An Inverted-U Relationship Between Spatial Openness and Cognitive Engagement: 3D Isovist and EEG

Abstract

This paper investigates the relationship between spatial openness and cognitive engagement, integrating geometric and neurophysiological indicators to address the lack of frameworks directly coupling spatial structure with neural responses. Spatial openness is quantified using three-dimensional isovist volume. Engagement is measured via an EEG-based index (β/(θ + α)). Twenty-six participants completed an experiment in a virtual reality environment in which 16 spatial conditions of varying openness were presented. A node-based framework couples spatial metrics with EEG responses at the level of individual observation points and temporal segments. Linear and quadratic mixed-effects models reveal a small but statistically detectable inverted-U relationship between openness and engagement (marginal R2 = 0.020) that persists after correction for spatial–temporal autocorrelation, with the pattern replicated in 18 of 26 participants. We interpret these findings as preliminary neurophysiological evidence that spatial openness modulates engagement through an optimal range of stimulation, supporting designs that balance visual exposure against spatial boundaries. Generalisation is constrained by the VR-based setting, the limited sample size, and the small absolute effect.