From Nominal Capacity to Effective Visibility: 3D Ray-Casting Evaluation of Learning Environments

Learning environments are typically designed according to nominal seating capacity, yet their actual visual performance often falls well below this figure—a discrepancy defined here as an illusion of capacity. Conventional two-dimensional sightline analysis, the standard method for assessing visibility, cannot fully capture the three-dimensional effects of human occlusion or the influence of room scale on visual performance. To address this gap, the study evaluates three higher-education classroom typologies—a flat-floor classroom, a terraced classroom, and a constant-slope auditorium—using a Python-based three-dimensional ray-casting framework. Each seating position is assessed against four criteria: horizontal legibility, vertical strain, two-dimensional sectional clearance, and three-dimensional functional visibility. The results reveal marked differences between the two analytical approaches. In the smaller configuration, the three-dimensional analysis uncovered visible areas overlooked by sectional analysis: effective capacity in the flat-floor classroom increased from 12.50% to 29.16%, and total obstruction in the terraced classroom fell from 45.45% to 36.36%. The large auditorium showed the opposite trend—owing to cumulative shoulder overlap and a phenomenon termed perspective closure, its effective capacity dropped to 6.42% (versus 9.28% by sectional analysis), with 73.57% of seats fully obstructed.