I can certainly do it with interparc. But it gets tricky, because interparc is set up to find points that are designated in terms of given arclengths along the curve itself. Simplest is to just understand how to build an interpolant of this sort, then to use it directly.
Interparc uses a linear chordal arclength to parameterize the spline that it builds. I think that idea came from Eugene Lee, as I recall. Pick some random points to interpolate.
x = rand(1,5);
y = rand(1,5);
Now, suppose I decide to insert exactly 3 intermediate points between each (x,y) pair? First, compute a cumulative linear chordal arclength. Think of it as the distance along the line, as computed by a connect the dots interpolant.
t = [0,cumsum(sqrt(diff(x).^2 + diff(y).^2))];
0 0.20299 0.53787 1.1588 1.5837
In fact you can see that my arclength function returns the same final number for the total arclength, when the "linear" method is used. So each of those arclength numbers are the cumulative lengths of the line segments connecting the points.
Now, I'll build a set of splines, representing x(t) and y(t).
x_t = pchip(t,x);
y_t = pchip(t,y);
Now, suppose I want to see 3 intermediate points between each pair. (I've chosen a small number here because I want to be easily able to count those points.)
nint = 3;
tint = cumsum([0,repelem(diff(t)/(nint+1),nint+1)]);
xint = ppval(x_t,tint);
yint = ppval(y_t,tint);
So 3 additional intermediate points between each of the original points, using a pchip interpolant on a completely general set of points. To get 13 points, just change nint to 13 instead of 3.
They don't have the property of being equally spaced in arclength along the curve, as interparc would generate. I know how to get interparc to do the work too, but it is late at night, and I'm feeling lazy if I can avoid actual thought.
Finally, see that I used repelem to build tint there. Repelem is a nice tool, introduced moderately recently in MATLAB. (In R2015a, according to the docs.) I could write it without repelem, but then it is late at night, as I said, and that one line seems elegant as it is.