#! /usr/bin/python
# Encoding: UTF-8
"""
Adapded partially from Robert Penner's Easing Equations, as they
appear in the Qt library. The original license follows:
TERMS OF USE - EASING EQUATIONS
Open source under the BSD License.
Copyright © 2001 Robert Penner
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the author nor the names of contributors may be
used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
"""
from __future__ import division
import math
[docs]def normalized(func):
"""Decorator to normalize another easing function
Normalizing is done so that f(0) == 0 and f(1) == 1.
"""
min = func(0)
max = func(1)
if (min, max) == (0, 1):
return func
range = max - min
def normalized(t):
return min + func(t) / range
try:
normalized.__name__ = func.__name__ + '_normalized'
except AttributeError:
pass
return normalized
def _add_postfix(decorated, func, postfix):
try:
decorated.__name__ = func.__name__ + '_' + postfix
except AttributeError:
pass
def easeIn(func):
return func
def easeOut(func):
def ease_out(t):
return 1 - func(1 - t)
_add_postfix(ease_out, func, 'out')
return ease_out
def easeOutIn(func):
def ease_outIn(t):
if t < 0.5:
return (1 - func(1 - 2 * t)) / 2
else:
return func(2 * (t - .5)) / 2 + .5
_add_postfix(ease_outIn, func, 'outIn')
return ease_outIn
def easeInOut(func):
def ease_outIn(t):
if t < 0.5:
return func(2 * t) / 2
else:
return 1 - func(1 - 2 * (t - .5)) / 2
_add_postfix(ease_outIn, func, 'outIn')
return ease_outIn
def tweenfunc(func):
func.in_ = easeIn(func)
func.out = easeOut(func)
func.inOut = easeInOut(func)
func.outIn = easeOutIn(func)
return func
@tweenfunc
[docs]def linear(t):
"""Linear interpolation
t → t
"""
return t
@tweenfunc
[docs]def quad(t):
"""Quadratic easing
t → t**2
"""
return t ** 2
@tweenfunc
[docs]def cubic(t):
"""Cubic easing
t → t**3
"""
return t ** 3
@tweenfunc
[docs]def quart(t):
"""Quartic easing
t → t**4
"""
return t ** 4
@tweenfunc
[docs]def quint(t):
"""Quintic easing
t → t**5
"""
return t ** 5
@tweenfunc
[docs]def sin(t):
"""Sinusoidal easing
Quarter of a cosine wave
"""
return (-math.cos(t / 2 * math.pi) + 1)
@tweenfunc
[docs]def exp(t):
"""Exponential easing
"""
if t in (0, 1):
return t
else:
return 2.0 ** (10 * (t - 1)) - 0.001
@tweenfunc
[docs]def circ(t):
"""Circular easing
"""
try:
return 1 - math.sqrt(1 - t * t)
except ValueError:
return 0
[docs]def elastic(period, amplitude=1):
"""Elastic easing
"""
@tweenfunc
def elastic(t):
return exp(t) * math.cos((1 - t) * 2 * math.pi / period) * amplitude
return elastic
[docs]def overshoot(amount):
"""Overshoot easing
"""
@tweenfunc
def overshoot(t):
t = 1 - t
return 1 - t * t * ((amount + 1) * t - amount)
return overshoot
def _bounce_helper(t, c, a):
if t == 1:
return c
if t < 4 / 11:
return c * (7.5625 * t * t)
elif t < 8 / 11:
t -= 6 / 11.0
return -a * (1. - (7.5625 * t * t + .75)) + c
elif t < 10 / 11:
t -= 9 / 11
return -a * (1. - (7.5625 * t * t + .9375)) + c
else:
t -= 21 / 22
return -a * (1. - (7.5625 * t * t + .984375)) + c
[docs]def bounce(amplitude):
"""Bounce easing
"""
@tweenfunc
def bounce(t):
return _bounce_helper(t, 1, amplitude)
return bounce
# Execute the file for a gallery of easing funcs (matplotlib must be installed)
elastic_example = elastic(.15)
overshoot_example = overshoot(1)
bounce_example = bounce(1)
[docs]def showcase(
items='(poly) sin exp circ elastic_example overshoot_example '
'bounce_example'.split()
):
"""Show graphs of the easing functions in this module
"""
import pylab
time = pylab.arange(0.0, 1.01, 0.01)
for i, n in enumerate(items):
if n == '(poly)':
funcs = 'linear quad cubic quart quint'.split()
else:
funcs = [n]
for j, a in enumerate((easeIn, easeOut, easeInOut, easeOutIn)):
pylab.subplot(len(items), 4, i * 4 + 1 + j)
for funcname in funcs:
func = a(globals()[funcname])
s = [func(t) for t in time]
pylab.plot(time, s, linewidth=1.0)
if i == 0:
pylab.title(a.__name__)
if j == 0:
title, sep, end = n.partition('_example')
pylab.ylabel(title)
pylab.show()
if __name__ == '__main__':
showcase()