Integrated circuit designs are continually shrinking in size. Lithographic processes are used to transfer these designs to a semiconductor substrate. These processes typically require that the exposure wavelength of light be shorter than the smallest dimension of the elements within the circuit design. When this is not the case, exposure energy such as light behaves more like a wave than a particle. Additionally, mask manufacturing, photoresist chemical diffusion, and etch effects cause pattern transfer distortions. The result is that circuit elements do not print as designed. To counter this effect the circuit designs themselves can be altered so that the final printed results better matches the initial desired design. The process of altering designs in this way is called Lithographic Proximity Correction (LPC). Square (142), cross (162), octagon (172), and hammerhead (202) serifs are added to integrated circuit designs by shape manipulation functions to perform two dimensional (2-D) LPC.