Parametric spline interpolation for airfoil

Hi! I have a set of points from an airfoil:

x = [0 ... 1]
yUp = [ ... ] Leading edge -> trailing edge
yLow = [ ... ] Leading edge -> trailing edge

I would like to interpolate them on a finer mesh that is a Tchebycheff mesh. I easily created my mesh with:

N = 140;
xx = zeros(1, N);
for i = 1:N
    theta = (i-1)*pi/(N-1);
    xx(i) = 0.5*(1-cos(theta));
end

Now I would like to interpolate both upper and lower side of the airfoil with the same spline, starting from the trailing edge (x=1), to the leading edge (x=0) and back to the trailing edge (x=1). I should use a parametric spline, so I created these two vectors:

xt = [fliplr(x) x]; % 1-->0-->1
yt = [fliplr(yL) yU];

The question is, which mesh should I use in the interp1 function?

xn = interp1( ?? , xt, xx?,  'spline');
yn = interp1( ?? , yt, xx?,  'spline');

Should I use a curve length parameter? If so, how? Thank you for your help!