#! /usr/bin/python
# Encoding: UTF-8
"""
Adapded roughly and 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 unicode_literals, division, print_function
import sys
import functools
import math
[docs]def normalized(func):
"""Decorator that normalizes an easing function
Normalizing is done so that func(0) == 0 and func(1) == 1.
"""
minimum = func(0)
maximum = func(1)
if (minimum, maximum) == (0, 1):
return func
range_ = maximum - minimum
@functools.wraps(func)
def _normalized(t):
return (func(t) - minimum) / range_
_add_postfix(_normalized, func, 'normalized')
return _normalized
def _add_postfix(decorated, func, postfix):
try:
decorated.__name__ = str(func.__name__ + '_' + postfix)
except AttributeError: # pragma: no cover
pass
def ease_out(func):
"""Given an "in" easing function, return corresponding "out" function"""
def _ease_out(t):
return 1 - func(1 - t)
_add_postfix(_ease_out, func, 'out')
return _ease_out
def ease_out_in(func):
"""Given an "in" easing function, return corresponding "out-in" function"""
def _ease_out_in(t):
if t < 0.5:
return (1 - func(1 - 2 * t)) / 2
else:
return func(2 * (t - .5)) / 2 + .5
_add_postfix(_ease_out_in, func, 'out_in')
return _ease_out_in
def ease_in_out(func):
"""Given an "in" easing function, return corresponding "in-out" function"""
def _ease_in_out(t):
if t < 0.5:
return func(2 * t) / 2
else:
return 1 - func(1 - 2 * (t - .5)) / 2
_add_postfix(_ease_in_out, func, 'in_out')
return _ease_in_out
def ease_in(func):
"""Return ``func`` itself. Included for symmetry."""
return func
[docs]def easefunc(func):
"""Decorator for easing functions.
Adds the **in_**, **out**, **in_out** and **out_in** attributes to
an easing function.
"""
func.in_ = ease_in(func)
func.out = ease_out(func)
func.in_out = ease_in_out(func)
func.out_in = ease_out_in(func)
return func
@easefunc
[docs]def linear(t):
"""Linear interpolation
t → t
"""
return t
@easefunc
[docs]def quadratic(t):
"""Quadratic easing
t → t**2
"""
return t ** 2
@easefunc
[docs]def cubic(t):
"""Cubic easing
t → t**3
"""
return t ** 3
@easefunc
[docs]def quartic(t):
"""Quartic easing
t → t**4
"""
return t ** 4
@easefunc
[docs]def quintic(t):
"""Quintic easing
t → t**5
"""
return t ** 5
@easefunc
[docs]def sine(t):
"""Sinusoidal easing
Quarter of a cosine wave
"""
return (-math.cos(t / 2 * math.pi) + 1)
@easefunc
[docs]def exponential(t):
"""Exponential easing
"""
if t in (0, 1):
return t
else:
return 2.0 ** (10 * (t - 1)) - 0.001
@easefunc
[docs]def circular(t):
"""Circular easing
"""
try:
return 1 - math.sqrt(1 - t * t)
except ValueError:
return 1
[docs]def elastic(period, amplitude=1):
"""Elastic easing factory
"""
@easefunc
def _elastic(t):
b = exponential(t) * math.cos((1 - t) * 2 * math.pi / period)
return b * amplitude
return _elastic
[docs]def overshoot(amount):
"""Overshoot easing factory
"""
@easefunc
def _overshoot(t):
return t * t * ((amount + 1) * t - amount)
return _overshoot
def _bounce_helper(t, c, a):
t = 1 - t
if t == 1:
return 1 - c
if t < 4 / 11:
return 1 - c * (7.5625 * t * t)
elif t < 8 / 11:
t -= 6 / 11.0
return 1 + a * (1. - (7.5625 * t * t + .75)) - c
elif t < 10 / 11:
t -= 9 / 11
return 1 + a * (1. - (7.5625 * t * t + .9375)) - c
else:
t -= 21 / 22
return 1 + a * (1. - (7.5625 * t * t + .984375)) - c
[docs]def bounce(amplitude):
"""Bounce easing factory
"""
@easefunc
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)
def showcase(
items='(poly) sine exponential circular elastic_example '
'overshoot_example bounce_example'.split(),
filename=None,
): # pragma: no cover; pylint: disable=R0914, W0621, W0404, F0401
"""Show graphs of the easing functions in this module
"""
import pylab
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator
pyplot.figure(figsize=(7, 7))
pyplot.subplots_adjust(wspace=0.3, hspace=0.7)
time = pylab.arange(0.0, 1.01, 0.01)
for i, n in enumerate(items):
if n == '(poly)':
funcs = 'linear quadratic cubic quartic quintic'.split()
else:
funcs = [n]
for j, a in enumerate('in_ out in_out out_in'.split()):
ax = pylab.subplot(len(items), 4, i * 4 + 1 + j)
ax.xaxis.set_major_locator(MultipleLocator(1))
ax.yaxis.set_major_locator(MultipleLocator(1))
for funcname in funcs:
func = getattr(globals()[funcname], a)
s = [func(t) for t in time]
pylab.plot(time, s, linewidth=1.0)
if i == 0:
pylab.title('.' + a)
if j == 0:
title, sep, _end = n.partition('_example')
pylab.ylabel(title)
if filename:
pylab.savefig(filename, transparent=True)
else:
pylab.show()
if __name__ == '__main__':
try:
filename = sys.argv[1]
except IndexError:
filename = None
showcase(filename=filename)