Crear curvas PARAMeTRICAS en 2 y 3 dimensiones con Manim. Ejemplos: la epicicloide.

from manim import *

class curva2d(Scene):
    def construct(self):
        cielo = "#C4DDFF"
        purpura="#800080"
        self.camera.background_color = cielo
        self.add(Text("Epicicloide",color=RED).move_to(UP * 3.5))
        ax = Axes(x_range=[-3.5, 3.5, 1],
                  y_range=[-3.5, 3.5, 1],
                  x_length=7,
                  y_length=7,
                  axis_config={"include_tip": True},
                  ).move_to(np.array([-3.5, 0, 0]))
        ax.set_color(GREY)
        self.add(ax)
        circulo_grande = ParametricFunction(
            lambda u: np.array([
                2 * np.sin(u),
                2 * np.cos(u),
                0
            ]),
            color=BLUE, t_range=np.array([0, 2 * PI, 0.01])
        ).move_to(ax.coords_to_point(0, 0))
        self.play(
            Write(circulo_grande, run_time=0.5),
        )
        self.wait(3)
        epicicloide = ParametricFunction(
            lambda u: np.array([
                2.5 * np.cos(u) - 0.5 * np.cos((5 * u)),
                2.5 * np.sin(u) - 0.5 * np.sin((5 * u)),
                0
            ]),
            color=purpura, t_range=np.array([0, 4 * PI, 0.01])
        ).move_to(ax.coords_to_point(0, 0))
        self.play(
            Write(epicicloide), run_time=15)

        namex = MathTex("x=2.5\cos(\theta)-0.5\cos(5\theta)").move_to(RIGHT * 3.5 + UP).set_color(BLACK)
        namey = MathTex("y=2.5\sin(\theta)-0.5\sin(5\theta)").move_to(RIGHT * 3.5 + UP * 0).set_color(BLACK)
        rango = MathTex("\theta \in (0,5\pi)").move_to(RIGHT * 3.5 + DOWN).set_color(BLACK)
        self.play(
            Write(namex),
            Write(namey),
            Write(rango)
        )
        self.wait(10)