class ContinuousMotion(Scene):
    def create(self):
        func=lambda pos: np.sin(pos[0] / 2) UR + np.cos(pos[1] / 2) LEFT
        stream_lines=StreamLines(func, stroke_width=2, max_anchors_per_line=30)
        self.add(stream_lines)
        stream_lines.start_animation(warm_up=False, flow_speed=1.5)
        self.wait(stream_lines.virtual_time / stream_lines.flow_speed)

class OpeningManim(Scene):
    def create(self):
        title=Tex(r"That is just a few LaTeX")
        basel=MathTex(r"sum_{n=1}^infty frac{1}{n^2}=frac{pi^2}{6}")
        VGroup(title, basel).manage(DOWN)
        self.play(
            Write(title),
            FadeIn(basel, shift=DOWN),
        )
        self.wait()

        transform_title=Tex("That modified into once a remodel")
        transform_title.to_corner(UP + LEFT)
        self.play(
            Remodel(title, transform_title),
            LaggedStart(*(FadeOut(obj, shift=DOWN) for obj in basel)),
        )
        self.wait()

        grid=NumberPlane()
        grid_title=Tex("That is a grid", font_size=72)
        grid_title.move_to(transform_title)

        self.add(grid, grid_title)  # Be obvious title is on top of grid
        self.play(
            FadeOut(title),
            FadeIn(grid_title, shift=UP),
            Make(grid, run_time=3, lag_ratio=0.1),
        )
        self.wait()

        grid_transform_title=Tex(
            r"That modified into once a non-linear characteristic \ applied to the grid",
        )
        grid_transform_title.move_to(grid_title, UL)
        grid.prepare_for_nonlinear_transform()
        self.play(
            grid.animate.apply_function(
                lambda p: p
                + np.array(
                    [
                        np.sin(p[1]),
                        np.sin(p[0]),
                        0,
                    ],
                ),
            ),
            run_time=3,
        )
        self.wait()
        self.play(Remodel(grid_title, grid_transform_title))
        self.wait()

class SquareToCircle(Scene):
    def create(self):
        circle=Circle()
        sq.=Square()
        sq..flip(RIGHT)
        sq..rotate(-3 TAU / 8)
        circle.set_fill(PINK, opacity=0.5)

        self.play(Make(sq.))
        self.play(Remodel(sq., circle))
        self.play(FadeOut(sq.))

class UnionExample(Scene):
    def create(self):
        sq=Square(coloration=RED, fill_opacity=1).move_to([-2, 0, 0])
        cr=Circle(coloration=BLUE, fill_opacity=1).move_to([-1.3, 0.7, 0])
        un=Union(sq, cr, coloration=GREEN, fill_opacity=1).move_to([1.5, 0.3, 0])
        self.add(sq, cr, un)

class WarpSquare(Scene):
    def create(self):
        sq.=Square()
        self.play(
            ApplyPointwiseFunction(
                lambda level: complex_to_R3(np.exp(R3_to_complex(level))),
                sq.,
            ),
        )
        self.wait()