diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py index 0d816f225..ba307e57a 100644 --- a/python/damask/_rotation.py +++ b/python/damask/_rotation.py @@ -489,7 +489,7 @@ class Rotation: def as_Euler_angles(self, degrees = False): """ - Represent as Bunge–Euler angles. + Represent as Bunge Euler angles. Parameters ---------- @@ -499,12 +499,16 @@ class Rotation: Returns ------- phi : numpy.ndarray of shape (...,3) - Bunge–Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π]) + Bunge Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π]) or (φ_1 ∈ [0,360], ϕ ∈ [0,180], φ_2 ∈ [0,360]) if degrees == True. + Notes + ----- + Bunge Euler angles correspond to a rotation axis sequence of z–x'–z''. + Examples -------- - Cube orientation as Bunge–Euler angles. + Cube orientation as Bunge Euler angles. >>> import damask >>> import numpy as np @@ -532,7 +536,7 @@ class Rotation: Returns ------- axis_angle : numpy.ndarray of shape (...,4) or tuple ((...,3), (...)) if pair == True - Axis and angle (n_1, n_2, n_3, ω) with ǀnǀ = 1 and ω ∈ [0,π] + Axis and angle [n_1, n_2, n_3, ω] with ǀnǀ = 1 and ω ∈ [0,π] or ω ∈ [0,180] if degrees == True. Examples @@ -587,7 +591,7 @@ class Rotation: ------- rho : numpy.ndarray of shape (...,4) or (...,3) if compact == True Rodrigues–Frank vector [n_1, n_2, n_3, tan(ω/2)] with ǀnǀ = 1 and ω ∈ [0,π] - or tan(ω/2) [n_1, n_2, n_3] with ω ∈ [0,π] if compact == True. + or [n_1, n_2, n_3] with |n| = tan(ω/2) and ω ∈ [0,π] if compact == True. Examples -------- @@ -690,15 +694,19 @@ class Rotation: def from_Euler_angles(phi, degrees = False): """ - Initialize from Bunge–Euler angles. + Initialize from Bunge Euler angles. Parameters ---------- phi : numpy.ndarray of shape (...,3) - Bunge–Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π]) + Euler angles (φ_1 ∈ [0,2π], ϕ ∈ [0,π], φ_2 ∈ [0,2π]) or (φ_1 ∈ [0,360], ϕ ∈ [0,180], φ_2 ∈ [0,360]) if degrees == True. degrees : boolean, optional - Bunge–Euler angles are given in degrees. Defaults to False. + Euler angles are given in degrees. Defaults to False. + + Notes + ----- + Bunge Euler angles correspond to a rotation axis sequence of z–x'–z''. """ eu = np.array(phi,dtype=float) @@ -1137,7 +1145,7 @@ class Rotation: @staticmethod def _qu2eu(qu): - """Quaternion to Bunge-Euler angles.""" + """Quaternion to Bunge Euler angles.""" q02 = qu[...,0:1]*qu[...,2:3] q13 = qu[...,1:2]*qu[...,3:4] q01 = qu[...,0:1]*qu[...,1:2] @@ -1255,7 +1263,7 @@ class Rotation: @staticmethod def _om2eu(om): - """Rotation matrix to Bunge–Euler angles.""" + """Rotation matrix to Bunge Euler angles.""" with np.errstate(invalid='ignore',divide='ignore'): zeta = 1.0/np.sqrt(1.0-om[...,2,2:3]**2) eu = np.where(np.isclose(np.abs(om[...,2,2:3]),1.0,0.0), @@ -1309,10 +1317,10 @@ class Rotation: return Rotation._ho2cu(Rotation._om2ho(om)) - #---------- Bunge-Euler angles ---------- + #---------- Bunge Euler angles ---------- @staticmethod def _eu2qu(eu): - """Bunge–Euler angles to quaternion.""" + """Bunge Euler angles to quaternion.""" ee = 0.5*eu cPhi = np.cos(ee[...,1:2]) sPhi = np.sin(ee[...,1:2]) @@ -1325,7 +1333,7 @@ class Rotation: @staticmethod def _eu2om(eu): - """Bunge–Euler angles to rotation matrix.""" + """Bunge Euler angles to rotation matrix.""" c = np.cos(eu) s = np.sin(eu) om = np.block([+c[...,0:1]*c[...,2:3]-s[...,0:1]*s[...,2:3]*c[...,1:2], @@ -1343,7 +1351,7 @@ class Rotation: @staticmethod def _eu2ax(eu): - """Bunge–Euler angles to axis–angle pair.""" + """Bunge Euler angles to axis–angle pair.""" t = np.tan(eu[...,1:2]*0.5) sigma = 0.5*(eu[...,0:1]+eu[...,2:3]) delta = 0.5*(eu[...,0:1]-eu[...,2:3]) @@ -1362,7 +1370,7 @@ class Rotation: @staticmethod def _eu2ro(eu): - """Bunge–Euler angles to Rodrigues–Frank vector.""" + """Bunge Euler angles to Rodrigues–Frank vector.""" ax = Rotation._eu2ax(eu) ro = np.block([ax[...,:3],np.tan(ax[...,3:4]*.5)]) ro[ax[...,3]>=np.pi,3] = np.inf @@ -1371,12 +1379,12 @@ class Rotation: @staticmethod def _eu2ho(eu): - """Bunge–Euler angles to homochoric vector.""" + """Bunge Euler angles to homochoric vector.""" return Rotation._ax2ho(Rotation._eu2ax(eu)) @staticmethod def _eu2cu(eu): - """Bunge–Euler angles to cubochoric vector.""" + """Bunge Euler angles to cubochoric vector.""" return Rotation._ho2cu(Rotation._eu2ho(eu)) @@ -1408,7 +1416,7 @@ class Rotation: @staticmethod def _ax2eu(ax): - """Rotation matrix to Bunge–Euler angles.""" + """Rotation matrix to Bunge Euler angles.""" return Rotation._om2eu(Rotation._ax2om(ax)) @staticmethod @@ -1448,7 +1456,7 @@ class Rotation: @staticmethod def _ro2eu(ro): - """Rodrigues–Frank vector to Bunge–Euler angles.""" + """Rodrigues–Frank vector to Bunge Euler angles.""" return Rotation._om2eu(Rotation._ro2om(ro)) @staticmethod @@ -1488,7 +1496,7 @@ class Rotation: @staticmethod def _ho2eu(ho): - """Homochoric vector to Bunge–Euler angles.""" + """Homochoric vector to Bunge Euler angles.""" return Rotation._ax2eu(Rotation._ho2ax(ho)) @staticmethod @@ -1571,7 +1579,7 @@ class Rotation: @staticmethod def _cu2eu(cu): - """Cubochoric vector to Bunge–Euler angles.""" + """Cubochoric vector to Bunge Euler angles.""" return Rotation._ho2eu(Rotation._cu2ho(cu)) @staticmethod