Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Development and evaluation of a digital tool for virtual reconstruction of historic Islamic geometric patterns

For the purpose of cultural heritage preservation, the task of recording and reconstructing visually complicated architectural geometrical patterns is facing many practical challenges. Existing traditional technologies rely heavily on the subjective nature of our perceptual power in understanding its complexity and depicting its color differences. This study explores one possible solution, through utilizing digital techniques for reconstructing detailed historical Islamic geometric patterns. Its main hypothesis is that digital techniques offer many advantages over the human eye in terms of recognizing subtle differences in light and color. The objective of the study is to design, test and evaluate an automatic visual tool for identifying deteriorated or incomplete archaeological Islamic geometrical patterns captured in digital images, and then restoring them digitally, for the purpose of producing accurate 2D reconstructed metric models. An experimental approach is used to develop, test and evaluate the specialized software. The goal of the experiment is to analyze the output reconstructed patterns for the purpose of evaluating the digital tool in respect to reliability and structural accuracy, from the point of view of the researcher in the context of historic preservation. The research encapsulates two approaches within its methodology; Qualitative approach is evident in the process of program design, algorithm selection, and evaluation. Quantitative approach is manifested through using mathematical knowledge of pattern generation to interpret available data and to simulate the rest based on it. The reconstruction process involves induction, deduction and analogy. The proposed method was proven to be successful in capturing the accurate structural geometry of the deteriorated straight-lines patterns generated based on the octagon-square basic grid. This research also concluded that it is possible to apply the same conceptual method to reconstruct all two-dimensional Islamic geometric patterns. Moreover, the same methodology can be applied to reconstruct many other pattern systems. The conceptual framework proposed by this study can serve as a platform for developing professional softwares related to historic documentation. Future research should be directed more towards developing artificial intelligence and pattern recognition techniques that have the ability to suplement human power in accomplishing difficult tasks

Computational Investigation of the Morphological Design Dimensions of Historic Hexagonal-Based Islamic Geometric Patterns

This dissertation examines the morphology of Islamic Geometric Patterns (IGP). Using mixed methods, including the simulation of historical designs and content analysis, this dissertation explores the question of how it is possible to mathematically describe the IGP. The study argues that the compositional analysis of geometry is not solely sufficient to investigate the design characteristics of the IGP, and the underlying mathematics and computational nature of the IGP should be considered when investigating historical IGP. The study presents a parametric description method that captures the reality of the IGP in numeric form and utilizes the form to derive representational codes that include the information necessary to construct a geometry. The representational codes are utilized to further investigate the actual and virtual design space of the IGP, aiming at identifying morphological similarities between historical designs. This research challenges the long-standing paradigm that considers compositional analysis to be the key to researching historical IGP. Adopting a mathematical description shows that the historical focus on existing forms has left the relevant structural similarities between historical IGPs understudied. The research focused on the historical, hexagonal-based IGP and found that hexagonal-based IGP designs correlate to each other beyond just the actualized dimension and that deep, morphological connections exist in the virtual dimension. Using historical evidence, this dissertation identifies these connections and presents a categorization system that groups designs together based on their ‘morphogenetic’ characteristics

Geometric Patterns in Egyptian Architecture & Interior Design

This study will examine the role of geometric patterns in selected examples of Egyptian architecture, interior architecture and art. Ancient Egyptian, Coptic, and Islamic periods are the selected historical ages from Egyptian heritage due to the abundance of different works and styles with geometric pattern characteristics during their periods. In addition to the historical periods, the study will demonstrate some selected models from Egyptian contemporary architecture and arts. These models include architectural projects, traditional craft products and artistic works with geometrical characteristics. The study aims, through the extracted information, to increase the awareness about the effective role of geometric patterns as an architectural and artistic capability and to clarify the degree of freedom, flexibility and functionality as an inherent feature through demonstrating the different practices, styles and materials

A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns

[EN] This article presents a new method for analysing mosaics based on the mathematical principles of Symmetry Groups. This method has been developed to get the understanding present in patterns by extracting the objects that form them, their lattice, and the Wallpaper Group. The main novelty of this method resides in the creation of a higher level of knowledge based on objects, which makes it possible to classify the objects, to extract their main features (Point Group, principal axes, etc.), and the relationships between them. In order to validate the method, several tests were carried out on a set of Islamic Geometric Patterns from different sources, for which the Wallpaper Group has been successfully obtained in 85% of the cases. This method can be applied to any kind of pattern that presents a Wallpaper Group. Possible applications of this computational method include pattern classification, cataloguing of ceramic coatings, creating databases of decorative patterns, creating pattern designs, pattern comparison between different cultures, tile cataloguing, and so on.The authors wish to thank the Patronato de la Alhambra y Generalife (Granada, Spain) and the Patronato del Real Alcázar de Sevilla (Seville, Spain) for their valuable collaboration in this research work.Albert Gil, FE.; Gomis Martí, JM.; Blasco, J.; Valiente González, JM.; Aleixos Borrás, MN. (2015). A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns. Computer Vision and Image Understanding. 130:54-70. doi:10.1016/j.cviu.2014.09.002S547013

The sources of Ibn Tulun\u27s soffit decoration

Ornamental decoration has been studied extensively by various art historians who have provided a multitude of interpretations for the underlying reasons behind the use of different ornaments as well as the influence different eras had on the design of ornament. Stucco played an important role as a decorative element used throughout the ages; it is considered an inexpensive way of decoration as well as a speedy one. Stucco decoration was also perceived by some to convey special meaning and has been analysed from an architectural as well as a geometrical perspective. This thesis proposes to examine the source of the stucco decoration of the mosque of Ibn Tulun’s soffits according to their pattern. Some previous scholars have attributed them to Byzantine sources, others to Abbasid Samarra. This study will attempt to determine where the closest parallels lie. It will also trace the origins of the patterns, examining the question of whether the Samarra patterns are completely original, or whether they in turn are indebted to Byzantine or Roman prototypes

Re-inventing ceramic tiles: Using shape grammars as a generative method and the impact on design methodology

The following paper describes the process and results achieved with the workshop entitled ‘Re-inventing Portuguese ceramic tiles’ reflecting on design methodology and design teaching. Workshop participants were invited to rethink ceramic tile patterns developing a different process which used shape grammars as a generative system. Each participant group developed a three stage task using shape grammars principles and methodology. The preliminary results the work developed are of particular relevance in shape grammar research: firstly shape grammar formulae does not constitute an intuitive process to most creative designers which are often trained to design singular solutions for a specific problem, secondly more than one operative shape grammar can be formulated to represent the same corpus of solutions and lastly the generative potential of grammars transcends the normal capacities of the original grammarist aiding in design exploration and enlarging the corpus of feasible solutions. This paper also reflects on the impact of shape grammars as a design methodology.info:eu-repo/semantics/submittedVersio