• • Single irregular heliostats achieve an optical efficiency of 0.8022, outperforming square (0.7372), pentagonal (0.7453), hexagonal (0.7485), heptagonal (0.7491), octagonal (0.7502), and circular (0.7513) geometries by 6.8–8.8% relative improvement, directly reducing the mirror area required per unit of thermal power and lowering capital expenditure on heliostat fields.
• • The reverse projection method eliminates ray-intersection checks with the receiver by transforming the problem into ray-heliostat intersection tests, reducing computational overhead for optical efficiency evaluation; this enables rapid iteration over thousands of heliostat shapes and layouts without sacrificing accuracy, as validated by the consistency of the north-high/south-low and center-high/edge-low energy density patterns with established models.
• • The no-blocking dense layout, combining Campo and EB arrangements, avoids the need to compute shadowing and blocking arrays, simplifying the efficiency calculation to a product of effective flux density, shadowing array, and shape array; this reduces simulation complexity while maintaining a stable optical efficiency of 0.8022 for irregular heliostats, demonstrating robustness across varying field positions.
• • The effective energy flux density distribution on heliostats, derived by reordering the total power integral to integrate over the receiver first, provides a direct spatial map of irradiance that can be thresholded to define optimal heliostat shapes; this data-driven shaping yields a 0.8022 efficiency versus 0.7372 for squares, translating to a 8.8% reduction in mirror area for equivalent power and a corresponding decrease in land use and structural costs.