def get_rotations(normal):
x = np.array([1,0,0]); y = np.array([0,1,0]); z = np.array([0,0,1])
yz_proj = np.dot(y, normal)*y + np.dot(z, normal)*z
# <z, yz_proj> = vnorm(z)*vnorm(yz_proj)*cos(theta)
theta = np.arccos( np.dot(z, yz_proj)/vnorm(yz_proj) )
xz_proj = np.dot(x, normal)*x + np.dot(z, normal)*z
psi = -np.arccos( np.dot(z, xz_proj)/vnorm(xz_proj) )
xy_proj = np.dot(x, normal)*x + np.dot(y, normal)*y
phi = np.arccos( np.dot(y, xy_proj)/vnorm(xy_proj) )
return util.eulerRot(theta=theta, psi=psi, phi=phi)
def get_rotations(normal):
x = np.array([1, 0, 0])
y = np.array([0, 1, 0])
z = np.array([0, 0, 1])
yz_proj = np.dot(y, normal) * y + np.dot(z, normal) * z
# <z, yz_proj> = vnorm(z)*vnorm(yz_proj)*cos(theta)
theta = np.arccos(np.dot(z, yz_proj) / vnorm(yz_proj))
xz_proj = np.dot(x, normal) * x + np.dot(z, normal) * z
psi = -np.arccos(np.dot(z, xz_proj) / vnorm(xz_proj))
xy_proj = np.dot(x, normal) * x + np.dot(y, normal) * y
phi = np.arccos(np.dot(y, xy_proj) / vnorm(xy_proj))
return util.eulerRot(theta=theta, psi=psi, phi=phi)
def nearest_simple_transform(M):
"""Finds the closest transformation to M that is composed of only n*(PI/2)
rotations and axis reflections.
"""
# if det(M) < 0, then M has some reflections going on (which is still fine)
tag = np.linalg.det(M) < 0 and -1 or 1
M[:,2] *= tag
(theta, psi, phi) = decompose_rot(M)
angs = np.array([theta, psi, phi])
angs = np.pi/2 * ((angs + np.sign(angs)*np.pi/4)/(np.pi/2)).astype('i')
M2 = eulerRot(theta=angs[0], psi=angs[1], phi=angs[2])
M[:,2] *= tag
M2[:,2] *= tag
return M2
