A Method to Assess the Geometric Purity of Shadow Lines: A Case Study of Daylighting Conditions

Abstract

Some naturally occurring proportional relationships and geometries have been associated with harmony and the perception of beauty. The Golden Ratio, for example has been a source of inspiration and composition for many art specialties, including architecture. Although there is a relatively large body of literature demonstrating that certain geometries, those with mathematically pure expressions, are visually pleasing, little scholarship exists concerning how these relationships might be integrated into architectural design. This paper aims to describe a method that allows architects to test the geometric purity of lines formed by the edge of light and shadow that result from proposed daylight conditions. The method was applied to different daylighting conditions where the geometric relationships between the aperture, the room walls, and the sun position create the resulting shadow lines. The test for purity includes a statistical
comparison, using R2 as an indicator of correlation between the resulting shadow lines and similar lines with a pure mathematical expression. This methodology is an initial step for developing a design decision-making representation tool that considers integrating geometric purity of daylight within the architectural design process.