||Automating this could entail a large amount of work. There is a dataset in Minnesota that is a mathematically created quarter-quarter coverage of the entire state at http://deli.dnr.state.mn.us/metadata.html?id=L230000012102 ... click on the FULL metadata option to find contact info. This also contains good documentation of how it was done and with what inputs.
Conceptually, it is just a matter of measuring sides, halving them, connecting the dots, then repeating for the quarters. If an intersection is created at the section center, it will even work with irregular shapes.
Not sure if that will help, but it might get you started. If you are doing a smaller number of sections, it will probably save you time to do the work manually. AutoCAD has some very good, easy functions that make the work quick.