Did not run the code, but i think that error occurs, because you don’t have a constructor for Hyperplane that explicitly takes the type parameter, but only one where the parameter is deduced from the argument, no?
So defining that (although it seems redundant at first) should fix the issue.
EDIT:
Basically, adding the following
Hyperplane{N}(v::VectorNd{N}) where N = Hyperplane(v)