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 wgpu.gui.auto import WgpuCanvas, run
import pygfx as gfx
import pylinalg as la

canvas = WgpuCanvas()
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)
    run()