Abstract: Methods for determining laser pulse positions for shaping an optical element may comprise: determining a stress field for at least a portion of a substrate, wherein the stress field comprises at least three components of stress, wherein the stress field comprises a plurality of stress states for the at least a portion of the substrate; determining, based at least on the stress field and a calibration model, a spot density over the at least a portion of the substrate; determining, based on the spot density, a laser spot position allocation that arranges a number of laser pulses into a minimum number of lines that achieves the spot density; and causing, based on the laser spot position allocation, output of a machine program that coordinates a rotation stage, beam shaping, a translation stage, and a laser firing parameter for surface shaping of the at least a portion of the substrate.