Modelling hidden geometry in Madrid “malice houses” (1561–1788): Reversing traces in enlargements to discover original, ingenious designs

This paper introduces a pioneering 2D analytical framework for unveiling unique “malice houses” (1561–1788)—low-rise, ugly, and uneven in appearance—in Madrid's historic city. The research focuses on how the main floor was either cleverly or awkwardly concealed, circumventing the imposed lodgement. “Malice” geometry must be uncovered, as no records or preserved examples exist. Critical findings regarding two-storey houses and a primary approach to the non-existent “Malice” archives established essential parameters. Strategies developed include facade height regulations, traditional carpentry roof design (1636), cross-section agreement methodology, and hidden floor possibilities. The necessary structural coherence between elevation components, load-bearing wall spans, and roof design revealed crucial adjustments to explore in a basic two-span model. The relationship between proportion, uneven elevations, and symmetrical (1–4) and asymmetrical (5–6) cross-section models is highlighted. Breakthroughs are achieved by unveiling two enlarged malice houses leading to Model 7, an incomplete cross-section with a symmetrical gable (1759) and an uneven high-rise facade with a low-rise floor (1777). Reversing construction in later enlargement by featuring ingenious roof geometry and low-rise floors opens future research opportunities for discovering preserved historic buildings, uncommon carpentry designs and 2D-to-3D modelling in complex buildings.