keyframed 0.3.2

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Keyframed

Simple, Expressive Datatypes
For Manipulating Parameter Curves

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

n = 1000
low, high = 0.0001, 0.3
step1 = 50
step2 = 2 * step1

# Define some curves, related through shared parameters.
# Each curve loops through three keyframes, smoothly interpolating between each.
curves = ParameterGroup((
    SmoothCurve({0:low,  (step1-1):high, (2*step1-1):low},  loop=True),
    SmoothCurve({0:high, (step1-1):low,  (2*step1-1):high}, loop=True),
    SmoothCurve({0:low,  (step2-1):high, (2*step2-1):low},  loop=True),
    SmoothCurve({0:high, (step2-1):low,  (2*step2-1):high}, loop=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 channel
channel_name = list(really_fancy[0].keys())[-1]
red_channel = Curve.from_function(lambda k: really_fancy[k][channel_name])

# built-in plotting
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()

Summary

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.

Installation

pip install keyframed

Curve Construction

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)])

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()

Curve Properties

• 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

Curve Indexing

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

Curve Assignment

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})"

Curve Arithmetic

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

Interpolation

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

Looping

The Curve class has a loop attribute that can be set to True 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)

Using the ParameterGroup class

The ParameterGroup class provides a convenient way to manipulate parameters together. To use it, you will first need to create a dictionary of parameters, where the keys are the names of the parameters and the values are Curve objects. You can then pass this dictionary to the ParameterGroup constructor, along with an optional weight parameter which can be a Curve or a Number. If not provided, the weight defaults to Curve(1) (constant value of 1). The names provided in this dict will be used for the label attribute of the associated curves, overriding each curve's label if one was already assigned.

from keyframed import Curve, ParameterGroup

# create a dictionary of parameters
parameters = {
    "volume": Curve(0.5),
    "pitch": Curve(1.0),
    "rate": Curve(1.0),
}

# create a parameter group with a weight of 1.0
parameter_group = ParameterGroup(parameters, weight=1.0)

# access the current parameter values at key 0
print(parameter_group[0])  # {"volume": 0.5, "pitch": 1.0, "rate": 1.0}

# modify the weight parameter
parameter_group.weight *= 2.0

# access the current parameter values at key 0 again
print(parameter_group[0])  # {"volume": 1.0, "pitch": 2.0, "rate": 2.0}

The return value from indexing into a ParameterGroup is a modified dict that similarly propogates arithmetic operations to its values.

# access the current parameter values at key 0 again
returned_value = parameter_group[0]
print(returned_value)  # {"volume": 1.0, "pitch": 2.0, "rate": 2.0}

modified = returned_value * 2
print(modified) # {"volume": 2.0, "pitch": 4.0, "rate": 4.0}

ParameterGroups can also be used to visualize curves together. The ParameterGroup.plot() method will use the duration of the longest curve in the group as the domain for the plot.

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

kfs = {0:0,1:1,10:10}
pg = ParameterGroup({
    'stepfunc':Curve(kfs),
    'smoothfunc':SmoothCurve(kfs),
    'longstep':Curve({15:15}),
})


pg.plot()
plt.legend()
plt.show()

Advanced: Peeking under the hood

The following sections provide implementation details for advanced users

How Curves work

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.

How arithmetic operations on Curves works

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.