Homotopy

Qualified name: manim.animation.movement.Homotopy

class Homotopy(mobject=None, *args, use_override=True, **kwargs)[source]

Bases: Animation

A Homotopy.

This is an animation transforming the points of a mobject according to the specified transformation function. With the parameter \(t\) moving from 0 to 1 throughout the animation and \((x, y, z)\) describing the coordinates of the point of a mobject, the function passed to the homotopy keyword argument should transform the tuple \((x, y, z, t)\) to \((x', y', z')\), the coordinates the original point is transformed to at time \(t\).

Parameters:

  • homotopy (Callable[[float, float, float, float], tuple[float, float, float]]) – A function mapping \((x, y, z, t)\) to \((x', y', z')\).

  • mobject (Mobject) – The mobject transformed under the given homotopy.

  • run_time (float) – The run time of the animation.

  • apply_function_kwargs (dict[str, Any] | None) – Keyword arguments propagated to Mobject.apply_function().

  • kwargs (Any) – Further keyword arguments passed to the parent class.

Examples

Example: HomotopyExample 

from manim import *

class HomotopyExample(Scene):
    def construct(self):
        square = Square()

        def homotopy(x, y, z, t):
            if t <= 0.25:
                progress = t / 0.25
                return (x, y + progress * 0.2 * np.sin(x), z)
            else:
                wave_progress = (t - 0.25) / 0.75
                return (x, y + 0.2 * np.sin(x + 10 * wave_progress), z)

        self.play(Homotopy(homotopy, square, rate_func= linear, run_time=2))

class HomotopyExample(Scene):
    def construct(self):
        square = Square()

        def homotopy(x, y, z, t):
            if t <= 0.25:
                progress = t / 0.25
                return (x, y + progress * 0.2 * np.sin(x), z)
            else:
                wave_progress = (t - 0.25) / 0.75
                return (x, y + 0.2 * np.sin(x + 10 * wave_progress), z)

        self.play(Homotopy(homotopy, square, rate_func= linear, run_time=2))

Methods

function_at_time_t

interpolate_submobject

Attributes

run_time

_original__init__(homotopy, mobject, run_time=3, apply_function_kwargs=None, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

Parameters:

  • homotopy (Callable[[float, float, float, float], tuple[float, float, float]])

  • mobject (Mobject)

  • run_time (float)

  • apply_function_kwargs (dict[str, Any] | None)

  • kwargs (Any)