Este trabalho consiste numa pesquisa pictórica a partir de uma experiência de contemplação de mosaicos geométricos islâmicos medievais. A pesquisa busca fazer um percurso desde o estudo pictórico da urdidura dos mosaicos, mostrando a natureza de seu ritmo e seu movimento até a elaboração e apresentação de um corpo de trabalhos em desenho e pintura que se apropriam deste movimento \"encapsulado\" nos mosaicos, revelando-os. / This work consists in a pictorical research based on the contemplation of Islamic Medieval Geometric Mosaics. The research comprehends the trajectory from the study of Mosaics\' warp, in which are shown their rithm and movement, towards the preparation and presentation of a corpus of works in design and painting that reveals the countless possibilities of moves \"encapsulated\" in the Mosaics.

Este trabalho consiste numa pesquisa pictórica a partir de uma experiência de contemplação de mosaicos geométricos islâmicos medievais. A pesquisa busca fazer um percurso desde o estudo pictórico da urdidura dos mosaicos, mostrando a natureza de seu ritmo e seu movimento até a elaboração e apresentação de um corpo de trabalhos em desenho e pintura que se apropriam deste movimento \"encapsulado\" nos mosaicos, revelando-os. / This work consists in a pictorical research based on the contemplation of Islamic Medieval Geometric Mosaics. The research comprehends the trajectory from the study of Mosaics\' warp, in which are shown their rithm and movement, towards the preparation and presentation of a corpus of works in design and painting that reveals the countless possibilities of moves \"encapsulated\" in the Mosaics.

In this thesis a novel approach in generating 3D IGP is applied using shape grammar, an effective pattern generation method. The particular emphasis here is to generate the motifs (repeat unit) in 3D using parameterization, which can then be manipulated within 3D space to construct architectural structures. Three unique distinctive shape grammar algorithms were developed in 3D; Parameterized Shape Grammar (PSG), Auto-Parameterized Shape Grammar (APSG) and Volumetric Shell Shape Grammar (VSSG). Firstly, the PSG generates the motifs in 3D. It allows one to use a single changeable regular 3D polygon, and forms a motif by given grammar rules including, Euclidean transformations and Boolean operations. Next, APSG was used to construct the architectural structures that manipulates the motif by automating the grammar rules. The APSG forms a wall, a column, a self-similarity star and a dome, the main features of Islamic architecture. However, applying Euclidean transformations to create non-Euclidean surfaces resulted in gaps and or overlaps which does not form a perfect tessellation. This is improved upon by the VSSM, which integrates two key methods, shell mapping and coherent point drift, to map an aesthetically accurate 3D IGM on a given surface. This work has successfully presented methods for creating complex intricate 3D Islamic Geometric Motifs (IGM), and provided an efficient mapping technique to form visually appealing decorated structures. / Partially funded by the Centre of Visual Computing (CVC)