-
Notifications
You must be signed in to change notification settings - Fork 1
/
interp.py
161 lines (136 loc) · 4.18 KB
/
interp.py
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
import torch
import numpy as np
import math
def sigmoid(x, scale=10.0):
return 1.0 / (1.0 + np.exp(scale * (-x + 0.5)))
def iden(x):
return x
def B(x, k, i, t):
if k == 0:
return 1.0 if torch.all((t[i] <= x) == True) and torch.all((x < t[i+1]) == True) else 0.0
c1 = (x - t[i])/(t[i+k] - t[i] + EPS_F) * B(x, k-1, i, t)
c2 = (t[i+k+1] - x)/(t[i+k+1] - t[i+1] + EPS_F) * B(x, k-1, i+1, t)
return c1 + c2
def bspline_interp(x, t, c, k):
#https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html
n = len(t) - k - 1
assert (n >= k+1) and (len(c) >= n)
return sum(c[i] * B(x, k, i, t) for i in range(n))
def bspline(x, ibf=1, ease=iden):
'''
linearly interpolate between frames
x : encoded tensor (n, encode_dim)
ibf : inbetween frame num
'''
n, encode_dim = x.shape
y = torch.Tensor((n-1)*(ibf+1)+1, encode_dim)
idx = 0
for i in range(n-1):
y[idx] = x[i]
idx += 1
for f in range(1,ibf+1):
t = ease(f / (ibf + 2.0))
xt = linear_interp(x[i], x[i+1], t)
k = 2
c = np.zeros(n - k - 1)
c[0] = -1
c[-1] = 1
ibtwn = bspline_interp(xt, x, c, k)
y[idx] = ibtwn
idx += 1
y[idx] = x[n-1]
return y
def catmullRom_interp(x0, x1, x2, x3, t):
# https://www.mvps.org/directx/articles/catmull/
return 0.5 * ((2*x1) +\
(-x0 + x2) * t +\
(2*x0 - 5*x1 + 4*x2 - x3) * t**2 +\
(-x0 + 3*x1- 3*x2 + x3) * t**3)
def catmullRom(x, ibf=1, ease=iden):
'''
linearly interpolate between frames
x : encoded tensor (n, encode_dim)
ibf : inbetween frame num
'''
n, encode_dim = x.shape
y = torch.Tensor((n-1)*(ibf+1)+1, encode_dim)
idx = 0
'''
for i in range(n-1):
y[idx] = x[i]
idx += 1
for f in range(1,ibf+1):
t = ease(f / (ibf + 2.0))
if i == 0:
ibtwn = catmullRom_interp(x[i], x[i], x[i+1], x[i+2], t)
elif i == n - 2:
ibtwn = catmullRom_interp(x[i-1], x[i], x[i+1], x[i+1], t)
else:
ibtwn = catmullRom_interp(x[i-1], x[i], x[i+1], x[i+2], t)
y[idx] = ibtwn
idx += 1
y[idx] = x[n-1]
'''
L = []
T = []
for f in range(n):
tn = f / float(n)
t = ease(tn)
T.append(t)
for f in range((n-1)*(ibf+1)+1):
tn = f / ((n-1)*(ibf+1)+1.0)
t = ease(tn)
i = math.floor(t * (n-1))
t1 = i / float(n-1)
t2 = (i+1) / float(n-1)
t = (t - t1) / (t2 - t1)
#print(t)
if i == n - 1:
ibtwn = x[i]
else:
L.append(t)
if n == 2:
ibtwn = catmullRom_interp(x[i], x[i], x[i+1], x[i+1], t)
elif i == 0:
ibtwn = catmullRom_interp(x[i], x[i], x[i+1], x[i+2], t)
elif i == n - 2:
ibtwn = catmullRom_interp(x[i-1], x[i], x[i+1], x[i+1], t)
else:
ibtwn = catmullRom_interp(x[i-1], x[i], x[i+1], x[i+2], t)
y[f] = ibtwn
return y
def linear_interp(x0, x1, t):
return (1.0 - t) * x0 + t * x1
def linear(x, ibf=1, ease=iden, p=[(1,1)]):
'''
linearly interpolate between frames
x : encoded tensor (n, encode_dim)
ibf : inbetween frame num
'''
n, encode_dim = x.shape
y = torch.Tensor((n-1)*(ibf+1)+1, encode_dim)
idx = 0
for i in range(n-1):
y[idx] = x[i]
idx += 1
for f in range(1,ibf+1):
t = (f / (ibf + 2.0))
lastA = 0
lastB = 0
currA = 0
currB = 0
for a, b in p:
currA = a
currB = b
if lastA <= t and t <= currA:
break
lastA = currA
lastB = currB
t = (t - lastA) / (currA - lastA)
t = ease(t)
t = lastB * (1 - t) + currB * t
ibtwn = linear_interp(x[i], x[i+1], t)
y[idx] = ibtwn
idx += 1
y[idx] = x[n-1]
return y