prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  reST in ``MoveAlongPath`` not correct
  [https://docs.manim.community/en/stable/reference/manim.animation.movement.MoveAlongPath.html](https://docs.manim.community/en/stable/reference/manim.animation.movement.MoveAlongPath.html)
  
  ![image](https://github.com/ManimCommunity/manim/assets/110117391/cb0a1d4a-a766-486b-9986-9e4fcb15e74a)
  
  The ``..rubric:: Example`` should not be shown in the docs.
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `manim/animation/movement.py`
  Content:
  ```
  1 """Animations related to movement."""
  2 
  3 from __future__ import annotations
  4 
  5 __all__ = [
  6     "Homotopy",
  7     "SmoothedVectorizedHomotopy",
  8     "ComplexHomotopy",
  9     "PhaseFlow",
  10     "MoveAlongPath",
  11 ]
  12 
  13 from typing import TYPE_CHECKING, Any, Callable
  14 
  15 import numpy as np
  16 
  17 from ..animation.animation import Animation
  18 from ..utils.rate_functions import linear
  19 
  20 if TYPE_CHECKING:
  21     from ..mobject.mobject import Mobject, VMobject
  22 
  23 
  24 class Homotopy(Animation):
  25     """A Homotopy.
  26 
  27     This is an animation transforming the points of a mobject according
  28     to the specified transformation function. With the parameter :math:`t`
  29     moving from 0 to 1 throughout the animation and :math:`(x, y, z)`
  30     describing the coordinates of the point of a mobject,
  31     the function passed to the ``homotopy`` keyword argument should
  32     transform the tuple :math:`(x, y, z, t)` to :math:`(x', y', z')`,
  33     the coordinates the original point is transformed to at time :math:`t`.
  34 
  35     Parameters
  36     ----------
  37     homotopy
  38         A function mapping :math:`(x, y, z, t)` to :math:`(x', y', z')`.
  39     mobject
  40         The mobject transformed under the given homotopy.
  41     run_time
  42         The run time of the animation.
  43     apply_function_kwargs
  44         Keyword arguments propagated to :meth:`.Mobject.apply_function`.
  45     kwargs
  46         Further keyword arguments passed to the parent class.
  47     """
  48 
  49     def __init__(
  50         self,
  51         homotopy: Callable[[float, float, float, float], tuple[float, float, float]],
  52         mobject: Mobject,
  53         run_time: float = 3,
  54         apply_function_kwargs: dict[str, Any] | None = None,
  55         **kwargs,
  56     ) -> None:
  57         self.homotopy = homotopy
  58         self.apply_function_kwargs = (
  59             apply_function_kwargs if apply_function_kwargs is not None else {}
  60         )
  61         super().__init__(mobject, run_time=run_time, **kwargs)
  62 
  63     def function_at_time_t(self, t: float) -> tuple[float, float, float]:
  64         return lambda p: self.homotopy(*p, t)
  65 
  66     def interpolate_submobject(
  67         self,
  68         submobject: Mobject,
  69         starting_submobject: Mobject,
  70         alpha: float,
  71     ) -> None:
  72         submobject.points = starting_submobject.points
  73         submobject.apply_function(
  74             self.function_at_time_t(alpha), **self.apply_function_kwargs
  75         )
  76 
  77 
  78 class SmoothedVectorizedHomotopy(Homotopy):
  79     def interpolate_submobject(
  80         self,
  81         submobject: Mobject,
  82         starting_submobject: Mobject,
  83         alpha: float,
  84     ) -> None:
  85         super().interpolate_submobject(submobject, starting_submobject, alpha)
  86         submobject.make_smooth()
  87 
  88 
  89 class ComplexHomotopy(Homotopy):
  90     def __init__(
  91         self, complex_homotopy: Callable[[complex], float], mobject: Mobject, **kwargs
  92     ) -> None:
  93         """
  94         Complex Homotopy a function Cx[0, 1] to C
  95         """
  96 
  97         def homotopy(
  98             x: float,
  99             y: float,
  100             z: float,
  101             t: float,
  102         ) -> tuple[float, float, float]:
  103             c = complex_homotopy(complex(x, y), t)
  104             return (c.real, c.imag, z)
  105 
  106         super().__init__(homotopy, mobject, **kwargs)
  107 
  108 
  109 class PhaseFlow(Animation):
  110     def __init__(
  111         self,
  112         function: Callable[[np.ndarray], np.ndarray],
  113         mobject: Mobject,
  114         virtual_time: float = 1,
  115         suspend_mobject_updating: bool = False,
  116         rate_func: Callable[[float], float] = linear,
  117         **kwargs,
  118     ) -> None:
  119         self.virtual_time = virtual_time
  120         self.function = function
  121         super().__init__(
  122             mobject,
  123             suspend_mobject_updating=suspend_mobject_updating,
  124             rate_func=rate_func,
  125             **kwargs,
  126         )
  127 
  128     def interpolate_mobject(self, alpha: float) -> None:
  129         if hasattr(self, "last_alpha"):
  130             dt = self.virtual_time * (
  131                 self.rate_func(alpha) - self.rate_func(self.last_alpha)
  132             )
  133             self.mobject.apply_function(lambda p: p + dt * self.function(p))
  134         self.last_alpha = alpha
  135 
  136 
  137 class MoveAlongPath(Animation):
  138     """Make one mobject move along the path of another mobject.
  139     Example
  140     --------
  141     .. manim:: MoveAlongPathExample
  142 
  143         class MoveAlongPathExample(Scene):
  144             def construct(self):
  145                 d1 = Dot().set_color(ORANGE)
  146                 l1 = Line(LEFT, RIGHT)
  147                 l2 = VMobject()
  148                 self.add(d1, l1, l2)
  149                 l2.add_updater(lambda x: x.become(Line(LEFT, d1.get_center()).set_color(ORANGE)))
  150                 self.play(MoveAlongPath(d1, l1), rate_func=linear)
  151     """
  152 
  153     def __init__(
  154         self,
  155         mobject: Mobject,
  156         path: VMobject,
  157         suspend_mobject_updating: bool | None = False,
  158         **kwargs,
  159     ) -> None:
  160         self.path = path
  161         super().__init__(
  162             mobject, suspend_mobject_updating=suspend_mobject_updating, **kwargs
  163         )
  164 
  165     def interpolate_mobject(self, alpha: float) -> None:
  166         point = self.path.point_from_proportion(self.rate_func(alpha))
  167         self.mobject.move_to(point)
  168
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/manim/animation/movement.py b/manim/animation/movement.py
  --- a/manim/animation/movement.py
  +++ b/manim/animation/movement.py
  @@ -136,8 +136,7 @@
   
   class MoveAlongPath(Animation):
       """Make one mobject move along the path of another mobject.
  -    Example
  -    --------
  +
       .. manim:: MoveAlongPathExample
   
           class MoveAlongPathExample(Scene):
  
verification_info: {"golden_diff": "diff --git a/manim/animation/movement.py b/manim/animation/movement.py\n--- a/manim/animation/movement.py\n+++ b/manim/animation/movement.py\n@@ -136,8 +136,7 @@\n \n class MoveAlongPath(Animation):\n     \"\"\"Make one mobject move along the path of another mobject.\n-    Example\n-    --------\n+\n     .. manim:: MoveAlongPathExample\n \n         class MoveAlongPathExample(Scene):\n", "issue": "reST in ``MoveAlongPath`` not correct\n[https://docs.manim.community/en/stable/reference/manim.animation.movement.MoveAlongPath.html](https://docs.manim.community/en/stable/reference/manim.animation.movement.MoveAlongPath.html)\r\n\r\n![image](https://github.com/ManimCommunity/manim/assets/110117391/cb0a1d4a-a766-486b-9986-9e4fcb15e74a)\r\n\r\nThe ``..rubric:: Example`` should not be shown in the docs.\n", "before_files": [{"content": "\"\"\"Animations related to movement.\"\"\"\n\nfrom __future__ import annotations\n\n__all__ = [\n    \"Homotopy\",\n    \"SmoothedVectorizedHomotopy\",\n    \"ComplexHomotopy\",\n    \"PhaseFlow\",\n    \"MoveAlongPath\",\n]\n\nfrom typing import TYPE_CHECKING, Any, Callable\n\nimport numpy as np\n\nfrom ..animation.animation import Animation\nfrom ..utils.rate_functions import linear\n\nif TYPE_CHECKING:\n    from ..mobject.mobject import Mobject, VMobject\n\n\nclass Homotopy(Animation):\n    \"\"\"A Homotopy.\n\n    This is an animation transforming the points of a mobject according\n    to the specified transformation function. With the parameter :math:`t`\n    moving from 0 to 1 throughout the animation and :math:`(x, y, z)`\n    describing the coordinates of the point of a mobject,\n    the function passed to the ``homotopy`` keyword argument should\n    transform the tuple :math:`(x, y, z, t)` to :math:`(x', y', z')`,\n    the coordinates the original point is transformed to at time :math:`t`.\n\n    Parameters\n    ----------\n    homotopy\n        A function mapping :math:`(x, y, z, t)` to :math:`(x', y', z')`.\n    mobject\n        The mobject transformed under the given homotopy.\n    run_time\n        The run time of the animation.\n    apply_function_kwargs\n        Keyword arguments propagated to :meth:`.Mobject.apply_function`.\n    kwargs\n        Further keyword arguments passed to the parent class.\n    \"\"\"\n\n    def __init__(\n        self,\n        homotopy: Callable[[float, float, float, float], tuple[float, float, float]],\n        mobject: Mobject,\n        run_time: float = 3,\n        apply_function_kwargs: dict[str, Any] | None = None,\n        **kwargs,\n    ) -> None:\n        self.homotopy = homotopy\n        self.apply_function_kwargs = (\n            apply_function_kwargs if apply_function_kwargs is not None else {}\n        )\n        super().__init__(mobject, run_time=run_time, **kwargs)\n\n    def function_at_time_t(self, t: float) -> tuple[float, float, float]:\n        return lambda p: self.homotopy(*p, t)\n\n    def interpolate_submobject(\n        self,\n        submobject: Mobject,\n        starting_submobject: Mobject,\n        alpha: float,\n    ) -> None:\n        submobject.points = starting_submobject.points\n        submobject.apply_function(\n            self.function_at_time_t(alpha), **self.apply_function_kwargs\n        )\n\n\nclass SmoothedVectorizedHomotopy(Homotopy):\n    def interpolate_submobject(\n        self,\n        submobject: Mobject,\n        starting_submobject: Mobject,\n        alpha: float,\n    ) -> None:\n        super().interpolate_submobject(submobject, starting_submobject, alpha)\n        submobject.make_smooth()\n\n\nclass ComplexHomotopy(Homotopy):\n    def __init__(\n        self, complex_homotopy: Callable[[complex], float], mobject: Mobject, **kwargs\n    ) -> None:\n        \"\"\"\n        Complex Homotopy a function Cx[0, 1] to C\n        \"\"\"\n\n        def homotopy(\n            x: float,\n            y: float,\n            z: float,\n            t: float,\n        ) -> tuple[float, float, float]:\n            c = complex_homotopy(complex(x, y), t)\n            return (c.real, c.imag, z)\n\n        super().__init__(homotopy, mobject, **kwargs)\n\n\nclass PhaseFlow(Animation):\n    def __init__(\n        self,\n        function: Callable[[np.ndarray], np.ndarray],\n        mobject: Mobject,\n        virtual_time: float = 1,\n        suspend_mobject_updating: bool = False,\n        rate_func: Callable[[float], float] = linear,\n        **kwargs,\n    ) -> None:\n        self.virtual_time = virtual_time\n        self.function = function\n        super().__init__(\n            mobject,\n            suspend_mobject_updating=suspend_mobject_updating,\n            rate_func=rate_func,\n            **kwargs,\n        )\n\n    def interpolate_mobject(self, alpha: float) -> None:\n        if hasattr(self, \"last_alpha\"):\n            dt = self.virtual_time * (\n                self.rate_func(alpha) - self.rate_func(self.last_alpha)\n            )\n            self.mobject.apply_function(lambda p: p + dt * self.function(p))\n        self.last_alpha = alpha\n\n\nclass MoveAlongPath(Animation):\n    \"\"\"Make one mobject move along the path of another mobject.\n    Example\n    --------\n    .. manim:: MoveAlongPathExample\n\n        class MoveAlongPathExample(Scene):\n            def construct(self):\n                d1 = Dot().set_color(ORANGE)\n                l1 = Line(LEFT, RIGHT)\n                l2 = VMobject()\n                self.add(d1, l1, l2)\n                l2.add_updater(lambda x: x.become(Line(LEFT, d1.get_center()).set_color(ORANGE)))\n                self.play(MoveAlongPath(d1, l1), rate_func=linear)\n    \"\"\"\n\n    def __init__(\n        self,\n        mobject: Mobject,\n        path: VMobject,\n        suspend_mobject_updating: bool | None = False,\n        **kwargs,\n    ) -> None:\n        self.path = path\n        super().__init__(\n            mobject, suspend_mobject_updating=suspend_mobject_updating, **kwargs\n        )\n\n    def interpolate_mobject(self, alpha: float) -> None:\n        point = self.path.point_from_proportion(self.rate_func(alpha))\n        self.mobject.move_to(point)\n", "path": "manim/animation/movement.py"}], "after_files": [{"content": "\"\"\"Animations related to movement.\"\"\"\n\nfrom __future__ import annotations\n\n__all__ = [\n    \"Homotopy\",\n    \"SmoothedVectorizedHomotopy\",\n    \"ComplexHomotopy\",\n    \"PhaseFlow\",\n    \"MoveAlongPath\",\n]\n\nfrom typing import TYPE_CHECKING, Any, Callable\n\nimport numpy as np\n\nfrom ..animation.animation import Animation\nfrom ..utils.rate_functions import linear\n\nif TYPE_CHECKING:\n    from ..mobject.mobject import Mobject, VMobject\n\n\nclass Homotopy(Animation):\n    \"\"\"A Homotopy.\n\n    This is an animation transforming the points of a mobject according\n    to the specified transformation function. With the parameter :math:`t`\n    moving from 0 to 1 throughout the animation and :math:`(x, y, z)`\n    describing the coordinates of the point of a mobject,\n    the function passed to the ``homotopy`` keyword argument should\n    transform the tuple :math:`(x, y, z, t)` to :math:`(x', y', z')`,\n    the coordinates the original point is transformed to at time :math:`t`.\n\n    Parameters\n    ----------\n    homotopy\n        A function mapping :math:`(x, y, z, t)` to :math:`(x', y', z')`.\n    mobject\n        The mobject transformed under the given homotopy.\n    run_time\n        The run time of the animation.\n    apply_function_kwargs\n        Keyword arguments propagated to :meth:`.Mobject.apply_function`.\n    kwargs\n        Further keyword arguments passed to the parent class.\n    \"\"\"\n\n    def __init__(\n        self,\n        homotopy: Callable[[float, float, float, float], tuple[float, float, float]],\n        mobject: Mobject,\n        run_time: float = 3,\n        apply_function_kwargs: dict[str, Any] | None = None,\n        **kwargs,\n    ) -> None:\n        self.homotopy = homotopy\n        self.apply_function_kwargs = (\n            apply_function_kwargs if apply_function_kwargs is not None else {}\n        )\n        super().__init__(mobject, run_time=run_time, **kwargs)\n\n    def function_at_time_t(self, t: float) -> tuple[float, float, float]:\n        return lambda p: self.homotopy(*p, t)\n\n    def interpolate_submobject(\n        self,\n        submobject: Mobject,\n        starting_submobject: Mobject,\n        alpha: float,\n    ) -> None:\n        submobject.points = starting_submobject.points\n        submobject.apply_function(\n            self.function_at_time_t(alpha), **self.apply_function_kwargs\n        )\n\n\nclass SmoothedVectorizedHomotopy(Homotopy):\n    def interpolate_submobject(\n        self,\n        submobject: Mobject,\n        starting_submobject: Mobject,\n        alpha: float,\n    ) -> None:\n        super().interpolate_submobject(submobject, starting_submobject, alpha)\n        submobject.make_smooth()\n\n\nclass ComplexHomotopy(Homotopy):\n    def __init__(\n        self, complex_homotopy: Callable[[complex], float], mobject: Mobject, **kwargs\n    ) -> None:\n        \"\"\"\n        Complex Homotopy a function Cx[0, 1] to C\n        \"\"\"\n\n        def homotopy(\n            x: float,\n            y: float,\n            z: float,\n            t: float,\n        ) -> tuple[float, float, float]:\n            c = complex_homotopy(complex(x, y), t)\n            return (c.real, c.imag, z)\n\n        super().__init__(homotopy, mobject, **kwargs)\n\n\nclass PhaseFlow(Animation):\n    def __init__(\n        self,\n        function: Callable[[np.ndarray], np.ndarray],\n        mobject: Mobject,\n        virtual_time: float = 1,\n        suspend_mobject_updating: bool = False,\n        rate_func: Callable[[float], float] = linear,\n        **kwargs,\n    ) -> None:\n        self.virtual_time = virtual_time\n        self.function = function\n        super().__init__(\n            mobject,\n            suspend_mobject_updating=suspend_mobject_updating,\n            rate_func=rate_func,\n            **kwargs,\n        )\n\n    def interpolate_mobject(self, alpha: float) -> None:\n        if hasattr(self, \"last_alpha\"):\n            dt = self.virtual_time * (\n                self.rate_func(alpha) - self.rate_func(self.last_alpha)\n            )\n            self.mobject.apply_function(lambda p: p + dt * self.function(p))\n        self.last_alpha = alpha\n\n\nclass MoveAlongPath(Animation):\n    \"\"\"Make one mobject move along the path of another mobject.\n\n    .. manim:: MoveAlongPathExample\n\n        class MoveAlongPathExample(Scene):\n            def construct(self):\n                d1 = Dot().set_color(ORANGE)\n                l1 = Line(LEFT, RIGHT)\n                l2 = VMobject()\n                self.add(d1, l1, l2)\n                l2.add_updater(lambda x: x.become(Line(LEFT, d1.get_center()).set_color(ORANGE)))\n                self.play(MoveAlongPath(d1, l1), rate_func=linear)\n    \"\"\"\n\n    def __init__(\n        self,\n        mobject: Mobject,\n        path: VMobject,\n        suspend_mobject_updating: bool | None = False,\n        **kwargs,\n    ) -> None:\n        self.path = path\n        super().__init__(\n            mobject, suspend_mobject_updating=suspend_mobject_updating, **kwargs\n        )\n\n    def interpolate_mobject(self, alpha: float) -> None:\n        point = self.path.point_from_proportion(self.rate_func(alpha))\n        self.mobject.move_to(point)\n", "path": "manim/animation/movement.py"}]}