Update

UpdateFromFunc

UpdateFromFuncExample

class UpdateFromFuncExample(Scene):
    def construct(self):
        square = Square().to_edge(UP)
        mobject = Text("Text").scale(2).next_to(square, RIGHT)
        def update_func(mob):
            mob.next_to(square, RIGHT)

        self.add(square, mobject)
        self.wait()
        self.play(
            square.to_edge, DOWN,
            UpdateFromFunc(mobject, update_func)
        )
        self.wait()

UpdateFromAlphaFunc

UpdateFromAlphaFuncExample

class UpdateFromAlphaFuncExample(Scene):
    def construct(self):
        circle = Circle(radius=2).to_edge(UP)
        mobject = Text("Text")
        mobject.move_to(circle.get_start())
        mobject.save_state()

        def update_func(mob, alpha):
            mob.restore()
            mob.move_to(circle.point_from_proportion(alpha))
            mob.rotate(TAU * alpha)

        self.add(circle, mobject)
        self.wait()
        self.play(
            circle.animate.to_edge(DOWN),
            UpdateFromAlphaFunc(mobject, update_func),
            run_time=3
        )
        self.wait()

MaintainPositionRelativeTo

MaintainPositionRelativeToExample

class MaintainPositionRelativeToExample(Scene):
    def construct(self):
        square = Square().to_edge(UP)
        mobject = Text("Text").scale(2)
        mobject.next_to(square, RIGHT)

        self.add(square, mobject)
        self.wait()
        self.play(
            square.to_edge, DOWN,
            MaintainPositionRelativeTo(mobject, square)
        )
        self.wait()