[pstricks] node calculations

[John Frampton]

Several times, I have needed a macro which could be used as follows:

     \midpoint{A1}{A2}{A3}

would label the midpoint of the line joining A1 and A2 as node A3.

It would be even better to have a macro which could be used as follows:

   \interpolate{A1}{A2}{.7}{A3}

would label the point  .3*Point(A1) + .7*Point(A2) with the lable A3.

Still better would be a macro so that

   \linearcombination{1.2}{A1}{2.3}{A2}{A3}

would label the appropriate linear combination of the points labeled A1 and A2 
with the label A3.

Has anyone has already figured out how to incorporate this into PSTricks?  I assume that
raw Postscript code is required.

Thanks,
John Frampton