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Visualizing the Klein bottle with Makie.jl
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using Makie, WGLMakie | |
# implementation from the PGFPlots example gallery, at https://pgfplots.net/klein-bottle/ | |
klein(u, v) = Point3f((-2/15 * cos(u) * ( | |
3*cos(v) - 30*sin(u) | |
+ 90 *cos(u)^4 * sin(u) | |
- 60 *cos(u)^6 * sin(u) | |
+ 5 * cos(u)*cos(v) * sin(u)) | |
), | |
(-1/15 * sin(u) * (3*cos(v) | |
- 3*cos(u)^2 * cos(v) | |
- 48 * cos(u)^4*cos(v) | |
+ 48*cos(u)^6 *cos(v) | |
- 60 *sin(u) | |
+ 5*cos(u)*cos(v)*sin(u) | |
- 5*cos(u)^3 * cos(v) *sin(u) | |
- 80*cos(u)^5 * cos(v)*sin(u) | |
+ 80*cos(u)^7 * cos(v) * sin(u)) | |
), | |
(2/15 * (3 + 5*cos(u) *sin(u))*sin(v))) | |
us = LinRange(0, π, 41) | |
vs = LinRange(0, 2π, 25) | |
points = klein.(us', vs) | |
xt, yt, zt = map(i -> getindex.(points, i), 1:3) | |
index_color = (((u, v),) -> v + (u-1)*length(vs)).(tuple.(axes(us, 1)', axes(vs, 1))) | |
u_color = first.(tuple.(us', vs)) | |
colormap = cgrad([:blue, :yellow, :orange, :red, :orange, :yellow, :blue]) | |
surface(xt, yt, zt; color = color, colormap = colormap, shading = false, axis = (; type = Axis3)) | |
scatter(xt |> vec, yt |> vec, zt |> vec; color = u_color |> vec, colormap = :viridis) # produces the correct topology |
Author
asinghvi17
commented
Feb 20, 2023
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