Klein Bottle

kleinbottle.py

# sudo apt install -y && sudo apt-get -y install libcogl-pango-dev && pip install manim
from manim import *
from math import *
class KleinBottle(ThreeDScene):
    def construct(self):
        def klein_bottle(u, v):
            u = u * 2 * PI
            v = v * 2 * PI
            half = (u < PI)  

            if half:
                x = 3 * cos(u) * (1 + sin(u)) + (2 * (1 - cos(u) / 2)) * cos(u) * cos(v)
                y = 8 * sin(u) + (2 * (1 - cos(u) / 2)) * sin(u) * cos(v)
            else:
                x = 3 * cos(u) * (1 + sin(u)) + (2 * (1 - cos(u) / 2)) * cos(v + PI)
                y = 8 * sin(u)
            
            z = -2 * (1 - cos(u) / 2) * sin(v)
            return np.array([x, y, z])

        surface = Surface(
            lambda u, v: klein_bottle(u, v),
            u_range=[0, 1],
            v_range=[0, 1],
            resolution=(50, 50)
        ).scale(0.2)  

        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        self.begin_ambient_camera_rotation(rate=0.2)  
        
        self.add(surface)
        self.wait(10)  

if __name__ == "__main__":
    scene = KleinBottle()
    scene.render()