Dynamic Shading Geometric Models for Buildings Based on Boundary Projection and Polygonal Boolean Operations

Addressing the complexity of evaluating dynamic shading performance in building energy-efficient design, this study constructs a full-time solar radiation geometric projection model. The research first establishes a calculation framework for ground-normal direct irradiance considering atmospheric path attenuation, based on solar trajectory theory combined with Beer-Lambert's law and the Kasten & Young correction formula. Subsequently, for complex cantilevered shading structures, an innovative boundary projection algorithm and polygonal Boolean operation logic were introduced. Computational geometry techniques enabled precise determination of the effective sun-exposed area of windows on all facades at any given time. Sensitivity analysis identified the cantilever depth of shading elements as the dominant geometric factor influencing shading performance and demonstrated the necessity of integrating horizontal and vertical shading designs. Experimental validation demonstrates that this model successfully intercepts 86% of radiant energy during the critical summer period, exhibiting significantly superior all-day shading performance compared to conventional standard solutions. This research provides a precise physical modeling foundation and parameter optimization pathway for building cooling and all-day dynamic shading strategies in low-latitude regions.