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73 lines
2.2 KiB
Python
73 lines
2.2 KiB
Python
from manimlib.animation.animation import Animation
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from manimlib.constants import *
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from manimlib.utils.config_ops import digest_config
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class Homotopy(Animation):
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CONFIG = {
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"run_time": 3,
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"apply_function_kwargs": {},
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}
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def __init__(self, homotopy, mobject, **kwargs):
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"""
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Homotopy a function from (x, y, z, t) to (x', y', z')
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"""
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def function_at_time_t(t):
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return lambda p: homotopy(p[0], p[1], p[2], t)
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self.function_at_time_t = function_at_time_t
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digest_config(self, kwargs)
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Animation.__init__(self, mobject, **kwargs)
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def update_submobject(self, submob, start, alpha):
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submob.points = start.points
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submob.apply_function(
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self.function_at_time_t(alpha),
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**self.apply_function_kwargs
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)
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class SmoothedVectorizedHomotopy(Homotopy):
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def update_submobject(self, submob, start, alpha):
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Homotopy.update_submobject(self, submob, start, alpha)
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submob.make_smooth()
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class ComplexHomotopy(Homotopy):
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def __init__(self, complex_homotopy, mobject, **kwargs):
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"""
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Complex Hootopy a function Cx[0, 1] to C
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"""
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def homotopy(x, y, z, t):
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c = complex_homotopy(complex(x, y), t)
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return (c.real, c.imag, z)
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Homotopy.__init__(self, homotopy, mobject, **kwargs)
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class PhaseFlow(Animation):
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CONFIG = {
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"virtual_time": 1,
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"rate_func": None,
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}
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def __init__(self, function, mobject, **kwargs):
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digest_config(self, kwargs, locals())
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Animation.__init__(self, mobject, **kwargs)
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def update_mobject(self, alpha):
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if hasattr(self, "last_alpha"):
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dt = self.virtual_time * (alpha - self.last_alpha)
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self.mobject.apply_function(
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lambda p: p + dt * self.function(p)
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)
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self.last_alpha = alpha
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class MoveAlongPath(Animation):
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def __init__(self, mobject, path, **kwargs):
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digest_config(self, kwargs, locals())
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Animation.__init__(self, mobject, **kwargs)
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def update_mobject(self, alpha):
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point = self.path.point_from_proportion(alpha)
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self.mobject.move_to(point)
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