3D Reconstruction of Moroccan-Andalusian Muqarnas Domes

Abstract

Muqarnas is a three-dimensional Islamic architecture decoration conceived as a spatial arrangement of 3D shapes according to precise geometric rules. Muqarnas work can be performed on several types of materials such as stone, wood, plaster or brick. This paper aims to propose an algorithmic method to construct the circular Moroccan-Andalusian Muqarnas Ornaments from their 2D representation models. The principle is to extract from a 2D design geometric information and underlying rules useful for the construction of its corresponding 3D model. To do so, the first stage consists to determine for each 2D shape of the 2D design model its corresponding 3D Muqarnas element. The second stage consists to perform the spatial composition of these identified 3D elements by using their neighborhood properties. The performance of the proposed method is evaluated by its capacity to reconstruct historical circular Muqarnas ornaments appeared during the Almoravids (1040-1147) and Almohads periods (1147-1269). This performance is further evaluated by the ability of the proposed method to construct all possible variants of a historical 3D Muqarnas ornament by considering the different 3D shapes which can be associated to the same 2D shape.