Future NASA flagship missions will require the collecting area and resolving power of 6 meter or larger aperture telescopes. Due to limits in fairing size, highly accurate and stable segmented primary mirrors are desirable for achieving these apertures. Due to periodic discontinuities, hexagonally segmented mirrors have intrinsic diffraction grating-like structures, causing pronounced starburst point spread functions (PSFs). To mitigate unwanted image plane diffraction, we have designed and simulated a novel curved-edge segmentation method, called pinwheel segmentation, which more closely emulates a filled circular primary aperture. A parametric solution space for pinwheel segmentation has been developed and used to create in-house Python code which can be integrated with two optical propagation software: Physical Optics Propagation in Python (POPPY) and High Contrast Imaging in Python (HCIPy). Using HCIPy, we demonstrate optimized pinwheel design solutions which are less sensitive to realistic degradation scenarios on-orbit such as optical surface errors and beamwalk due to observatory pointing errors. Additionally, to demonstrate its potential benefits for high-contrast astrophysics, coronagraphy was compared using 6-meter class hexagonal and pinwheel segmented primary mirrors. Preliminary results demonstrate the advantages of alternative segmentation geometries when degraded PSFs are considered. The increased performance and robustness of pinwheel segmentation have the potential of significantly increasing science returns for future missions while reducing spacecraft operational constraints and cost.