no 'dangling' functions
@staticmethod is what we need here
This commit is contained in:
Martin Diehl
parent
1e1cb3f151
commit
c84a6e90c9
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@ -4,6 +4,13 @@ from . import Lambert
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P = -1
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def isone(a):
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return np.isclose(a,1.0,atol=1.0e-7,rtol=0.0)
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def iszero(a):
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return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
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####################################################################################################
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class Rotation:
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u"""
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@ -183,7 +190,7 @@ class Rotation:
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return angles in degrees.
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"""
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eu = qu2eu(self.quaternion)
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eu = Rotation.qu2eu(self.quaternion)
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if degrees: eu = np.degrees(eu)
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return eu
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@ -201,13 +208,13 @@ class Rotation:
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return tuple of axis and angle.
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"""
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ax = qu2ax(self.quaternion)
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ax = Rotation.qu2ax(self.quaternion)
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if degrees: ax[3] = np.degrees(ax[3])
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return (ax[:3],np.degrees(ax[3])) if pair else ax
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def asMatrix(self):
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"""Rotation matrix."""
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return qu2om(self.quaternion)
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return Rotation.qu2om(self.quaternion)
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def asRodrigues(self,
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vector = False):
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@ -221,16 +228,16 @@ class Rotation:
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return as actual Rodrigues--Frank vector, i.e. rotation axis scaled by tan(ω/2).
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"""
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ro = qu2ro(self.quaternion)
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ro = Rotation.qu2ro(self.quaternion)
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return ro[:3]*ro[3] if vector else ro
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def asHomochoric(self):
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"""Homochoric vector: (h_1, h_2, h_3)."""
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return qu2ho(self.quaternion)
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return Rotation.qu2ho(self.quaternion)
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def asCubochoric(self):
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"""Cubochoric vector: (c_1, c_2, c_3)."""
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return qu2cu(self.quaternion)
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return Rotation.qu2cu(self.quaternion)
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def asM(self):
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"""
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@ -276,7 +283,7 @@ class Rotation:
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if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
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raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].\n{} {} {}.'.format(*eu))
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return Rotation(eu2qu(eu))
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return Rotation(Rotation.eu2qu(eu))
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@staticmethod
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def fromAxisAngle(angleAxis,
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@ -294,7 +301,7 @@ class Rotation:
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if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
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raise ValueError('Axis angle rotation axis is not of unit length.\n{} {} {}'.format(*ax[0:3]))
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return Rotation(ax2qu(ax))
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return Rotation(Rotation.ax2qu(ax))
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@staticmethod
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def fromBasis(basis,
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@ -316,7 +323,7 @@ class Rotation:
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or not np.isclose(np.dot(om[2],om[0]), 0.0):
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raise ValueError('matrix is not orthogonal.\n{}'.format(om))
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return Rotation(om2qu(om))
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return Rotation(Rotation.om2qu(om))
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@staticmethod
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def fromMatrix(om,
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@ -338,7 +345,7 @@ class Rotation:
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if ro[3] < 0.0:
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raise ValueError('Rodriques rotation angle not positive.\n'.format(ro[3]))
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return Rotation(ro2qu(ro))
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return Rotation(Rotation.ro2qu(ro))
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@staticmethod
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def fromHomochoric(homochoric,
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@ -348,7 +355,7 @@ class Rotation:
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else np.array(homochoric,dtype=float)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return Rotation(ho2qu(ho))
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return Rotation(Rotation.ho2qu(ho))
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@staticmethod
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def fromCubochoric(cubochoric,
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@ -356,10 +363,10 @@ class Rotation:
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cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
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else np.array(cubochoric,dtype=float)
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ho = cu2ho(cu)
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ho = Rotation.cu2ho(cu)
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if P > 0: ho *= -1 # convert from P=1 to P=-1
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return Rotation(ho2qu(ho))
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return Rotation(Rotation.ho2qu(ho))
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@staticmethod
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@ -437,15 +444,8 @@ class Rotation:
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# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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####################################################################################################
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def isone(a):
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return np.isclose(a,1.0,atol=1.0e-7,rtol=0.0)
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def iszero(a):
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return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
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#---------- Quaternion ----------
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@staticmethod
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def qu2om(qu):
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"""Quaternion to rotation matrix."""
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qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
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@ -459,7 +459,7 @@ def qu2om(qu):
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om[2,0] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
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return om if P > 0.0 else om.T
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@staticmethod
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def qu2eu(qu):
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"""Quaternion to Bunge-Euler angles."""
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q03 = qu[0]**2+qu[3]**2
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@ -478,7 +478,7 @@ def qu2eu(qu):
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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@staticmethod
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def qu2ax(qu):
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"""
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Quaternion to axis angle pair.
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@ -496,7 +496,7 @@ def qu2ax(qu):
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return np.array(ax)
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@staticmethod
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def qu2ro(qu):
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"""Quaternion to Rodriques-Frank vector."""
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if iszero(qu[0]):
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@ -508,7 +508,7 @@ def qu2ro(qu):
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return np.array(ro)
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@staticmethod
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def qu2ho(qu):
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"""Quaternion to homochoric vector."""
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omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0)) # avoid numerical difficulties
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@ -522,23 +522,23 @@ def qu2ho(qu):
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return ho
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@staticmethod
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def qu2cu(qu):
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"""Quaternion to cubochoric vector."""
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return ho2cu(qu2ho(qu))
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return Rotation.ho2cu(Rotation.qu2ho(qu))
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#---------- Rotation matrix ----------
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@staticmethod
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def om2qu(om):
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"""
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Rotation matrix to quaternion.
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The original formulation (direct conversion) had (numerical?) issues
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"""
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return eu2qu(om2eu(om))
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return Rotation.eu2qu(Rotation.om2eu(om))
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@staticmethod
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def om2eu(om):
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"""Rotation matrix to Bunge-Euler angles."""
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if abs(om[2,2]) < 1.0:
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@ -553,7 +553,7 @@ def om2eu(om):
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eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
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return eu
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@staticmethod
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def om2ax(om):
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"""Rotation matrix to axis angle pair."""
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ax=np.empty(4)
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@ -574,24 +574,24 @@ def om2ax(om):
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return np.array(ax)
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@staticmethod
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def om2ro(om):
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"""Rotation matrix to Rodriques-Frank vector."""
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return eu2ro(om2eu(om))
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return Rotation.eu2ro(Rotation.om2eu(om))
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@staticmethod
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def om2ho(om):
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"""Rotation matrix to homochoric vector."""
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return ax2ho(om2ax(om))
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return Rotation.ax2ho(Rotation.om2ax(om))
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@staticmethod
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def om2cu(om):
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"""Rotation matrix to cubochoric vector."""
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return ho2cu(om2ho(om))
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return Rotation.ho2cu(Rotation.om2ho(om))
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#---------- Bunge-Euler angles ----------
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@staticmethod
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def eu2qu(eu):
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"""Bunge-Euler angles to quaternion."""
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ee = 0.5*eu
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@ -604,7 +604,7 @@ def eu2qu(eu):
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if qu[0] < 0.0: qu*=-1
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return qu
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@staticmethod
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def eu2om(eu):
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"""Bunge-Euler angles to rotation matrix."""
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c = np.cos(eu)
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@ -617,7 +617,7 @@ def eu2om(eu):
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om[np.where(iszero(om))] = 0.0
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return om
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@staticmethod
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def eu2ax(eu):
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"""Bunge-Euler angles to axis angle pair."""
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t = np.tan(eu[1]*0.5)
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@ -636,7 +636,7 @@ def eu2ax(eu):
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return ax
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@staticmethod
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def eu2ro(eu):
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"""Bunge-Euler angles to Rodriques-Frank vector."""
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ro = eu2ax(eu) # convert to axis angle pair representation
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@ -649,19 +649,19 @@ def eu2ro(eu):
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return ro
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@staticmethod
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def eu2ho(eu):
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"""Bunge-Euler angles to homochoric vector."""
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return ax2ho(eu2ax(eu))
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return Rotation.ax2ho(Rotation.eu2ax(eu))
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@staticmethod
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def eu2cu(eu):
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"""Bunge-Euler angles to cubochoric vector."""
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return ho2cu(eu2ho(eu))
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return Rotation.ho2cu(Rotation.eu2ho(eu))
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#---------- Axis angle pair ----------
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@staticmethod
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def ax2qu(ax):
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"""Axis angle pair to quaternion."""
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if iszero(ax[3]):
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@ -673,7 +673,7 @@ def ax2qu(ax):
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return qu
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@staticmethod
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def ax2om(ax):
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"""Axis angle pair to rotation matrix."""
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c = np.cos(ax[3])
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@ -688,12 +688,12 @@ def ax2om(ax):
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return om if P < 0.0 else om.T
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@staticmethod
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def ax2eu(ax):
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"""Rotation matrix to Bunge Euler angles."""
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return om2eu(ax2om(ax))
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return Rotation.om2eu(Rotation.ax2om(ax))
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@staticmethod
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def ax2ro(ax):
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"""Axis angle pair to Rodriques-Frank vector."""
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if iszero(ax[3]):
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@ -706,36 +706,36 @@ def ax2ro(ax):
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return np.array(ro)
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@staticmethod
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def ax2ho(ax):
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"""Axis angle pair to homochoric vector."""
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f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
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ho = ax[0:3] * f
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return ho
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@staticmethod
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def ax2cu(ax):
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"""Axis angle pair to cubochoric vector."""
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return ho2cu(ax2ho(ax))
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return Rotation.ho2cu(Rotation.ax2ho(ax))
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#---------- Rodrigues-Frank vector ----------
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@staticmethod
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def ro2qu(ro):
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"""Rodriques-Frank vector to quaternion."""
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return ax2qu(ro2ax(ro))
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return Rotation.ax2qu(Rotation.ro2ax(ro))
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@staticmethod
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def ro2om(ro):
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"""Rodgrigues-Frank vector to rotation matrix."""
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return ax2om(ro2ax(ro))
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return Rotation.ax2om(Rotation.ro2ax(ro))
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@staticmethod
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def ro2eu(ro):
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"""Rodriques-Frank vector to Bunge-Euler angles."""
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return om2eu(ro2om(ro))
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return Rotation.om2eu(Rotation.ro2om(ro))
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@staticmethod
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def ro2ax(ro):
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"""Rodriques-Frank vector to axis angle pair."""
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ta = ro[3]
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@ -751,7 +751,7 @@ def ro2ax(ro):
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return np.array(ax)
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@staticmethod
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def ro2ho(ro):
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"""Rodriques-Frank vector to homochoric vector."""
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if iszero(np.sum(ro[0:3]**2.0)):
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@ -762,29 +762,29 @@ def ro2ho(ro):
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return np.array(ho)
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@staticmethod
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def ro2cu(ro):
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"""Rodriques-Frank vector to cubochoric vector."""
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return ho2cu(ro2ho(ro))
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#---------- Homochoric vector----------
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@staticmethod
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def ho2qu(ho):
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"""Homochoric vector to quaternion."""
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return ax2qu(ho2ax(ho))
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return Rotation.ax2qu(Rotation.ho2ax(ho))
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@staticmethod
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def ho2om(ho):
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"""Homochoric vector to rotation matrix."""
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return ax2om(ho2ax(ho))
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return Rotation.ax2om(Rotation.ho2ax(ho))
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@staticmethod
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def ho2eu(ho):
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"""Homochoric vector to Bunge-Euler angles."""
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return ax2eu(ho2ax(ho))
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return Rotation.ax2eu(Rotation.ho2ax(ho))
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@staticmethod
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def ho2ax(ho):
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"""Homochoric vector to axis angle pair."""
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tfit = np.array([+1.0000000000018852, -0.5000000002194847,
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@ -810,44 +810,44 @@ def ho2ax(ho):
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ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
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return ax
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@staticmethod
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def ho2ro(ho):
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"""Axis angle pair to Rodriques-Frank vector."""
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return ax2ro(ho2ax(ho))
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return Rotation.ax2ro(Rotation.ho2ax(ho))
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@staticmethod
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def ho2cu(ho):
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"""Homochoric vector to cubochoric vector."""
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return Lambert.BallToCube(ho)
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#---------- Cubochoric ----------
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@staticmethod
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def cu2qu(cu):
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"""Cubochoric vector to quaternion."""
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return ho2qu(cu2ho(cu))
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return Rotation.ho2qu(Rotation.cu2ho(cu))
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@staticmethod
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def cu2om(cu):
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"""Cubochoric vector to rotation matrix."""
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return ho2om(cu2ho(cu))
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return Rotation.ho2om(Rotation.cu2ho(cu))
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@staticmethod
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def cu2eu(cu):
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"""Cubochoric vector to Bunge-Euler angles."""
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return ho2eu(cu2ho(cu))
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return Rotation.ho2eu(Rotation.cu2ho(cu))
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@staticmethod
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def cu2ax(cu):
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"""Cubochoric vector to axis angle pair."""
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return ho2ax(cu2ho(cu))
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return Rotation.ho2ax(Rotation.cu2ho(cu))
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@staticmethod
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def cu2ro(cu):
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"""Cubochoric vector to Rodriques-Frank vector."""
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return ho2ro(cu2ho(cu))
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return Rotation.ho2ro(Rotation.cu2ho(cu))
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@staticmethod
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def cu2ho(cu):
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"""Cubochoric vector to homochoric vector."""
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return Lambert.CubeToBall(cu)
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