
P2 = f(point, normal, perspective=persp)
P3 = f(point, normal, perspective=persp, pseudo=True)
assert_equal(t.is_same_transform(P2, np.dot(P0, P3)), True)
def test_shear_from_matrix():
# This seems to fail sometimes if the random numbers
# roll certain values....
# angle = (random.random() - 0.5) * 4*math.pi
# direct = np.random.random(3) - 0.5
# point = np.random.random(3) - 0.5
# normal = np.cross(direct, np.random.random(3))
# So here are some of my random numbers
angle = 2.8965075413405783
direct = np.array([-0.31117458, -0.41769518, -0.01188556])
point = np.array([-0.0035982, -0.40997482, 0.42241425])
normal = np.cross(direct, np.array([0.08122421, 0.4747914, 0.19851859]))
S0 = t.shear_matrix(angle, direct, point, normal)
angle, direct, point, normal = t.shear_from_matrix(S0)
S1 = t.shear_matrix(angle, direct, point, normal)
assert_equal(t.is_same_transform(S0, S1), True)
def test_shear_from_matrix():
# This seems to fail sometimes if the random numbers
# roll certain values....
# angle = (random.random() - 0.5) * 4*math.pi
# direct = np.random.random(3) - 0.5
# point = np.random.random(3) - 0.5
# normal = np.cross(direct, np.random.random(3))
# So here are some of my random numbers
angle = 2.8965075413405783
direct = np.array([-0.31117458, -0.41769518, -0.01188556])
point = np.array([-0.0035982, -0.40997482, 0.42241425])
normal = np.cross(direct, np.array([ 0.08122421, 0.4747914 , 0.19851859]))
S0 = t.shear_matrix(angle, direct, point, normal)
angle, direct, point, normal = t.shear_from_matrix(S0)
S1 = t.shear_matrix(angle, direct, point, normal)
assert_equal(t.is_same_transform(S0, S1), True)
def test_shear_from_matrix():
# This seems to fail sometimes if the random numbers
# roll certain values....
# angle = (random.random() - 0.5) * 4*np.pi
# direct = np.random.random(3) - 0.5
# point = np.random.random(3) - 0.5
# normal = np.cross(direct, np.random.random(3))
# In this random configuration the test will fail about 0.05% of all times.
# Then we hit some edge-cases of the algorithm. The edge cases for these
# values are slightly different for the linalg library used (MKL/LAPACK).
# So here are some of my random numbers
angle = 2.8969075413405783 # arbitrary values
direct = np.array([-0.31117458, -0.41769518, -0.01188556])
point = np.array([-0.0035982, -0.40997482, 0.42241425])
normal = np.cross(direct, np.array([0.08122421, 0.4747914, 0.19851859]))
S0 = t.shear_matrix(angle, direct, point, normal)
angle, direct, point, normal = t.shear_from_matrix(S0)
S1 = t.shear_matrix(angle, direct, point, normal)
assert_equal(t.is_same_transform(S0, S1), True)
def test_shear_from_matrix():
# This seems to fail sometimes if the random numbers
# roll certain values....
# angle = (random.random() - 0.5) * 4*np.pi
# direct = np.random.random(3) - 0.5
# point = np.random.random(3) - 0.5
# normal = np.cross(direct, np.random.random(3))
# In this random configuration the test will fail about 0.05% of all times.
# Then we hit some edge-cases of the algorithm. The edge cases for these
# values are slightly different for the linalg library used (MKL/LAPACK).
# So here are some of my random numbers
angle = 2.8969075413405783 # arbitrary values
direct = np.array([-0.31117458, -0.41769518, -0.01188556])
point = np.array([-0.0035982, -0.40997482, 0.42241425])
normal = np.cross(direct, np.array([0.08122421, 0.4747914, 0.19851859]))
S0 = t.shear_matrix(angle, direct, point, normal)
angle, direct, point, normal = t.shear_from_matrix(S0)
S1 = t.shear_matrix(angle, direct, point, normal)
assert_equal(t.is_same_transform(S0, S1), True)
def test_quaternion_from_matrix_6(self):
R = t.random_rotation_matrix()
q = self.f(R)
assert_equal(t.is_same_transform(R, t.quaternion_matrix(q)), True)
def test_projection_from_matrix_2(self):
P0 = t.projection_matrix(self.point, self.normal, self.direct)
result = t.projection_from_matrix(P0)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_projection_from_matrix_2(self):
P0 = t.projection_matrix(self.point, self.normal, self.direct)
result = t.projection_from_matrix(P0)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_projection_from_matrix_4(self):
P0 = t.projection_matrix(self.point, self.normal,
perspective=self.persp, pseudo=True)
result = t.projection_from_matrix(P0, pseudo=True)
P1 = t.projection_matrix(*result)
assert_equal(t.is_same_transform(P0, P1), True)
def test_quaternion_from_matrix_6(self):
R = t.random_rotation_matrix()
q = self.f(R)
assert_equal(t.is_same_transform(R, t.quaternion_matrix(q)), True)
