Systems and methods for controlling support structures in manufacturing are provided. In particular, the present disclosure provides systems and methods for characterizing the support volume in the design phase based on a perimeter length of a boundary with undercut, projected along a build direction, referred to as a projected undercut perimeter (PUP). By constraining this PUP, the amount of support structures in resulting designs are effectively controlled. By constraining overhang able based PUP, the resulting designs can self support.