Locus Demo

class Locus(Scene):
  def construct(self):
    circle = Circle(radius=3, color=GREY)
    point_A = Dot(point=circle.point_from_proportion(0.5),color=BLUE_C)
    point_B = Dot(point=circle.point_from_proportion(0.85),color=BLUE_C)
    point_C = Dot(point=circle.point_from_proportion(0.1),color=BLUE_C)
    line_AB = ParametricFunction(function=lambda t: point_A.get_arc_center()+t*(point_A.get_arc_center()-point_B.get_arc_center()), t_min=-10,t_max=10,color=GREY)
    line_BC = ParametricFunction(function=lambda t: point_B.get_arc_center()+t*(point_B.get_arc_center()-point_C.get_arc_center()), t_min=-10,t_max=10,color=GREY)
    line_AC = ParametricFunction(function=lambda t: point_A.get_arc_center()+t*(point_A.get_arc_center()-point_C.get_arc_center()), t_min=-10,t_max=10,color=GREY)

    moving_point = Dot(point=circle.point_from_proportion(point_value.get_value()),color=GREEN)
    proj_AB = Dot(point=point_B.get_arc_center()+np.dot(moving_point.get_arc_center()-point_B.get_arc_center(),point_A.get_arc_center()-point_B.get_arc_center())/np.dot(point_A.get_arc_center()-point_B.get_arc_center(),point_A.get_arc_center()-point_B.get_arc_center())*(point_A.get_arc_center()-point_B.get_arc_center()),color=YELLOW)
    proj_BC = Dot(point=point_C.get_arc_center()+np.dot(moving_point.get_arc_center()-point_C.get_arc_center(),point_B.get_arc_center()-point_C.get_arc_center())/np.dot(point_B.get_arc_center()-point_C.get_arc_center(),point_B.get_arc_center()-point_C.get_arc_center())*(point_B.get_arc_center()-point_C.get_arc_center()),color=YELLOW)
    proj_AC = Dot(point=point_C.get_arc_center()+np.dot(moving_point.get_arc_center()-point_C.get_arc_center(),point_A.get_arc_center()-point_C.get_arc_center())/np.dot(point_A.get_arc_center()-point_C.get_arc_center(),point_A.get_arc_center()-point_C.get_arc_center())*(point_A.get_arc_center()-point_C.get_arc_center()),color=YELLOW)
    follow_line = ParametricFunction(function=lambda t: proj_AB.get_arc_center()+t*(proj_AB.get_arc_center()-proj_BC.get_arc_center()), t_min=-10,t_max=10,color=RED)

    trace = VGroup()
    collective = VGroup(follow_line,trace,moving_point,proj_AB,proj_BC,proj_AC)

    self.add(circle,trace,collective,line_AB,line_AC,line_BC,point_A,point_B,point_C)

    def update(obj,dt):
      alpha = interpolate(0.65,2.65,dt)
      moving_point.become(Dot(point=circle.point_from_proportion(math.modf(alpha)[0]),color=GREEN))
      proj_AB.become(Dot(point=point_B.get_arc_center()+np.dot(moving_point.get_arc_center()-       point_B.get_arc_center(),point_A.get_arc_center()-point_B.get_arc_center())/np.dot(point_A.get_arc_center()-point_B.get_arc_center(),point_A.get_arc_center()-point_B.get_arc_center())*(point_A.get_arc_center()-point_B.get_arc_center()),color=YELLOW))
      proj_BC.become(Dot(point=point_C.get_arc_center()+np.dot(moving_point.get_arc_center()-point_C.get_arc_center(),point_B.get_arc_center()-point_C.get_arc_center())/np.dot(point_B.get_arc_center()-point_C.get_arc_center(),point_B.get_arc_center()-point_C.get_arc_center())*(point_B.get_arc_center()-point_C.get_arc_center()),color=YELLOW))
      proj_AC.become(Dot(point=point_C.get_arc_center()+np.dot(moving_point.get_arc_center()-point_C.get_arc_center(),point_A.get_arc_center()-point_C.get_arc_center())/np.dot(point_A.get_arc_center()-point_C.get_arc_center(),point_A.get_arc_center()-point_C.get_arc_center())*(point_A.get_arc_center()-point_C.get_arc_center()),color=YELLOW))
      follow_line.become(ParametricFunction(function=lambda t: proj_AB.get_arc_center()+t*(proj_AB.get_arc_center()-proj_BC.get_arc_center()), t_min=-10,t_max=10,color=RED))
      trace.add(follow_line.deepcopy())

    self.wait()
    self.play(UpdateFromAlphaFunc(collective,update),rate_func=linear,run_time=3)
    self.wait()