text: """Mobject representing curly braces."""
  
  __all__ = ["Brace", "BraceLabel", "ArcBrace", "BraceText", "BraceBetweenPoints"]
  
  from typing import Optional, Sequence
  
  import numpy as np
  
  from manim._config import config
  from manim.mobject.opengl_compatibility import ConvertToOpenGL
  
  from ...animation.composition import AnimationGroup
  from ...animation.fading import FadeIn
  from ...animation.growing import GrowFromCenter
  from ...constants import *
  from ...mobject.geometry import Arc, Line
  from ...mobject.svg.svg_path import SVGPathMobject
  from ...mobject.svg.tex_mobject import MathTex, Tex
  from ...mobject.types.vectorized_mobject import VMobject
  from ...utils.color import BLACK
  from ...utils.deprecation import deprecated_params
  
  
  class Brace(SVGPathMobject):
      """Takes a mobject and draws a brace adjacent to it.
  
      Passing a direction vector determines the direction from which the
      brace is drawn. By default it is drawn from below.
  
      Parameters
      ----------
      mobject : :class:`~.Mobject`
          The mobject adjacent to which the brace is placed.
      direction :
          The direction from which the brace faces the mobject.
  
      See Also
      --------
      :class:`BraceBetweenPoints`
  
      Examples
      --------
      .. manim:: BraceExample
          :save_last_frame:
  
          class BraceExample(Scene):
              def construct(self):
                  s = Square()
                  self.add(s)
                  for i in np.linspace(0.1,1.0,4):
                      br = Brace(s, sharpness=i)
                      t = Text(f"sharpness= {i}").next_to(br, RIGHT)
                      self.add(t)
                      self.add(br)
                  VGroup(*self.mobjects).arrange(DOWN, buff=0.2)
  
      """
  
      def __init__(
          self,
          mobject,
          direction: Optional[Sequence[float]] = DOWN,
          buff=0.2,
          sharpness=2,
          stroke_width=0,
          fill_opacity=1.0,
          background_stroke_width=0,
          background_stroke_color=BLACK,
          **kwargs
      ):
          path_string_template = (
              "m0.01216 0c-0.01152 0-0.01216 6.103e-4 -0.01216 0.01311v0.007762c0.06776 "
              "0.122 0.1799 0.1455 0.2307 0.1455h{0}c0.03046 3.899e-4 0.07964 0.00449 "
              "0.1246 0.02636 0.0537 0.02695 0.07418 0.05816 0.08648 0.07769 0.001562 "
              "0.002538 0.004539 0.002563 0.01098 0.002563 0.006444-2e-8 0.009421-2.47e-"
              "5 0.01098-0.002563 0.0123-0.01953 0.03278-0.05074 0.08648-0.07769 0.04491"
              "-0.02187 0.09409-0.02597 0.1246-0.02636h{0}c0.05077 0 0.1629-0.02346 "
              "0.2307-0.1455v-0.007762c-1.78e-6 -0.0125-6.365e-4 -0.01311-0.01216-0.0131"
              "1-0.006444-3.919e-8 -0.009348 2.448e-5 -0.01091 0.002563-0.0123 0.01953-"
              "0.03278 0.05074-0.08648 0.07769-0.04491 0.02187-0.09416 0.02597-0.1246 "
              "0.02636h{1}c-0.04786 0-0.1502 0.02094-0.2185 0.1256-0.06833-0.1046-0.1706"
              "-0.1256-0.2185-0.1256h{1}c-0.03046-3.899e-4 -0.07972-0.004491-0.1246-0.02"
              "636-0.0537-0.02695-0.07418-0.05816-0.08648-0.07769-0.001562-0.002538-"
              "0.004467-0.002563-0.01091-0.002563z"
          )
          default_min_width = 0.90552
  
          self.buff = buff
  
          angle = -np.arctan2(*direction[:2]) + np.pi
          mobject.rotate(-angle, about_point=ORIGIN)
          left = mobject.get_corner(DOWN + LEFT)
          right = mobject.get_corner(DOWN + RIGHT)
          target_width = right[0] - left[0]
          linear_section_length = max(
              0, (target_width * sharpness - default_min_width) / 2
          )
  
          path = path_string_template.format(
              linear_section_length, -linear_section_length
          )
  
          SVGPathMobject.__init__(
              self,
              path_string=path,
              stroke_width=stroke_width,
              fill_opacity=fill_opacity,
              background_stroke_width=background_stroke_width,
              background_stroke_color=background_stroke_color,
              **kwargs
          )
          self.stretch_to_fit_width(target_width)
          self.shift(left - self.get_corner(UP + LEFT) + self.buff * DOWN)
  
          for mob in mobject, self:
              mob.rotate(angle, about_point=ORIGIN)
  
      def put_at_tip(self, mob, use_next_to=True, **kwargs):
          if use_next_to:
              mob.next_to(self.get_tip(), np.round(self.get_direction()), **kwargs)
          else:
              mob.move_to(self.get_tip())
              buff = kwargs.get("buff", DEFAULT_MOBJECT_TO_MOBJECT_BUFFER)
              shift_distance = mob.width / 2.0 + buff
              mob.shift(self.get_direction() * shift_distance)
          return self
  
      def get_text(self, *text, **kwargs):
          text_mob = Tex(*text)
          self.put_at_tip(text_mob, **kwargs)
          return text_mob
  
      def get_tex(self, *tex, **kwargs):
          tex_mob = MathTex(*tex)
          self.put_at_tip(tex_mob, **kwargs)
          return tex_mob
  
      def get_tip(self):
          # Returns the position of the seventh point in the path, which is the tip.
          if config["renderer"] == "opengl":
              return self.get_points()[34]
  
          return self.get_points()[28]  # = 7*4
  
      def get_direction(self):
          vect = self.get_tip() - self.get_center()
          return vect / np.linalg.norm(vect)
  
  
  class BraceLabel(VMobject, metaclass=ConvertToOpenGL):
      @deprecated_params(
          params="label_scale",
          since="v0.10.0",
          until="v0.11.0",
          message="Use font_size instead. To convert old scale factors to font size, multiply by 48.",
      )
      def __init__(
          self,
          obj,
          text,
          brace_direction=DOWN,
          label_constructor=MathTex,
          font_size=DEFAULT_FONT_SIZE,
          buff=0.2,
          **kwargs
      ):
          label_scale = kwargs.pop("label_scale", None)
          if label_scale:
              self.font_size = label_scale * DEFAULT_FONT_SIZE
          else:
              self.font_size = font_size
  
          self.label_constructor = label_constructor
          super().__init__(**kwargs)
  
          self.brace_direction = brace_direction
          self.buff = buff
          if isinstance(obj, list):
              obj = self.get_group_class()(*obj)
          self.brace = Brace(obj, brace_direction, buff, **kwargs)
  
          if isinstance(text, tuple) or isinstance(text, list):
              self.label = self.label_constructor(font_size=font_size, *text, **kwargs)
          else:
              self.label = self.label_constructor(str(text), font_size=font_size)
  
          self.brace.put_at_tip(self.label)
          self.add(self.brace, self.label)
  
      def creation_anim(self, label_anim=FadeIn, brace_anim=GrowFromCenter):
          return AnimationGroup(brace_anim(self.brace), label_anim(self.label))
  
      def shift_brace(self, obj, **kwargs):
          if isinstance(obj, list):
              obj = self.get_group_class()(*obj)
          self.brace = Brace(obj, self.brace_direction, **kwargs)
          self.brace.put_at_tip(self.label)
          return self
  
      def change_label(self, *text, **kwargs):
          self.label = self.label_constructor(*text, **kwargs)
  
          self.brace.put_at_tip(self.label)
          return self
  
      def change_brace_label(self, obj, *text, **kwargs):
          self.shift_brace(obj)
          self.change_label(*text, **kwargs)
          return self
  
  
  class BraceText(BraceLabel):
      def __init__(self, obj, text, label_constructor=Tex, **kwargs):
          super().__init__(obj, text, label_constructor=label_constructor, **kwargs)
  
  
  class BraceBetweenPoints(Brace):
      """Similar to Brace, but instead of taking a mobject it uses 2
      points to place the brace.
  
      A fitting direction for the brace is
      computed, but it still can be manually overridden.
      If the points go from left to right, the brace is drawn from below.
      Swapping the points places the brace on the opposite side.
  
      Parameters
      ----------
      point_1 :
          The first point.
      point_2 :
          The second point.
      direction :
          The direction from which the brace faces towards the points.
  
      Examples
      --------
          .. manim:: BraceBPExample
  
              class BraceBPExample(Scene):
                  def construct(self):
                      p1 = [0,0,0]
                      p2 = [1,2,0]
                      brace = BraceBetweenPoints(p1,p2)
                      self.play(Create(NumberPlane()))
                      self.play(Create(brace))
                      self.wait(2)
      """
  
      def __init__(
          self,
          point_1: Optional[Sequence[float]],
          point_2: Optional[Sequence[float]],
          direction: Optional[Sequence[float]] = ORIGIN,
          **kwargs
      ):
          if all(direction == ORIGIN):
              line_vector = np.array(point_2) - np.array(point_1)
              direction = np.array([line_vector[1], -line_vector[0], 0])
          Brace.__init__(self, Line(point_1, point_2), direction=direction, **kwargs)
  
  
  class ArcBrace(Brace):
      """Creates a :class:`~Brace` that wraps around an :class:`~.Arc`.
  
      The direction parameter allows the brace to be applied
      from outside or inside the arc.
  
      .. warning::
          The :class:`ArcBrace` is smaller for arcs with smaller radii.
  
      .. note::
          The :class:`ArcBrace` is initially a vertical :class:`Brace` defined by the
          length of the :class:`~.Arc`, but is scaled down to match the start and end
          angles. An exponential function is then applied after it is shifted based on
          the radius of the arc.
  
          The scaling effect is not applied for arcs with radii smaller than 1 to prevent
          over-scaling.
  
      Parameters
      ----------
      arc
          The :class:`~.Arc` that wraps around the :class:`Brace` mobject.
      direction
          The direction from which the brace faces the arc.
          ``LEFT`` for inside the arc, and ``RIGHT`` for the outside.
  
      Example
      -------
          .. manim:: ArcBraceExample
              :save_last_frame:
              :ref_classes: Arc
  
              class ArcBraceExample(Scene):
                  def construct(self):
                      arc_1 = Arc(radius=1.5,start_angle=0,angle=2*PI/3).set_color(RED)
                      brace_1 = ArcBrace(arc_1,LEFT)
                      group_1 = VGroup(arc_1,brace_1)
  
                      arc_2 = Arc(radius=3,start_angle=0,angle=5*PI/6).set_color(YELLOW)
                      brace_2 = ArcBrace(arc_2)
                      group_2 = VGroup(arc_2,brace_2)
  
                      arc_3 = Arc(radius=0.5,start_angle=-0,angle=PI).set_color(BLUE)
                      brace_3 = ArcBrace(arc_3)
                      group_3 = VGroup(arc_3,brace_3)
  
                      arc_4 = Arc(radius=0.2,start_angle=0,angle=3*PI/2).set_color(GREEN)
                      brace_4 = ArcBrace(arc_4)
                      group_4 = VGroup(arc_4,brace_4)
  
                      arc_group = VGroup(group_1, group_2, group_3, group_4).arrange_in_grid(buff=1.5)
                      self.add(arc_group.center())
  
      """
  
      def __init__(
          self,
          arc: Arc = Arc(start_angle=-1, angle=2, radius=1),
          direction: Sequence[float] = RIGHT,
          **kwargs
      ):
          arc_end_angle = arc.start_angle + arc.angle
          line = Line(UP * arc.start_angle, UP * arc_end_angle)
          scale_shift = RIGHT * np.log(arc.radius)
  
          if arc.radius >= 1:
              line.scale(arc.radius, about_point=ORIGIN)
              Brace.__init__(self, line, direction=direction, **kwargs)
              self.scale(1 / (arc.radius), about_point=ORIGIN)
          else:
              Brace.__init__(self, line, direction=direction, **kwargs)
  
          if arc.radius >= 0.3:
              self.shift(scale_shift)
          else:
              self.shift(RIGHT * np.log(0.3))
  
          self.apply_complex_function(np.exp)
          self.shift(arc.get_arc_center())
  