How to animate parametric curve smoothly

[tmelorc]

This is my first post here. So, greetings.

First of all, I'm using Manim Community v0.17.2.

I'd like to animate the construction of the following parametric curve:

x(t) = np.cos(t) * np.sin(1/4*t)
y(t) =  np.sin(t) * np.sin(1/4*t)

Well, the following code simply plot the curve on the scene, and it works like a charm. Observe in the screenshot that the curve is smooth enough.

class PlotParametricFunction(Scene):
    
    def func(self, t):
        ''' paramatric curve '''
        return np.array((np.cos(t) * np.sin(1/4*t), np.sin(t) * np.sin(1/4*t), 0))

    def construct(self):
        func = ParametricFunction(self.func, t_range = np.array([0, 8*PI])).set_color(ORANGE)

        self.add(func.scale(3))
        self.wait()

Now, in the following, after looking for similar codes over Internet, I was able to animate the construction, but as we can see the curve is far away from being smooth like the previous one.

class AnimateParametricFunction(Scene):
    
    def func(self, t):
        ''' paramatric curve '''
        return np.array((np.cos(t) * np.sin(1/4*t), np.sin(t) * np.sin(1/4*t), 0))

    def construct(self):
        func = ParametricFunction(self.func, t_range = np.array([0, 8*PI])).set_color(ORANGE)

        t = ValueTracker(0)

        dot = Dot(color=WHITE, radius=0.05)
        self.add(dot)
        dot.add_updater(lambda m: m.move_to(
            np.array([
                3 * np.cos(t.get_value()) * np.sin(1/4*t.get_value()), # .scale(3) ?
                3 * np.sin(t.get_value()) * np.sin(1/4*t.get_value()),
                0
            ])
        ))

        path = TracedPath(dot.get_center, stroke_color=ORANGE, stroke_width=3)

        self.add(path)

        self.play(t.animate.set_value(8*PI), run_time=3, rate_func=linear)

        self.remove(dot)
        self.wait()

So, I'd like to ask: what is the best way to animate the construction of a smooth parametric curve?
Thanks in advance.

[ynhuruc]

您好！这是QQ邮箱的自动回复，您的邮件已收到，谢谢！