By having GeometryTypes.Point interoperability, the Grassmann is now compatible with Makie:
using Grassmann, Makie
@basis S"∞+++" # 4D, Riemann sphere
sub = V(2,3,4) # 3D, SubManifold
glines(f,r=-2π:0.0001:2π) = lines([Point(sub(Grassmann.vector(f(t)))) for t ∈ r]);
f(t) = ↓(exp(t*v∞*(sin(3t)*3v1+cos(2t)*7v2-sin(5t)*4v3)/2)>>>↑(v1+v2-v3));
glines(f) # make plot in Makie
Note that Point(sub(Grassmann.vector(f(t)))) is used to convert the TensorAlgebra into the required GeometryTypes.Point format for AbstractPlotting.
Preferably, I’d like to completely bypass the Point abstraction and just directly plot and compute with the multivector TensorAlgebra type system… but I might need some help from @sdanisch for that.