Plotting the set of all unit vectors in different norms efficiently?

I'm trying to plot the set of all unit vectors in different norms and this is the code I've managed to make so far, the issue is that using randn is going to give me lots of redundant points and I'm looking for a cleaner way to plot this without having to rely on randn. I still want the values to be represented as vectors so that I can later apply transformations on them. Any ideas?

function plotUnitNorm(normType)
X = randn(10000,2);
if(strcmp(normType,'inf'))
    p_norm = max(abs(X), [], 2);
end
if(strcmp(normType,'1'))
    p_norm = sum(abs(X),2);
end
if(strcmp(normType,'2'))
    p_norm = sum(abs(X).^2,2).^(1/2);
end

Xn = bsxfun(@times, X, 1./p_norm);

figure(1); scatter(Xn(:, 1), Xn(:, 2), '.');
end

Answer 1

[Thiago Henrique Gomes Lobato]

Just make a meshgrid and convert it to a vector

%X = randn(10000,2);
step = 0.02;
[Xi,Yi] = meshgrid(-1:step:1,-1:step:1);
X       = [Xi(1:end)',Yi(1:end)'];

if(strcmp(normType,'inf'))
    p_norm = max(abs(X), [], 2);
end
...

[David Rannaleet]

This gives me 10201 points to plot, when the randn method gives me 10000. So this seems to be even more inefficient plottingwise, I also get blindspots near the corners of the 1-norm and inf-norm using this method.