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New implementation of smooth

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This commit is contained in:
Grant Sanderson
2020-07-22 18:19:07 -07:00
parent 5ee4b94ec3
commit ae8e8040d7
1 changed files with 12 additions and 16 deletions
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28
manimlib/utils/rate_functions.py
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@ -1,28 +1,25 @@
import numpy as np import numpy as np
from manimlib.utils.bezier import bezier from manimlib.utils.bezier import bezier
from manimlib.utils.simple_functions import sigmoid
from manimlib.utils.simple_functions import clip
def linear(t): def linear(t):
return t return t
def smooth(t, inflection=10.0): def smooth(t):
error = sigmoid(-inflection / 2) # Zero first and second derivatives at t=0 and t=1.
return clip( # Equivalent to bezier([0, 0, 0, 1, 1, 1])
(sigmoid(inflection * (t - 0.5)) - error) / (1 - 2 * error), s = 1 - t
0, 1, return (t**3) * (10 * s * s + 5 * s * t + t * t)
)
def rush_into(t, inflection=10.0): def rush_into(t):
return 2 * smooth(t / 2.0, inflection) return 2 * smooth(0.5 * t)
def rush_from(t, inflection=10.0): def rush_from(t):
return 2 * smooth(t / 2.0 + 0.5, inflection) - 1 return 2 * smooth(0.5 * (t + 1)) - 1
def slow_into(t): def slow_into(t):
@ -36,9 +33,9 @@ def double_smooth(t):
return 0.5 * (1 + smooth(2 * t - 1)) return 0.5 * (1 + smooth(2 * t - 1))
def there_and_back(t, inflection=10.0): def there_and_back(t):
new_t = 2 * t if t < 0.5 else 2 * (1 - t) new_t = 2 * t if t < 0.5 else 2 * (1 - t)
return smooth(new_t, inflection) return smooth(new_t)
def there_and_back_with_pause(t, pause_ratio=1. / 3): def there_and_back_with_pause(t, pause_ratio=1. / 3):
@ -69,8 +66,7 @@ def squish_rate_func(func, a=0.4, b=0.6):
def result(t): def result(t):
if a == b: if a == b:
return a return a
elif t < a:
if t < a:
return func(0) return func(0)
elif t > b: elif t > b:
return func(1) return func(1)