ZOCallable 1.0.1

ZOCallable is a library defining multiple functions f : [0, 1] -> R, and satisfying the condition f(0) = 0 and f(1) = 1. They can be used as transitions.

ZOCallable

ZOCallable is a python library providing several functions mapping a float from 0 to 1 into a float from 0 to 1, with f(0) = 0 and f(1) = 1, with some tools and type hints for validation. ZO stands for Zero-One

ZOCallables and ZOZOCallables

The package ZOCallable provides two classes to be used for validation and type hinting: ZOCallable and ZOZOCallable.

• ZOCallable is used to represent any function $f$ satifying $f: [0, 1] \mapsto \mathbb{R} \text{ and } f(0) = 0 \text{ and } f(1) = 1$. The function verify_ZOCallable can be called on any function to verify if it satisfies the conditions, (as well as isinstance(func, ZOCallable)). ZOCallable can also be used as type hinting.
• ZOZOCallable is a subclass of ZOCallable, the function must satisfy the same conditions and satifsy $f: [0, 1] \mapsto [0, 1]$. The function verify_ZOCallable can be called on any function to verify if it satifies the conditions, (as well as isinstance(func, ZOZOCallable)). ZOZOCallable can also be used as type hinting.

Two other functions are provided in the package, one is normalize_ZOCallable, use to create a function that would satisfy the conditions from another, and vectorize_ZOCallable used to return a numpy vectorized function satisfying the conditions.

Functions

On top of these functions, some ZOCallables and ZOZOCallables are already implemented in the library. Most of these functions are called something_in, something_out or something_in_out. In most cases, -_in functions are convex, -_out functions are convace, and -_in_out are convex before x = 0.5 and concave after. They can all be found in the ZOCallable.functions module.

Basic functions

Some basic ZOZOCallables are:

• linear (the identity function),
• square_in, square_out and square_in_out are based on quadratic equations
• power_in(n), power_out(n) and power_in_out(n) are generalizations based on polynomial equations of degree n.
• root_in and root_out are based on the square root.
• exp_in and exp_out are based on the exponential function.
• jump(n) are stairs functions with n jumps.

cubic bezier curves

The cubic bezier curves have been implemented in order to mimic the capabilities of CSS. The function cubic_bezier(x1, y1, x2, y2) allow defining ZOCallables based on cubic bezier curves. Four functions have already been implemnted:

• ease
• ease_in
• ease_out
• ease_in_out

Advanced functions

Some more advanced functions are also defined:

• sin_in, sin_out and sin_in_out are based on sinusoidal functions
• circulare_in, circular_out and circulare_in_out are based on circles
• elastic_in,elastic_out, elastic_in_out, back_in, back_out, back_in_out, bounce_in(n), bounce_out(n) which are more complex non-monotonous functions. (see example)

Example

You can use the ZOCallable and ZOZOCallable for type hints of your own functions for example:

from ZOCallable import ZOZOCallable

def non_linear_gradient(points: int, func: ZOZOCallable):
    if not verify_ZOZOCallable(func, test_vectorisation=True):
        raise ValueError("The provided function isn't a ZOZOCallable")
    return func(np.linspace(0, 1, points))

Here, lambda x:x**2 or ZOCallable.functions.ease_in will satisfy the conditions and so be accepted, while lambda x:2*x would raise a ValueError

You can also use them for transitions or moves

from ZOCallable.functions import bounce_out

class FallingBall:

    def __init__(self, height: float, bounces: int, duration: int)
        self.z = height
        self.height = height
        self.trajectory = bounce_out(bounces)
        self.duration = duration
        self.time = 0

    def udpate(self, dt):
        self.time += dt
        self.z = self.trajectory(self.time/self.duration)*self.height

    def get_altitude(self):
        return self.z

bounce_out(n) being a non-monotonous ZOZOCallable, the fall of the ball here would follow the curve of the bounce_out. A precomputed trajectory is faster and easier for modelization.

Demonstration

Some of the functions have been plotted and are shown below.

Contributing

Any feedback optimization or new function proposal is welcome.

License

This library is under a GNU License.