class ConicSection(ThreeDScene):
    def construct(self):
        # Заголовки
        Text.set_default(font = 'TT Firs Neue')
        h1 = Text('Поговорим про объемы', color = YELLOW).scale(0.8).to_edge(UL, buff=0.5)
        h2 = Text(
            "Принцип Кавальери"
        ).scale(0.65).next_to(h1, DOWN, aligned_edge=LEFT, buff = 0.3)

        self.add_fixed_in_frame_mobjects(h1, h2)
        self.remove(h2)
        # конус
        r = 2  # высота и радиус основания конуса
        cone = Cone(r, r).set_fill(BLUE, 1)
        cone.next_to(ORIGIN, OUT, buff=0).shift(2.5 * DOWN)
        #
        plane = Square(2 * r + 1).set_fill(TEAL, 0).set_stroke(opacity = 0).shift(2.5 * DOWN)
        circle = Circle(r).set_stroke(YELLOW, 3).set_fill(YELLOW, 0.2).shift(2.5 * DOWN)

        area_circ = circle.copy()
        area_circ.to_edge(DL)
        tex_c = always_redraw(lambda:
            MathTex("S_1").move_to(circle.get_center()).add_background_rectangle(color = BLACK)
        )
        self.add_fixed_in_frame_mobjects(area_circ, tex_c)
        self.remove(area_circ, tex_c)


        def upd_circle(circ):
            height = plane.get_center()[2]
            circ.move_to(height * OUT + 2.5 * DOWN)
            new_radius = r - height
            circ.set(width=2*new_radius)

        def upd_area_circ(circ):
            height = plane.get_center()[2]
            circ.to_edge(DL)
            new_radius = r - height
            circ.set(width=2*new_radius)


        circle.add_updater(upd_circle)
        area_circ.add_updater(upd_area_circ)

        # пирамида
        h = np.sqrt(4 * PI)/2
        c = Dot(radius=0.00001).move_to(plane.get_center()[2])
        vertex_coords = [
            [r, r, c.get_center()[2]],
            [r, -r, c.get_center()[2]],
            [-r, -r, c.get_center()[2]],
            [-r, r, c.get_center()[2]],
            [0, 0, 2]
        ]
        faces_list = [
            [0, 1, 4],
            [1, 2, 4],
            [2, 3, 4],
            [3, 0, 4],
            [0, 1, 2, 3]
        ]
        pyramid = Polyhedron(
            vertex_coords, faces_list
        ).next_to(ORIGIN, OUT, buff=0).set_stroke(WHITE, 2.5).shift(2.5 * UP)
        pyramid.graph.set_opacity(0)


        plane_2 = Square(
            4 * h + 1
        ).set_fill(TEAL, 0).next_to(c.get_center()[2], OUT, buff=0).set_stroke(opacity = 0)
        square = Square(
            2 * r
        ).set_stroke(PURPLE_A, 3).set_fill(PURPLE_A, 0.2).next_to(c.get_center()[2], OUT, buff=0).shift(0.1 * OUT + 2.5 * UP)

        cons = MathTex("=").next_to(area_circ, RIGHT, buff = 0.2)
        cons.add_updater(lambda obj: obj.next_to(area_circ, RIGHT, buff = 0.2))

        self.add_fixed_in_frame_mobjects(cons)
        self.remove(cons)

        area_squar = square.copy()
        area_squar.next_to(cons, RIGHT, buff = 0.2)
        tex_c2 = MathTex("S_2").move_to(square.get_center()).add_background_rectangle(color = BLACK)
        self.add_fixed_in_frame_mobjects(area_squar, tex_c, tex_c2)
        self.remove(area_squar, tex_c, tex_c2)

        tex_c2.add_updater(lambda obj: obj.move_to(area_squar.get_center()))

        # апдейтеры
        def upd_square(squar):
            height = plane_2.get_center()[2]
            squar.move_to(height * OUT + 2.5 * UP)
            new_lenght = r - height
            squar.set(width = 2 * new_lenght).shift(0.1 * OUT)

        def upd_area_square(squar):
            height = plane_2.get_center()[2]
            squar.next_to(cons, RIGHT, buff = 0.2)
            new_lenght = r - height
            squar.set(width = 2 * new_lenght).shift(0.1 * OUT)

        square.add_updater(upd_square)
        area_squar.add_updater(upd_area_square)

        big_plane = Rectangle(
            height = 12, width = 8
        ).set_fill(TEAL, 0.4).set_stroke(TEAL_A, 0).move_to(plane.get_center() + 3 * UP)

        # камера
        self.set_camera_orientation(
            phi= 70 * DEGREES,
            theta = 20 * DEGREES,
            zoom = 0.9
        )
        # анимации

        self.play(FadeIn(h2, shift = RIGHT))
        self.wait()
        self.play(FadeIn(cone, shift = OUT), FadeIn(pyramid, shift = OUT), run_time = 2)
        self.add(c, plane, plane_2)
        self.wait()
        self.play(Create(big_plane), Create(circle), Create(square), run_time = 3)
        self.wait()
        self.play(Write(tex_c), Write(tex_c2))
        # self.play(FadeIn(area_circ), FadeIn(cons), FadeIn(area_squar), Write(tex_c), Write(tex_c2))
        self.wait()
        self.play(
            plane.animate.shift(0.6 * OUT),
            plane_2.animate.shift(0.6 * OUT),
            big_plane.animate.shift(0.6 * OUT),
            run_time=5
        )
        self.wait()
        self.play(
            plane.animate.shift(0.6 * OUT),
            plane_2.animate.shift(0.6 * OUT),
            big_plane.animate.shift(0.6 * OUT),
            run_time=6
        )
        self.wait()
        self.play(
            plane.animate.shift(0.5 * OUT),
            plane_2.animate.shift(0.5 * OUT),
            big_plane.animate.shift(0.5 * OUT),
            run_time=7
        )
        self.wait()
        # выыод
        conclusion = MathTex(
            r"\Rightarrow", "V_1 = V_2"
        ).next_to(area_squar, RIGHT, buff = 0.2)

        self.add_fixed_in_frame_mobjects(conclusion)
        self.remove(conclusion)

        self.play(Write(conclusion), run_time = 2.5)
        self.wait()