Measuring Housing Privacy Defined as a Function in Urban Neighborhood Blocks: Modeling the Permeability-Opacity Tradeoff

Abstract

This paper is a theory-driven quantitative method in cultural contexts, to produce a novel method for evaluating the impact of Visual Permeability (VP) and Opacity (VO) with a focus on social norms of privacy on privacy in the urban neighborhood fabric. A mathematical model based on the Sigmoid function is developed to quantify privacy (P) by integrating key variables:  VP /VO, Shared Visual Area ( ), and a privacy coefficient (k). The proposed mathematical model based on the Sigmoid function. Across seven neighborhood plans, a non-linear model based on the Sigmoid function was employed across seven neighborhood plans to evaluate the privacy levels by analyzing the surface area of the VP, VO areas, and  network influencing the residential blocks within each neighborhood fabrics. To achieve this, the length and width of each block in the studied neighborhoods were calculated to determine the shaded areas of VP, VO, and  . However, the height as a third dimension was disregarded, since it lies beyond the scope of this study. The obtained results indicated statistically significant privacy outcomes (p<0.01), revealing that privacy levels increase asymptotically with the expansion of VP and VO gaps, since this threshold effects in shared space interactions across the model coefficient sensitivity around k ≈ 2.99. This work advances a quantifiable framework for privacy levels in the urban fabrics, though future studies should integrate dynamic factors, and perceptual validation for optimizing privacy-connectivity balances in neighborhood design.