Animation Curves Python

animations.py

# MIT License
# 
# Copyright (c) 2017 Snips
# 
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.


# https://en.wikipedia.org/wiki/Cubic_Hermite_spline
class CubicHermite(object):
    def __init__(self, m_0, m_1):
        self.m_0 = m_0
        self.m_1 = m_1

    def interpolate(self, t):
        t_squared = t * t
        t_cubed = t * t_squared
        start_factor = (t_cubed - 2 * t_squared + t) * self.m_0
        end_factor = (t_cubed - t_squared) * self.m_1
        return start_factor + end_factor - 2 * t_cubed + 3 * t_squared

    def interpolate_derivative(self, t):
        t_squared = t * t
        start_factor = (3 * t_squared - 4 * t + 1) * self.m_0
        end_factor = (3 * t_squared - 2 * t) * self.m_1
        return start_factor + end_factor - 6 * t_squared + 6 * t

    # Approximates time for given s in range 0...1
    # delta is acceptable error in the time coordinate
    # uses Newton-Raphson approximation with a maximum of 100 passes
    def interpolate_inverse(self, proportion, delta=0.01):
        if proportion < self.interpolate(delta):
            return 0
        elif proportion > self.interpolate(1 - delta):
            return 1

        def approximate_next(current):
            f = self.interpolate(current) - proportion
            f_prime = self.interpolate_derivative(current)
            return current - f / f_prime

        # start with same proportion in time
        current = proportion

        # max 100 iterations
        count = 100
        while (abs(self.interpolate(current) - proportion) > delta
               and 0 < count):
            current = approximate_next(current)
            count += 1

        return current


class AnimationCurve(object):
    def __init__(self, distance, duration, frequency_start, frequency_end):
        assert(0 < distance)
        self.distance = distance
        self.duration = duration
        self.frequency_start = frequency_start
        self.frequency_end = frequency_end
        self._cubic_hermite = CubicHermite(
            frequency_start / distance * duration,
            frequency_end / distance * duration
        )

    def distance_at_time(self, time):
        unscaled = self._cubic_hermite.interpolate(
            time / self.duration
        )
        return unscaled * self.distance

    def frequency_at_time(self, time):
        unscaled = self._cubic_hermite.interpolate_derivative(
            time / self.duration
        )
        return unscaled / self.duration * self.distance

    def time_to_distance(self, distance):
        unscaled = self._cubic_hermite.interpolate_inverse(
            distance / self.distance
        )
        return unscaled * self.duration

      
class Animation(object):
    def __init__(self, frames, duration, frequency_start, frequency_end):
        assert(0 < len(frames))
        self.frames = frames
        self.duration = duration
        self.frequency_start = frequency_start
        self.frequeny_end = frequency_end
        self._animation_curve = AnimationCurve(
            float(len(frames)),
            duration,
            frequency_start,
            frequency_end
        )

    def get_frames(self):
        return zip(self.frames, self.get_durations())

    def get_durations(self):
        times = map(
            lambda frame: self._animation_curve.time_to_distance(frame + 1),
            range(1, len(self.frames) + 1)
        )

        durations = [times[0]]
        for index in range(1, len(times)):
            durations.append(times[index] - times[index - 1])

        durations = map(lambda duration: duration * self.duration, durations)
        return durations

    @staticmethod
    def ease_in(frames, duration=None, end_frequency=None):
        if end_frequency is None:
            end_frequency = DEFAULT_FREQUENCY

        if duration is None:
            duration = 2 * len(frames) / end_frequency

        return Animation(frames, duration, 0, end_frequency)

    @staticmethod
    def ease_out(frames, duration=None, start_frequency=None):
        if start_frequency is None:
            start_frequency = DEFAULT_FREQUENCY

        if duration is None:
            duration = 2 * len(frames) / start_frequency

        return Animation(frames, duration, start_frequency, 0)

    @staticmethod
    def ease_in_out(frames, duration=None):
        if duration is None:
            duration = len(frames) * DEFAULT_PERIOD

        return Animation(frames, duration, 0, 0)

    @staticmethod
    def linear(frames, duration=None):
        if duration is None:
            duration = len(frames) * DEFAULT_PERIOD

        return AnimationCurve(
            frames,
            duration,
            DEFAULT_FREQUENCY,
            DEFAULT_FREQUENCY
        )