Math Compass Torus Transformation

political_compass_torus.jl

## source for math political compass torus meme:
## https://twitter.com/jessebett/status/1379162611414138885

## upcycled from torus knot fibration visualization:
## http://www.jessebett.com/TorusKnotFibration/torusknot.html

using Makie
using FileIO

compass = load("/Users/jessebett/Downloads/mathcompass.jpeg")

function torus(ϕ, θ , a, b)
	R = 2;
	r = 1;

	x = (R - r * ((1 - a) + a * cos(ϕ * b))) * ((1 - a) * θ  + sin(a * θ ))
	y = (1 - b) * ϕ + r * sin(b * ϕ)
	z = (R - r * cos(b * ϕ)) * -cos(a * θ ) + 1

	return (x,y,z)
end


function plot_torus(a,b)
	range = -π:0.01:π
	ϕ, θ = range,range
	meshgrid  = Iterators.product(ϕ, θ)

	xyz = [torus(ϕ,θ, a, b) for (ϕ,	θ) in meshgrid]

	# i am bad at unpacking matrix of tuples :(
	tx = [x for (x,y,z) in xyz]
	ty = [y for (x,y,z) in xyz]
	tz = [z for (x,y,z) in xyz]

	s = Scene(
		resolution=(1000,1000),
		scale = (1,1,1),
		show_axis = false,
		shading = false
		);

	cam = cam3d!(s;
		lookat=[0.,0., 0.],
		eyeposition=[1., -1. , -1.]
		)

	surface!(s,tx,ty,tz, color=compass)

	return s
end


display(plot_torus(0.,0.)) #plane
display(plot_torus(1.,0.)) #cylinder
display(plot_torus(0.,1.)) #cylinder
display(plot_torus(1.,1.)) #torus

# could animate with Makie directly but I use ffmpeg
# for (i,t) in enumerate(0:0.01:1)
# 	save(joinpath("anim/",lpad(i,5,"0")*".png"), plot_torus(t,t))
# end

# for (i,t) in enumerate(1:-0.01:0)
# 	i = i+100
# 	save(joinpath("anim/",lpad(i,5,"0")*".png"), plot_torus(t,t))
# end

##; ffmpeg -r 1/5 -pattern_type glob -i '/anim/*.png' -c:v libx264 -vf fps=25 -pix_fmt yuv420p out.mp4