Automatic 3D muqarnas architectural patterns reconstruction using plane representation

Abstract The main objective of this paper is to propose an algorithmic way to build the three-dimensional Islamic architectural muqarnas ornament directly from its plane representations (2D Design pattern). Thus, this paper focus on the extraction from the 2D representation of all the structure information needed for the reconstruction of the 3D muqarnas model. For this purpose, the proposed algorithm is based on two main phases. The first one consists to match each 2D-shape with each possible corresponding 3D-model element by using a 2D-to-3D shape matching approach. The second phase concerns the 3D spatial composition which is based on the neighboring properties of each 2D-shape and its identified 3D-element. Another contribution of this paper concerns the construction of a database of the 3D models corresponding to the set of different 2D-shapes which can be found in a 2D plane representation. The proposed algorithm focuses on the reconstruction of the Moroccan-Andalusian muqarnas style. The performance of this algorithm is assessed by reconstructing old muqarnas patterns and also by generating new ones, which preserve its styles’ authenticity.

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