This library implements a suite of pythonic datatypes for specifying and manipulating curves parameterized by keyframes and interpolators.

# generates the image above
!pip install keyframed
from keyframed import Composition, Curve, ParameterGroup, SmoothCurve
import math
import matplotlib.pyplot as plt

low, high = 0, 0.3
step1 = 50
step2 = 2 * step1

# Define some curves, related through shared parameters.
# Each curve "bounces" back and forth between two keyframes, smoothly interpolating the intermediate values.
curves = ParameterGroup((
    SmoothCurve({0:low,  step1:high},  bounce=True),
    SmoothCurve({0:high, step1:low}, bounce=True),
    SmoothCurve({0:low,  step2:high},  bounce=True),
    SmoothCurve({0:high, step2:low}, bounce=True)))

# Define another curve implicitly, extrapolating from a function
fancy = Curve.from_function(lambda k: high + math.sin(2*k/(step1+step2)))

# arithmetic on curves
curves_plus_fancy = curves + fancy + 1
curves_summed_by_frame = Composition(curves_plus_fancy, reduction='sum')
really_fancy = curves_plus_fancy / curves_summed_by_frame

# isolate a single curve from a ParameterGroup
red_channel = list(really_fancy.parameters.values())[-1]

# built-in plotting
n = 1000
really_fancy.plot(n=n)
red_channel.plot(n=n, linewidth=3, linestyle='-', color='#d62728')

plt.gca().axis('off')
plt.tight_layout()
plt.savefig('static/images/fancy.png')
plt.show()

The motivation for this library is to facilitate object-oriented parameterization of generative animations, specifically working towards a more expressive successor to the keyframing DSL developed by Chigozie Nri for parameterizing AI art animations (i.e. the keyframing syntax used by tools such as Disco Diffusion and Deforum).

The main purpose of this library is to implement the Curve class. "Keyframes" are special indices where the value of a Curve is defined. You can access data in a Curve using container indexing syntax, as if it were a list or dict. A Curve can be queried for values that aren't among its parameterizing keyframes: the result will be computed on the fly based on the interpolation method attached to the preceding keyframe and values on the surrounding keyframes.

The default method of interpolation is "previous", which will simply return the value of the closest preceding keyframe (i.e. the default curve is a step function). Several other interpolation methods are provided, and interpolation/extrapolation with user-defined functions is supported. Curves can also be modified via easing functions, which are essentially special interpolators.

Curve objects also support basic arithmetic operations like addition and multiplication, producing Compositions of curves (which also support arithmetic). Compositions also support several reducing operators over arbitrarily many curves, e.g. average, min, max, etc.

pip install keyframed

To create a new Curve object, you can pass in any of the following arguments to the Curve constructor:

• An integer or float: this creates a Curve with a single keyframe at t=0 with the given value.
• A dictionary: this creates a Curve with keyframes at the keys of the dictionary with the corresponding values, which can either be numeric values or Keyframe objects.
• A list/tuple of lists/tuples: this creates a Curve with keyframes at the keys in the tuple with the corresponding values. The tuple should be in the format ((k0,v0), (k1,v1), ...).

from keyframed import Curve

# create a curve with a single keyframe at t=0 with value 0
curve1 = Curve()

# create a curve with a single keyframe at t=0 with value 10
curve2 = Curve(10)

# create a curve with keyframes at t=0 and t=2 with values 0 and 2, respectively
curve3 = Curve({0:0, 2:2})

# create a curve with keyframes at t=0 and t=2 with values 0 and 2, respectively
curve4 = Curve([(0,0), (2,2)])

To facilitate compatibility with existing generative art tooling for AI animation, curve objects can also be initialized from the "Chigozie Nri string format" used by tools like Disco Diffusion and Deforum.

from keyframed.dsl import curve_from_cn_string
curve5 = curve_from_cn_string("1:(1), 10:(10)")

# Adding an arbitrary label for equivalence evaluation
curve5.label = "foobar"
assert curve5 == Curve({0:1, 1:1, 10:10}, default_interpolation='linear', label="foobar")

By default Curve objects behave as step functions. This can be modified by specifying different interpolation methods, which will be discussed at length further below. A versatile alternative default is provided via the SmoothCurve class, which simply has a different setting for default_interpolation (see more on interpolation methods and API below).

To visualize a curve, just call its .plot() method. Curves carry a label attribute: if this is populated, it will be used to label the curve in the plot.

from keyframed import Curve, SmoothCurve
import matplotlib.pyplot as plt

kfs = {0:0,1:1,10:10}
c = Curve(kfs, label='stepfunc')
sc = SmoothCurve(kfs, label='smoothfunc')

c.plot()
sc.plot(linestyle='dashed')

plt.legend()
plt.show()

• keyframes: returns a list of the keyframes in the curve.
• values: returns a list of the values at the corresponding keyframes.
• label: if not specified when initialized, a label will be auto-generated. labels can be modified any time by changing the .label attribute directly

curve = Curve({0:0,2:2})

print(curve.keyframes)  # prints [0, 2]
print(curve.values)  # prints [0, 2]
print(curve.label)  # prints something like "curve_SiF86D

You can access the value of a keyframe in the curve by indexing the curve object with the key. If the key is not in the curve, the curve will use interpolation (defaults to 'previous') to return a value.

from keyframed import Curve

curve = Curve({0:0,2:2})

print(curve[0])  # prints 0
print(curve[1])  # prints 0
print(curve[2])  # prints 2

Curves also support slice indexing. The result of a slice will be re-indexed such that the beginning of the slice corresponds to the 0th keyframe index (t=0). NB: The terminal index of the slice is inclusive, which is a little unpythonic but makes sense when considering that these are actually time indices rather than discrete container indices.

curve = Curve({i:i for i in range(10)})
print(curve[0], curve[3] curve[5]) # 0, 3, 5

sliced = curve[3:5]
print(sliced[0], sliced[2], sliced[5]) # 3, 5, 5

You can set the value of a keyframe in the curve by assigning to the curve object with the key. If the key is not in the curve, a new Keyframe will be created (see bottom for details).

from keyframed import Curve

curve = Curve() # equivalent to Curve({0:0})

curve[0] = 10
curve[1] = 20
curve[2] = 30

print(curve)  # prints "Curve({0: 10, 1: 20, 2: 30})"

All classes inheriting from CurveBase (Curve, ParameterGroup, Composition) support basic arithmetic with numeric values and with other CurveBase childclasses.

from keyframed import Curve

curve = Curve({0:0, 2:2})

curve1 = curve + 1
print(curve1[0]) # 1
print(curve1[1]) # 1
print(curve1[2]) # 3

curve2 = curve * 2
print(curve1[0]) # 0
print(curve1[1]) # 0
print(curve1[2]) # 4

curve3 = curve + Curve((1,1))
print(curve3[0]) # 0
print(curve3[1]) # 1
print(curve3[2]) # 3

The Curve class defaults to "previous" interpolation, which returns the value of the keyframe to the left of the given key if the given key is not already assigned a value. Other provided interpolation methods include "linear", "next" and "eased_lerp" (the default interpolator for SmoothCurve).

from keyframed import Curve

curve = Curve({0:0, 2:2})

print(curve[0]) # 0
print(curve[1]) # 0
print(curve[2]) # 2

# yes, setting t in the Keyframe object is redundant. working on it.
curve[0] = Keyframe(t=0, value=0, interpolation_method='linear')

print(curve[0]) # 0
print(curve[1]) # 1
print(curve[2]) # 2

You can also define custom interpolation methods. The call signature should take the a frame index as the first argument (k) and the Curve object itself (curve) as the second. You can then specify the custom method inside a Keyframe, assign the callable to the key directly, or register it as a named interpolation method,

from keyframed import (
    bisect_left_keyframe,
    bisect_right_keyframe,
    Curve,
    Keyframe,
    register_interpolation_method,
)

def my_linear(k, curve):
    # get the leftmost and rightmost keyframe objects
    left = bisect_left_keyframe(k, curve)
    right = bisect_right_keyframe(k, curve)

    # Get the coordinates between which we'll be interpolating
    x0, x1 = left.t, right.t
    y0, y1 = left.value, right.value

    # Convert the input keyframe index to a "progress" value -- `t` -- in [0,1]
    d = x1-x0
    t = (x1-k)/d

    # Calculate the interpolation
    # (this fomula is called "lerp", short for Linear intERPolation)
    outv =  t*y0 + (1-t)*y1
    return outv

curve = Curve({0:0, 2:2})

print(curve[0]) # 0
print(curve[1]) # 0
print(curve[2]) # 2
curve.plot(label='stepfunc')

# the interpolation method at frame 0 is still 'previous'.
curve[1] = Keyframe(t=1, value=1, interpolation_method=my_linear)

print(curve[0]) # 0
print(curve[1]) # 1
print(curve[2]) # 2
curve.plot(label='my_linear interpolated', linestyle='dashed')

plt.legend()

Alternatively, you can accomplish the same thing by assigning the callable to the keyframe index directly.

# shorthand: assign the callable directly
curve = Curve({0:0, 2:2})
curve[0] = my_linear

print(curve[0]) # 0
print(curve[1]) # 1
print(curve[2]) # 2

Both of the above methods will work, however: you'll need to use something like pickle for serialization. To facilitate safer serialization, you can "register" your custom interpolation method into the library's registry of available interpolation methods and then reference it by name as a string.

# register the function to a named interpolator
register_interpolation_method('my_interpolator', my_linear)

# invoke interpolator by name
curve = Curve({0:0, 2:2})
curve[0] =  Keyframe(t=0, value=0, interpolation_method='my_interpolator)

print(curve[0]) # 0
print(curve[1]) # 1
print(curve[2]) # 2

from keyframed.interpolation import get_context_left, get_context_right

import numpy as np
from scipy.interpolate import interp1d
import random
random.seed(123) # just for reproducibility

def user_defined_quadratic_interp(k, curve, n=2):
  xs = get_context_left(k, curve, n)
  xs += get_context_right(k, curve, n)
  ys = [curve[x] for x in xs]
  f = interp1d(xs, ys, kind='quadratic')
  return f(k)

# sample some random points that are linearly correlated with some jitter
d = {i:i+2*random.random() for i in range(10)}
curve = Curve(d, default_interpolation=user_defined_quadratic_interp)

xs = np.linspace(0,9,100)
curve.plot(xs=xs)

The Curve class has a loop attribute that can be set to True (either as an attribute or as an initialization argument) to make the curve loop indefinitely.

curve = Curve({0:0, 1:1}, loop=True)

print(curve[0])  # prints 0
print(curve[1])  # prints 1
print(curve[2])  # prints 0
print(curve[3])  # prints 1

curve.plot(n=5)

Alternatively, you can use the bounce setting to play every other loop in reverse. Only one of "bounce" or "loop" should be set to True.

All classes that inherit from CurveBase can be serialized to and from yaml via keyframed.serialization.to_yaml and keyframed.serialization.from_yaml.

Default to_yaml serialization generates a "simplified" output by default, which should be reasonably intuitive to manipulate in yaml form. For a more verbose, explicit yaml output, just set simplify=False.

# just play with to_yaml, you'll get the idea
from keyframed import SmoothCurve, ParameterGroup, serialization

low, high = 0.0001, 0.3
step1 = 50
curves = ParameterGroup({
    'foo':SmoothCurve({0:low, (step1-1):high, (2*step1-1):low}, loop=True),
    'bar':SmoothCurve({0:high, (step1-1):low, (2*step1-1):high}, loop=True)
})

txt = serialization.to_yaml(curves, simplify=True)

assert txt == """
parameters:
  foo:
    curve:
    - - 0
      - 0.0001
      - eased_lerp
    - - 49
      - 0.3
    - - 99
      - 0.0001
    loop: true
  bar:
    curve:
    - - 0
      - 0.3
      - eased_lerp
    - - 49
      - 0.0001
    - - 99
      - 0.3
    loop: true
""".strip()

curves = serialization.from_yaml(txt)

Breaking down the yaml syntax:

curve:
- - <time0>
  - <value0>
  - <interpolation method>
  - <interpolator arguments>
- - <time1>
  - <value1>
  - <another interpolation method, this one doesn't take arguments >
- - <time2>
  - <value2>
  # because no interpolator is specified, time2 falls back to the most recent keyframe where an interpolator was 
  # specified and re-uses the interpolation method from time1. To include redundant information like an 
  # interpolator that is implied by a previous frame (because it's the same), set `simplify=False` when calling
  # the serialization method (usually `to_yaml`).

Yaml serialization as just demonstrated will probably be the preferred approach for most use cases. The yaml serialization machinery is built around an intermediary dict structure that might be more appropriate for certain situations, such as users who want to serialize keyframed objects to JSON.

d = curves.to_dict(simplify=True, for_yaml=False)
## returned dict looks like this:
# {'parameters': {'foo': {'curve': {0: {'value': 0.0001,
#      'interpolation_method': 'eased_lerp'},
#     49: {'value': 0.3},
#     99: {'value': 0.0001}},
#    'loop': True},
#   'bar': {'curve': {0: {'value': 0.3, 'interpolation_method': 'eased_lerp'},
#     49: {'value': 0.0001},
#     99: {'value': 0.3}},
#    'loop': True}}}

curves = serialization.from_dict(d)

If you're using customization features like user-defined interpolators, use the "interpolator registration" functionality for compatibility with these serialization tools. The "registration" step will need to be repeated in the deserialization environment to ensure the named interpolator is available when evaluating the deserialized curve objects.

The following sections provide implementation details for advanced users

Curve objects are built on top of a sortedcontainer.SortedDict that lives on the Curve._data attribute (which you generally should not access directly). When you assign values to time indices on the curve, a key is written into _data and associated with a Keyframe object, which is basically just a named tuple that carries the attributes t, value, and interpolation_method. If the user queries a Curve for an index that is already assigned to _data, the corresponding Keyframe.value is returned directly. Otherwise, the Keyframe object associated with the leftmost populated index in _data is used to infer the appropriate interpolation method to use.

The return value of airthmetic on a CurveBase child class is a Composition object, which is a special kind of ParameterGroup that also has a reduction attribute. The Composition encapsulates the computation of the arithmetic. When a user queries the value for a key, the normal return value from querying a ParameterGroup is passed to functools.reduce, which applies the appropriate operator function based on the named Composition.reduction. The result of this reduction operation is then returned.

Although they inherit from the ParameterGroup class, Composition objects should generally be treated more like Curve objects. That being said, arithmetic on a ParameterGroup also returns a Composition object (which you may see referred to as a "compositional parameter group"), but one which will behave more like a ParameterGroup object. Normally, the ParameterGroup.parameters attribute can be used to isolate "channels" from the ParameterGroup, but at this time Composition.parameters can't be used this way: this attribute carries the operands of the arithmetic operation instead. Forthcoming changes will facilitate isolating/extracting/compiling specific"parameter channel" Curve objects from compositional pgroups.