Abstract
Persian architecture is characterised by shapes and patterns, which can be analysed through mathematical models. Beside 2D patterns, many of the traditional geometric ornaments are realised on 3D surfaces such as domes or vaults. Literature mainly addresses the 3D problem by means of a 2D scheme, which is an important and synthetic representation but is not exhaustive and lacks of clarity. This paper proposes a framework based on the integration of 2D drawings, as in the traditional approach, and a photogrammetric 3D model based on a sample of standard resolution images (tourist pictures). The framework is tested on a muqarnas, a characteristic Persian ornament, in order to study and analyse its modular design and hierarchy of elements. As a case study, the entrance iwan of the Shah Mosque in Isfahan, Iran, is considered. The result is a link between the 3D patterns and the geometry of architectural elements, which completes and overcomes their schematic 2D representation.
Highlights
The occurrence of geometric design language in traditional Persian and modern Iranian buildings reveals the very close relationship between geometry, mathematics, and Persian architecture
Persian architecture is characterised by shapes and patterns, which can be analysed through mathematical models
The framework is tested on a muqarnas, a characteristic Persian ornament, in order to study and analyse its modular design and hierarchy of elements
Summary
The occurrence of geometric design language in traditional Persian and modern Iranian buildings reveals the very close relationship between geometry, mathematics, and Persian architecture. Sarhangi underlines the emotional response evoked by harmonization of decorative elements and, at the same time, the intent of artists and architects of expressing their feelings and beliefs by means of geometrical harmonization The origin of this harmonization is the conscious use of geometric elements, arranged together by means of repetition, pattern, scale, symmetry, self-similarity, colour combination, etc. The second set of modular systems summarised by Cromwell consists of modules decorated with a motif, generally by composing tiles with different shapes and colours. The tiles are still arranged to form tessellation, but their boundaries are not shown in the finished pattern In these decorated modular systems, only the inner geometric decoration contributes to the final pattern. They contain a hierarchy of patterns at different scales
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