Hugging Face's logo

andrewatef
/
MoMask-test

Model card Files Community
MoMask-test
File size: 11,228 Bytes 
823807d
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
 
import numpy as np

# Calculate cross object of two 3D vectors.
def _fast_cross(a, b):
    return np.concatenate([
        a[...,1:2]*b[...,2:3] - a[...,2:3]*b[...,1:2],
        a[...,2:3]*b[...,0:1] - a[...,0:1]*b[...,2:3],
        a[...,0:1]*b[...,1:2] - a[...,1:2]*b[...,0:1]], axis=-1)

# Make origin quaternions (No rotations)
def eye(shape, dtype=np.float32):
    return np.ones(list(shape) + [4], dtype=dtype) * np.asarray([1, 0, 0, 0], dtype=dtype)

# Return norm of quaternions
def length(x):
    return np.sqrt(np.sum(x * x, axis=-1))

# Make unit quaternions
def normalize(x, eps=1e-8):
    return x / (length(x)[...,None] + eps)

def abs(x):
    return np.where(x[...,0:1] > 0.0, x, -x)

# Calculate inverse rotations
def inv(q):
    return np.array([1, -1, -1, -1], dtype=np.float32) * q

# Calculate the dot product of two quaternions
def dot(x, y):
    return np.sum(x * y, axis=-1)[...,None] if x.ndim > 1 else np.sum(x * y, axis=-1)

# Multiply two quaternions (return rotations).
def mul(x, y):
    x0, x1, x2, x3 = x[..., 0:1], x[..., 1:2], x[..., 2:3], x[..., 3:4]
    y0, y1, y2, y3 = y[..., 0:1], y[..., 1:2], y[..., 2:3], y[..., 3:4]

    return np.concatenate([
        y0 * x0 - y1 * x1 - y2 * x2 - y3 * x3,
        y0 * x1 + y1 * x0 - y2 * x3 + y3 * x2,
        y0 * x2 + y1 * x3 + y2 * x0 - y3 * x1,
        y0 * x3 - y1 * x2 + y2 * x1 + y3 * x0], axis=-1)

def inv_mul(x, y):
    return mul(inv(x), y)

def mul_inv(x, y):
    return mul(x, inv(y))

# Multiply quaternions and vectors (return vectors).
def mul_vec(q, x):
    t = 2.0 * _fast_cross(q[..., 1:], x)
    return x + q[..., 0][..., None] * t + _fast_cross(q[..., 1:], t)

def inv_mul_vec(q, x):
    return mul_vec(inv(q), x)

def unroll(x):
    y = x.copy()
    for i in range(1, len(x)):
        d0 = np.sum( y[i] * y[i-1], axis=-1)
        d1 = np.sum(-y[i] * y[i-1], axis=-1)
        y[i][d0 < d1] = -y[i][d0 < d1]
    return y

# Calculate quaternions between two 3D vectors (x to y).
def between(x, y):
    return np.concatenate([
        np.sqrt(np.sum(x*x, axis=-1) * np.sum(y*y, axis=-1))[...,None] + 
        np.sum(x * y, axis=-1)[...,None], 
        _fast_cross(x, y)], axis=-1)
        
def log(x, eps=1e-5):
    length = np.sqrt(np.sum(np.square(x[...,1:]), axis=-1))[...,None]
    halfangle = np.where(length < eps, np.ones_like(length), np.arctan2(length, x[...,0:1]) / length)
    return halfangle * x[...,1:]
    
def exp(x, eps=1e-5):
    halfangle = np.sqrt(np.sum(np.square(x), axis=-1))[...,None]
    c = np.where(halfangle < eps, np.ones_like(halfangle), np.cos(halfangle))
    s = np.where(halfangle < eps, np.ones_like(halfangle), np.sinc(halfangle / np.pi))
    return np.concatenate([c, s * x], axis=-1)

# Calculate global space rotations and positions from local space.
def fk(lrot, lpos, parents):
    
    gp, gr = [lpos[...,:1,:]], [lrot[...,:1,:]]
    for i in range(1, len(parents)):
        gp.append(mul_vec(gr[parents[i]], lpos[...,i:i+1,:]) + gp[parents[i]])
        gr.append(mul    (gr[parents[i]], lrot[...,i:i+1,:]))
        
    return np.concatenate(gr, axis=-2), np.concatenate(gp, axis=-2)

def fk_rot(lrot, parents):
    
    gr = [lrot[...,:1,:]]
    for i in range(1, len(parents)):
        gr.append(mul(gr[parents[i]], lrot[...,i:i+1,:]))
        
    return np.concatenate(gr, axis=-2)

# Calculate local space rotations and positions from global space.
def ik(grot, gpos, parents):
    
    return (
        np.concatenate([
            grot[...,:1,:],
            mul(inv(grot[...,parents[1:],:]), grot[...,1:,:]),
        ], axis=-2),
        np.concatenate([
            gpos[...,:1,:],
            mul_vec(
                inv(grot[...,parents[1:],:]),
                gpos[...,1:,:] - gpos[...,parents[1:],:]),
        ], axis=-2))

def ik_rot(grot, parents):
    
    return np.concatenate([grot[...,:1,:], 
                        mul(inv(grot[...,parents[1:],:]), grot[...,1:,:]),
                    ], axis=-2)
    
def fk_vel(lrot, lpos, lvel, lang, parents):
    
    gp, gr, gv, ga = [lpos[...,:1,:]], [lrot[...,:1,:]], [lvel[...,:1,:]], [lang[...,:1,:]]
    for i in range(1, len(parents)):
        gp.append(mul_vec(gr[parents[i]], lpos[...,i:i+1,:]) + gp[parents[i]])
        gr.append(mul    (gr[parents[i]], lrot[...,i:i+1,:]))
        gv.append(mul_vec(gr[parents[i]], lvel[...,i:i+1,:]) + 
            _fast_cross(ga[parents[i]], mul_vec(gr[parents[i]], lpos[...,i:i+1,:])) +
            gv[parents[i]])
        ga.append(mul_vec(gr[parents[i]], lang[...,i:i+1,:]) + ga[parents[i]])
        
    return (
        np.concatenate(gr, axis=-2), 
        np.concatenate(gp, axis=-2),
        np.concatenate(gv, axis=-2),
        np.concatenate(ga, axis=-2))

# Linear Interpolation of two vectors
def lerp(x, y, t):
    return (1 - t) * x + t * y

# LERP of quaternions
def quat_lerp(x, y, t):
    return normalize(lerp(x, y, t))

# Spherical linear interpolation of quaternions
def slerp(x, y, t):
    if t == 0:
        return x
    elif t == 1:
        return y
    
    if dot(x, y) < 0:
        y = - y
    ca = dot(x, y)
    theta = np.arccos(np.clip(ca, 0, 1))
    
    r = normalize(y - x * ca)
    
    return x * np.cos(theta * t) + r * np.sin(theta * t)


###################################################
# Calculate other rotations from other quaternions.
################################################### 

# Calculate euler angles from quaternions.
def to_euler(x, order='zyx'):
    
    q0 = x[...,0:1]
    q1 = x[...,1:2]
    q2 = x[...,2:3]
    q3 = x[...,3:4]
    
    if order == 'zyx':
    
        return np.concatenate([
            np.arctan2(2 * (q0 * q3 + q1 * q2), 1 - 2 * (q2 * q2 + q3 * q3)),
            np.arcsin((2 * (q0 * q2 - q3 * q1)).clip(-1,1)),
            np.arctan2(2 * (q0 * q1 + q2 * q3), 1 - 2 * (q1 * q1 + q2 * q2))], axis=-1)
            
    elif order == 'yzx':
    
        return np.concatenate([
            np.arctan2(2 * (q2 * q0 - q1 * q3),  q1 * q1 - q2 * q2 - q3 * q3 + q0 * q0),
            np.arcsin((2 * (q1 * q2 + q3 * q0)).clip(-1,1)), 
            np.arctan2(2 * (q1 * q0 - q2 * q3), -q1 * q1 + q2 * q2 - q3 * q3 + q0 * q0)],axis=-1)
            
    elif order == 'zxy':
        
        return np.concatenate([
            np.arctan2(2 * (q0 * q3 - q1 * q2), q0 * q0 - q1 * q1 + q2 * q2 - q3 * q3),
            np.arcsin((2 * (q0 * q1 + q2 * q3)).clip(-1,1)),
            np.arctan2(2 * (q0 * q2 - q1 * q3), q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3)], axis=-1)

    elif order == 'yxz':
        
        return np.concatenate([
            np.arctan2(2 * (q1 * q3 + q0 * q2), q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3),
            np.arcsin((2 * (q0 * q1 - q2 * q3)).clip(-1,1)),
            np.arctan2(2 * (q1 * q2 + q0 * q3), q0 * q0 - q1 * q1 + q2 * q2 - q3 * q3)], axis=-1)
        
    else:
        raise NotImplementedError('Cannot convert from ordering %s' % order)

# Calculate rotation matrix from quaternions.
def to_xform(x):

    qw, qx, qy, qz = x[...,0:1], x[...,1:2], x[...,2:3], x[...,3:4]
    
    x2, y2, z2 = qx + qx, qy + qy, qz + qz
    xx, yy, wx = qx * x2, qy * y2, qw * x2
    xy, yz, wy = qx * y2, qy * z2, qw * y2
    xz, zz, wz = qx * z2, qz * z2, qw * z2
    
    return np.concatenate([
        np.concatenate([1.0 - (yy + zz), xy - wz, xz + wy], axis=-1)[...,None,:],
        np.concatenate([xy + wz, 1.0 - (xx + zz), yz - wx], axis=-1)[...,None,:],
        np.concatenate([xz - wy, yz + wx, 1.0 - (xx + yy)], axis=-1)[...,None,:],
    ], axis=-2)

# Calculate 6d orthogonal rotation representation (ortho6d) from quaternions.
# https://github.com/papagina/RotationContinuity
def to_xform_xy(x):

    qw, qx, qy, qz = x[...,0:1], x[...,1:2], x[...,2:3], x[...,3:4]
    
    x2, y2, z2 = qx + qx, qy + qy, qz + qz
    xx, yy, wx = qx * x2, qy * y2, qw * x2
    xy, yz, wy = qx * y2, qy * z2, qw * y2
    xz, zz, wz = qx * z2, qz * z2, qw * z2
    
    return np.concatenate([
        np.concatenate([1.0 - (yy + zz), xy - wz], axis=-1)[...,None,:],
        np.concatenate([xy + wz, 1.0 - (xx + zz)], axis=-1)[...,None,:],
        np.concatenate([xz - wy, yz + wx], axis=-1)[...,None,:],
    ], axis=-2)

# Calculate scaled angle axis from quaternions.
def to_scaled_angle_axis(x, eps=1e-5):
    return 2.0 * log(x, eps)


#############################################
# Calculate quaternions from other rotations.
#############################################

# Calculate quaternions from axis angles.
def from_angle_axis(angle, axis):
    c = np.cos(angle / 2.0)[..., None]
    s = np.sin(angle / 2.0)[..., None]
    q = np.concatenate([c, s * axis], axis=-1)
    return q

# Calculate quaternions from axis-angle.
def from_axis_angle(rots):
    angle = np.linalg.norm(rots, axis=-1)
    axis = rots / angle[...,None]
    return from_angle_axis(angle, axis)

# Calculate quaternions from euler angles.
def from_euler(e, order='zyx'):
    axis = {
        'x': np.asarray([1, 0, 0], dtype=np.float32),
        'y': np.asarray([0, 1, 0], dtype=np.float32),
        'z': np.asarray([0, 0, 1], dtype=np.float32)}

    q0 = from_angle_axis(e[..., 0], axis[order[0]])
    q1 = from_angle_axis(e[..., 1], axis[order[1]])
    q2 = from_angle_axis(e[..., 2], axis[order[2]])

    return mul(q0, mul(q1, q2))

# Calculate quaternions from rotation matrix.
def from_xform(ts):
    
    return normalize(
        np.where((ts[...,2,2] < 0.0)[...,None],
            np.where((ts[...,0,0] >  ts[...,1,1])[...,None],
                np.concatenate([
                    (ts[...,2,1]-ts[...,1,2])[...,None], 
                    (1.0 + ts[...,0,0] - ts[...,1,1] - ts[...,2,2])[...,None], 
                    (ts[...,1,0]+ts[...,0,1])[...,None], 
                    (ts[...,0,2]+ts[...,2,0])[...,None]], axis=-1),
                np.concatenate([
                    (ts[...,0,2]-ts[...,2,0])[...,None], 
                    (ts[...,1,0]+ts[...,0,1])[...,None], 
                    (1.0 - ts[...,0,0] + ts[...,1,1] - ts[...,2,2])[...,None], 
                    (ts[...,2,1]+ts[...,1,2])[...,None]], axis=-1)),
            np.where((ts[...,0,0] < -ts[...,1,1])[...,None],
                np.concatenate([
                    (ts[...,1,0]-ts[...,0,1])[...,None], 
                    (ts[...,0,2]+ts[...,2,0])[...,None], 
                    (ts[...,2,1]+ts[...,1,2])[...,None], 
                    (1.0 - ts[...,0,0] - ts[...,1,1] + ts[...,2,2])[...,None]], axis=-1),
                np.concatenate([
                    (1.0 + ts[...,0,0] + ts[...,1,1] + ts[...,2,2])[...,None], 
                    (ts[...,2,1]-ts[...,1,2])[...,None], 
                    (ts[...,0,2]-ts[...,2,0])[...,None], 
                    (ts[...,1,0]-ts[...,0,1])[...,None]], axis=-1))))

# Calculate quaternions from ortho6d.
def from_xform_xy(x):

    c2 = _fast_cross(x[...,0], x[...,1])
    c2 = c2 / np.sqrt(np.sum(np.square(c2), axis=-1))[...,None]
    c1 = _fast_cross(c2, x[...,0])
    c1 = c1 / np.sqrt(np.sum(np.square(c1), axis=-1))[...,None]
    c0 = x[...,0]
    
    return from_xform(np.concatenate([
        c0[...,None], 
        c1[...,None], 
        c2[...,None]], axis=-1))

# Calculate quaternions from scaled angle axis.
def from_scaled_angle_axis(x, eps=1e-5):
    return exp(x / 2.0, eps)