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import operator
import numpy as np
import numpy.core.umath_tests as ut
from visualization.Quaternions import Quaternions
class Animation:
"""
Animation is a numpy-like wrapper for animation data
Animation data consists of several arrays consisting
of F frames and J joints.
The animation is specified by
rotations : (F, J) Quaternions | Joint Rotations
positions : (F, J, 3) ndarray | Joint Positions
The base pose is specified by
orients : (J) Quaternions | Joint Orientations
offsets : (J, 3) ndarray | Joint Offsets
And the skeletal structure is specified by
parents : (J) ndarray | Joint Parents
"""
def __init__(self, rotations, positions, orients, offsets, parents, names, frametime):
self.rotations = rotations
self.positions = positions
self.orients = orients
self.offsets = offsets
self.parents = parents
self.names = names
self.frametime = frametime
def __op__(self, op, other):
return Animation(
op(self.rotations, other.rotations),
op(self.positions, other.positions),
op(self.orients, other.orients),
op(self.offsets, other.offsets),
op(self.parents, other.parents))
def __iop__(self, op, other):
self.rotations = op(self.roations, other.rotations)
self.positions = op(self.roations, other.positions)
self.orients = op(self.orients, other.orients)
self.offsets = op(self.offsets, other.offsets)
self.parents = op(self.parents, other.parents)
return self
def __sop__(self, op):
return Animation(
op(self.rotations),
op(self.positions),
op(self.orients),
op(self.offsets),
op(self.parents))
def __add__(self, other):
return self.__op__(operator.add, other)
def __sub__(self, other):
return self.__op__(operator.sub, other)
def __mul__(self, other):
return self.__op__(operator.mul, other)
def __div__(self, other):
return self.__op__(operator.div, other)
def __abs__(self):
return self.__sop__(operator.abs)
def __neg__(self):
return self.__sop__(operator.neg)
def __iadd__(self, other):
return self.__iop__(operator.iadd, other)
def __isub__(self, other):
return self.__iop__(operator.isub, other)
def __imul__(self, other):
return self.__iop__(operator.imul, other)
def __idiv__(self, other):
return self.__iop__(operator.idiv, other)
def __len__(self):
return len(self.rotations)
def __getitem__(self, k):
if isinstance(k, tuple):
return Animation(
self.rotations[k],
self.positions[k],
self.orients[k[1:]],
self.offsets[k[1:]],
self.parents[k[1:]],
self.names[k[1:]],
self.frametime[k[1:]])
else:
return Animation(
self.rotations[k],
self.positions[k],
self.orients,
self.offsets,
self.parents,
self.names,
self.frametime)
def __setitem__(self, k, v):
if isinstance(k, tuple):
self.rotations.__setitem__(k, v.rotations)
self.positions.__setitem__(k, v.positions)
self.orients.__setitem__(k[1:], v.orients)
self.offsets.__setitem__(k[1:], v.offsets)
self.parents.__setitem__(k[1:], v.parents)
else:
self.rotations.__setitem__(k, v.rotations)
self.positions.__setitem__(k, v.positions)
self.orients.__setitem__(k, v.orients)
self.offsets.__setitem__(k, v.offsets)
self.parents.__setitem__(k, v.parents)
@property
def shape(self):
return (self.rotations.shape[0], self.rotations.shape[1])
def copy(self):
return Animation(
self.rotations.copy(), self.positions.copy(),
self.orients.copy(), self.offsets.copy(),
self.parents.copy(), self.names,
self.frametime)
def repeat(self, *args, **kw):
return Animation(
self.rotations.repeat(*args, **kw),
self.positions.repeat(*args, **kw),
self.orients, self.offsets, self.parents, self.frametime, self.names)
def ravel(self):
return np.hstack([
self.rotations.log().ravel(),
self.positions.ravel(),
self.orients.log().ravel(),
self.offsets.ravel()])
@classmethod
def unravel(cls, anim, shape, parents):
nf, nj = shape
rotations = anim[nf * nj * 0:nf * nj * 3]
positions = anim[nf * nj * 3:nf * nj * 6]
orients = anim[nf * nj * 6 + nj * 0:nf * nj * 6 + nj * 3]
offsets = anim[nf * nj * 6 + nj * 3:nf * nj * 6 + nj * 6]
return cls(
Quaternions.exp(rotations), positions,
Quaternions.exp(orients), offsets,
parents.copy())
# local transformation matrices
def transforms_local(anim):
"""
Computes Animation Local Transforms
As well as a number of other uses this can
be used to compute global joint transforms,
which in turn can be used to compete global
joint positions
Parameters
----------
anim : Animation
Input animation
Returns
-------
transforms : (F, J, 4, 4) ndarray
For each frame F, joint local
transforms for each joint J
"""
transforms = anim.rotations.transforms()
transforms = np.concatenate([transforms, np.zeros(transforms.shape[:2] + (3, 1))], axis=-1)
transforms = np.concatenate([transforms, np.zeros(transforms.shape[:2] + (1, 4))], axis=-2)
# the last column is filled with the joint positions!
transforms[:, :, 0:3, 3] = anim.positions
transforms[:, :, 3:4, 3] = 1.0
return transforms
def transforms_multiply(t0s, t1s):
"""
Transforms Multiply
Multiplies two arrays of animation transforms
Parameters
----------
t0s, t1s : (F, J, 4, 4) ndarray
Two arrays of transforms
for each frame F and each
joint J
Returns
-------
transforms : (F, J, 4, 4) ndarray
Array of transforms for each
frame F and joint J multiplied
together
"""
return ut.matrix_multiply(t0s, t1s)
def transforms_inv(ts):
fts = ts.reshape(-1, 4, 4)
fts = np.array(list(map(lambda x: np.linalg.inv(x), fts)))
return fts.reshape(ts.shape)
def transforms_blank(anim):
"""
Blank Transforms
Parameters
----------
anim : Animation
Input animation
Returns
-------
transforms : (F, J, 4, 4) ndarray
Array of identity transforms for
each frame F and joint J
"""
ts = np.zeros(anim.shape + (4, 4))
ts[:, :, 0, 0] = 1.0;
ts[:, :, 1, 1] = 1.0;
ts[:, :, 2, 2] = 1.0;
ts[:, :, 3, 3] = 1.0;
return ts
# global transformation matrices
def transforms_global(anim):
"""
Global Animation Transforms
This relies on joint ordering
being incremental. That means a joint
J1 must not be a ancestor of J0 if
J0 appears before J1 in the joint
ordering.
Parameters
----------
anim : Animation
Input animation
Returns
------
transforms : (F, J, 4, 4) ndarray
Array of global transforms for
each frame F and joint J
"""
locals = transforms_local(anim)
globals = transforms_blank(anim)
globals[:, 0] = locals[:, 0]
for i in range(1, anim.shape[1]):
globals[:, i] = transforms_multiply(globals[:, anim.parents[i]], locals[:, i])
return globals
# !!! useful!
def positions_global(anim):
"""
Global Joint Positions
Given an animation compute the global joint
positions at at every frame
Parameters
----------
anim : Animation
Input animation
Returns
-------
positions : (F, J, 3) ndarray
Positions for every frame F
and joint position J
"""
# get the last column -- corresponding to the coordinates
positions = transforms_global(anim)[:, :, :, 3]
return positions[:, :, :3] / positions[:, :, 3, np.newaxis]
""" Rotations """
def rotations_global(anim):
"""
Global Animation Rotations
This relies on joint ordering
being incremental. That means a joint
J1 must not be a ancestor of J0 if
J0 appears before J1 in the joint
ordering.
Parameters
----------
anim : Animation
Input animation
Returns
-------
points : (F, J) Quaternions
global rotations for every frame F
and joint J
"""
joints = np.arange(anim.shape[1])
parents = np.arange(anim.shape[1])
locals = anim.rotations
globals = Quaternions.id(anim.shape)
globals[:, 0] = locals[:, 0]
for i in range(1, anim.shape[1]):
globals[:, i] = globals[:, anim.parents[i]] * locals[:, i]
return globals
def rotations_parents_global(anim):
rotations = rotations_global(anim)
rotations = rotations[:, anim.parents]
rotations[:, 0] = Quaternions.id(len(anim))
return rotations
""" Offsets & Orients """
def orients_global(anim):
joints = np.arange(anim.shape[1])
parents = np.arange(anim.shape[1])
locals = anim.orients
globals = Quaternions.id(anim.shape[1])
globals[:, 0] = locals[:, 0]
for i in range(1, anim.shape[1]):
globals[:, i] = globals[:, anim.parents[i]] * locals[:, i]
return globals
def offsets_transforms_local(anim):
transforms = anim.orients[np.newaxis].transforms()
transforms = np.concatenate([transforms, np.zeros(transforms.shape[:2] + (3, 1))], axis=-1)
transforms = np.concatenate([transforms, np.zeros(transforms.shape[:2] + (1, 4))], axis=-2)
transforms[:, :, 0:3, 3] = anim.offsets[np.newaxis]
transforms[:, :, 3:4, 3] = 1.0
return transforms
def offsets_transforms_global(anim):
joints = np.arange(anim.shape[1])
parents = np.arange(anim.shape[1])
locals = offsets_transforms_local(anim)
globals = transforms_blank(anim)
globals[:, 0] = locals[:, 0]
for i in range(1, anim.shape[1]):
globals[:, i] = transforms_multiply(globals[:, anim.parents[i]], locals[:, i])
return globals
def offsets_global(anim):
offsets = offsets_transforms_global(anim)[:, :, :, 3]
return offsets[0, :, :3] / offsets[0, :, 3, np.newaxis]
""" Lengths """
def offset_lengths(anim):
return np.sum(anim.offsets[1:] ** 2.0, axis=1) ** 0.5
def position_lengths(anim):
return np.sum(anim.positions[:, 1:] ** 2.0, axis=2) ** 0.5
""" Skinning """
def skin(anim, rest, weights, mesh, maxjoints=4):
full_transforms = transforms_multiply(
transforms_global(anim),
transforms_inv(transforms_global(rest[0:1])))
weightids = np.argsort(-weights, axis=1)[:, :maxjoints]
weightvls = np.array(list(map(lambda w, i: w[i], weights, weightids)))
weightvls = weightvls / weightvls.sum(axis=1)[..., np.newaxis]
verts = np.hstack([mesh, np.ones((len(mesh), 1))])
verts = verts[np.newaxis, :, np.newaxis, :, np.newaxis]
verts = transforms_multiply(full_transforms[:, weightids], verts)
verts = (verts[:, :, :, :3] / verts[:, :, :, 3:4])[:, :, :, :, 0]
return np.sum(weightvls[np.newaxis, :, :, np.newaxis] * verts, axis=2) |