Klein Bottle Geometry

Example showing a Klein Bottle. Surface normals are shown on both sides of the mesh, in different colors. It can be seen how the object turns itself “inside out”.

from rendercanvas.auto import RenderCanvas, loop
import pygfx as gfx
import pylinalg as la

canvas = RenderCanvas()
renderer = gfx.renderers.WgpuRenderer(canvas)
scene = gfx.Scene()

geometry = gfx.klein_bottle_geometry(10, stitch=False)
geometry.texcoords = None
material = gfx.MeshPhongMaterial(color=(1, 0.5, 0, 1), flat_shading=True)
obj = gfx.Mesh(geometry, material)
scene.add(obj)

obj2 = gfx.Mesh(geometry, gfx.MeshNormalLinesMaterial(color="#00f", line_length=1))
obj3 = gfx.Mesh(geometry, gfx.MeshNormalLinesMaterial(color="#0ff", line_length=-1))
obj.add(obj2, obj3)

camera = gfx.PerspectiveCamera(70, 1)
camera.local.z = 30

scene.add(gfx.AmbientLight(), camera.add(gfx.DirectionalLight()))


def animate():
    rot = la.quat_from_euler((0.0071, 0.01), order="XY")
    obj.local.rotation = la.quat_mul(rot, obj.local.rotation)

    renderer.render(scene, camera)
    canvas.request_draw()


if __name__ == "__main__":
    canvas.request_draw(animate)
    loop.run()

Interactive example

Try this example in your browser using Pyodide. Might not work with all examples and all devices. Check the output and your browser’s console for details.