Irradiance-weighted cellular method for external shading geometry design: A Beijing case study

External shading intercepts direct-beam radiation before it reaches glazing, reducing cooling-season solar gains while potentially obstructing useful winter gains. Published cellular implementations remain largely restricted to rectangular openings and lack equal-area comparisons with both empirical overhangs and optimized rectangles. We develop a polygon-raster implementation for horizontal overhang planforms. Using a single Beijing International Weather for Energy Calculations typical meteorological year, the method constructs a seasonally signed field weighted by direct normal irradiance; diffuse radiation is excluded. Geometry extraction imposes a protrusion cap, a continuous wall root, and a morphological feature filter, after which all candidate outlines are re-evaluated by continuous forward clipping. Continuous forward and analytical reverse shadow areas agree within rounding, and a 2.5 mm re-extraction changes the continuous regularized score by 0.11 kWh. For a 1 m × 1 m south-facing window at equal panel area (0.344 m 2 ), the regularized outline scores 29.84 kWh. On this intercepted direct-beam-energy proxy at SHGC = 1 —not an HVAC-load metric—it is 19.1 % above the empirical overhang (25.05 kWh) and 5.7 % above the optimized rectangle (28.23 kWh). The optimized rectangle therefore captures most of the gain over the empirical overhang; on the west and east walls the additional free-form margin is only 0.6 % and 1.6 %, respectively.