This function computes the 3D spline interpolation of a 3D dataset. I did not write this code.

spline3d.m

function newCurve = spline3d(curve, dt) 
    % interpote a 3d curve using spline 
    % path 3*x 
    % newPath 3*x
    x = curve(1, :); 
    y = curve(2, :); 
    z = curve(3, :);
    t = cumsum([0;sqrt(diff(x(:)).^2 + diff(y(:)).^2 + diff(z(:)).^2)]); 
    sx = spline(t,x); 
    sy = spline(t,y); 
    sz = spline(t,z);
    tt = t(1):dt:t(end); 
    xp = ppval(sx, tt); 
    yp = ppval(sy, tt); 
    zp = ppval(sz, tt);
    newCurve = [xp; yp; zp]; 
end