def jacobian(self, x, fp, fr, ts, dsc, tdsc):
""" Find parent rotations """
prs = fr[:, self.animation.parents]
prs[:, 0] = Quaternions.id((1))
""" Find global positions of target joints """
tps = fp[:, np.array(list(ts.keys()))]
""" Get partial rotations """
qys = Quaternions.from_angle_axis(x[:, 1:prs.shape[1] * 3:3],
np.array([[[0, 1, 0]]]))
qzs = Quaternions.from_angle_axis(x[:, 2:prs.shape[1] * 3:3],
np.array([[[0, 0, 1]]]))
""" Find axis of rotations """
es = np.empty((len(x), fr.shape[1] * 3, 3))
es[:, 0::3] = ((prs * qzs) * qys) * np.array([[[1, 0, 0]]])
es[:, 1::3] = ((prs * qzs) * np.array([[[0, 1, 0]]]))
es[:, 2::3] = ((prs * np.array([[[0, 0, 1]]])))
""" Construct Jacobian """
j = fp.repeat(3, axis=1)
j = dsc[np.newaxis, :, :,
np.newaxis] * (tps[:, np.newaxis, :] - j[:, :, np.newaxis])
j = self.cross(es[:, :, np.newaxis, :], j)
j = np.swapaxes(j.reshape((len(x), fr.shape[1] * 3, len(ts) * 3)), 1,
2)
if self.translate:
es = np.empty((len(x), fr.shape[1] * 3, 3))
es[:, 0::3] = prs * np.array([[[1, 0, 0]]])
es[:, 1::3] = prs * np.array([[[0, 1, 0]]])
es[:, 2::3] = prs * np.array([[[0, 0, 1]]])
jt = tdsc[np.newaxis, :, :,
np.newaxis] * es[:, :, np.newaxis, :].repeat(
tps.shape[1], axis=2)
jt = np.swapaxes(
jt.reshape((len(x), fr.shape[1] * 3, len(ts) * 3)), 1, 2)
j = np.concatenate([j, jt], axis=-1)
return j