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A typical workflow for producing computer-generated Islamic patterns. Further transformations may include: interlacing, coloration, integration in a virtual scene, illumination, texture mapping etc.
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![Fig. 7. (a) Islamic pattern from [Bourgoin 1879, plate 97] (b) its...](profile/Victor-Ostromoukhov/publication/221448409/figure/fig5/AS:668928602812426@1536496415714/a-Islamic-pattern-from-Bourgoin-1879-plate-97-b-its-Cayley-diagram-c-its_Q320.jpg)
This article presents mathematical tools for computer-generated ornamental patterns, with a particular attention payed to
Islamic patterns. The article shows how, starting from a photo or a sketch of an ornamental figure, the designer analyzes
its structure and produces the analytical representation of the pattern. This analytical representation in...
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Citations
... Abas and Salman (1992), employ group theory to devise an IGP algorithm. Ostromoukhov (1998), extends Abas and Salman's approach to provide systematic guidelines for Moorish art's two predominant symmetry families. Hankin (1925), introduced an archaeological observation of geometric patterns in an Indian Turkish bath, featuring an underlying polygonal grid. ...
... Some researchers have utilized symmetry group theory to categorize, examine, and produce Islamic geometric patterns. Computerized methods based on symmetry group theory are also accessible for generating these patterns [18][19][20]. Furthermore, there are comparable methods capable of constructing Islamic self-similar and quasiperiodic patterns [21][22][23]. ...
6-point girihs (6-point Islamic geometric patterns) are among the earliest and most popular geometric patterns created by Muslim artists in Iran. Some of them have distinctive behavior compared to the majority of Islamic geometric patterns. This paper examines the motifs used in 6-point girihs and categorizes them into basic and secondary motifs. We propose a method for constructing 6-point girihs based on symmetry group theories. The method involves a step-by-step process starting from constructing the minimal essential information (template motif) required to generate a particular symmetry type within the fundamental region, to replicating the unit girih in a two-dimensional plane using a suitable net of 6-point girihs. Finally, we present a notation system consisting of six parameters to construct the basic motifs of p6m 6-point girihs.
... They are used in the creation of graphic designs of high artistic quality and in the field of security graphics [3]. In addition, the development of computer graphics allows for the research and creation of mathematical tools for computer-generated ornamental patterns to create images [4]. To improve image quality without increasing the resolution of the square pixels, variable shaped pixels are used [5,6]. ...
This paper proposes a method for changing pixel shape by converting a CMYK raster image (pixel) to an HSB vector image, replacing the square cells of the CMYK pixels with different vector shapes. The replacement of a pixel by the selected vector shape is done depending on the detected color values for each pixel. The CMYK values are first converted to the corresponding RGB values and then to the HSB system, and the vector shape is selected based on the obtained hue values. The vector shape is drawn in the defined space, according to the row and column matrix of the pixels of the original CMYK image. Twenty-one vector shapes are introduced to replace the pixels depending on the hue. The pixels of each hue are replaced by a different shape. The application of this conversion has its greatest value in the creation of security graphics for printed documents and the individualization of digital artwork by creating structured patterns based on the hue.
... By focusing on two-dimensional periodic patterns, many studies have used computer graphic facilities to generate, study and analyze IGPs through planar symmetry groups [45,109] or tiling-based methods [44]. Ostromoukhov [110] utilized mathematical tools to analyze and generate two-dimensional IGPs. Rasouli et al. [111] introduced two algorithms for computer-generated IGPs, 8-Zohreh, and 8-Sili. ...
Currently, there is a tendency to use Islamic Geometric Patterns (IGPs) as important identities and cultural elements of building design in the Middle East. Despite high demand, lack of information about the potential of IGPs principles have led to formal inspiration in the design of existing buildings. Many research studies have been carried out on the principles of IGPs. However, comprehensive studies relating to new possibilities, such as structure-based, sustainable-based, and aesthetic-based purposes, developed by computer science and related technologies, are relatively rare. This article reviews the state-of-the-art knowledge of IGPs, provides a survey of the main principles, presents the status quo, and identifies gaps in recent research directions. Finally, future prospects are discussed by focussing on different aspects of the principles in accordance with collected evidence obtained during the review process.
... In a two-dimensional plane, patterns are expressed as belonging to one of the seven frieze groups or to one of the seventeen wallpaper groups. The most comprehensive of these is considered classification by Abas and Salman (1994) (see also Ostromoukhov 1998). These symmetries are divided into seventeen symmetrical groups, allowing the same shape to be expanded with multiple copies. ...
The Islamic architectural heritage permits us to understand the formation and
development of geometric patterns. Many techniques are used to express the
patterns related to the forms, and the geometric principles underlying the designs
are revealed mainly via compass and ruler. Generally, it is not sufcient to express
complex patterns with a single technique, and diferent methods are used together.
In this context, in the analysis of geometric patterns of İzzettin Keykavus tomb, a
combined technique using simple drawing tools such as point-joining with the
composition technique according to the symmetrical background of the seventeen
wallpaper patterns is used. When the created patterns are compared, it is seen
that the patterns with similar basic units can difer with the change of symmetry
elements.
... Alternatively, other works have been based on symmetry group theory to analyze and classify Islamic star patterns (Grünbaum, Grünbaum and Shepard, 1986;Ostromoukhov, 1998;Djibril, Hadi and Thami, 2006;Wichmann, 2008;Rønning, 2009;Yassine et al., 2020;Ouazene, Khamjane and Benslimane, 2022). The investigations are largely analytical in all the papers above and focus on existing patterns. ...
Thanks to its beauty and its mathematical rigor, Islamic art has attracted the
attention of crystallographers, mathematicians, designers, artists, and architects. Among
scientific literature, various works have been performed to analyze the mathematical
structures of its ornaments and investigate their construction techniques. This paper will
first analyze the traditional Tastir style to design the sixteen-fold rosettes frequently used
in Moroccan and Andalusian geometric art. Based on this analysis, we will then propose
a computerized method to construct patterns with a sixteen-fold rosette.
... In 1998 Ostromoukhov developed Abas and Salman's in 17 groups format. His method uses a Cayley graph for drawing a pattern [29]. This diagram encodes group information in a graph. ...
Hundreds of years ago, Muslim artisans began to decorate architectural surfaces with geometric designs, And they created great masterpieces. Unfortunately, there is not much documentation on calculating and designing these artifacts, but few studies have examined these patterns from an algorithmic perspective. This article reviews the existing studies in the field of algorithmic analysis of Islamic geometric patterns. Its main purpose was to provide a classification of algorithms for drawing and analyzing Islamic geometric patterns. Finally, the advantages and disadvantages of the most important algorithms in this field are described.
... For what WHITEHEAD [Whi10] calls mathematical/scientific ornamentation in the context of games, the author describes tiling and symmetry as the most relevant rules. Combined with interlacing parts of the pattern while repeating and tiling elements, these principles are able to systematically describe Islamic [Ost98] and Celtic [Cro93] patterns, moving towards the traditional designs given in Figure 3. ...
We review recent methods in 2D creative pattern generation and their control mechanisms, focusing on procedural methods. The review is motivated by an artist's perspective and investigates interactive pattern generation as a complex design problem. While the repetitive nature of patterns is well‐suited to algorithmic creation and automation, an artist needs more flexible control mechanisms for adaptable and inventive designs. We organize the state of the art around pattern design features, such as repetition, frames, curves, directionality, and single visual accents. Within those areas, we summarize and discuss the techniques' control mechanisms for enabling artist intent. The discussion includes questions of how input is given by the artist, what type of content the artist inputs, where the input affects the canvas spatially, and when input can be given in the timeline of the creation process. We categorize the available control mechanisms on an algorithmic level and categorize their input modes based on exemplars, parameterization, handling, filling, guiding, and placing interactions. To better understand the potential of the current techniques for creative design and to make such an investigation more manageable, we motivate our discussion with how navigation, transparency, variation, and stimulation enable creativity. We conclude our review by identifying possible new directions that can inspire innovation for artist‐centered creation processes and algorithms.
... Our approach is closer in spirit to that of Ostromoukhov [27], who explained how to represent a plane ornamental pattern, such as an Islamic pattern, by manually analyzing its structure. He also showed how to render the pattern from its representation. ...
We describe a representation for periodic tilings of the plane by regular polygons. Our approach is to represent explicitly a small subset of seed vertices from which we systematically generate all elements of the tiling by translations. We represent a tiling concretely by a (2+n)×4 integer matrix containing lattice coordinates for two translation vectors and n seed vertices. We discuss several properties of this representation and describe how to exploit the representation elegantly and efficiently for reconstruction, rendering, and automatic crystallographic classification by symmetry detection.
... They derive mathematical tools to analyze and predict the properties of Islamic star patterns when elaborated over the en-tire plane. Ostromoukhov [22] 26,27]. Jowers et al. [28] propose a generative method based on the symmetry group approach and on the shape grammar formalism. ...
In this paper, we will present a method based on the symmetry group theory to construct Islamic star patterns. The method builds star patterns using one or multiple kinds of stars/rosettes from a fundamental region of a given symmetry group and a few intuitive parameters. This paper explains the procedure used in the arrangement and construction of the stars/rosettes within the fundamental region. Given a symmetry group, the method begins by constructing, within the fundamental region, the minimal essential information (template motif) needed to generate a particular symmetry type. The constructed template motif, on which we operate a set of transformations that depend on the symmetry group, gives birth to the unit motif (content of the unit cell). Finally, the entire pattern is obtained by replicating the unit motif in a suitable net. The paper gives a set of generated patterns for the most encountered symmetry groups in Islamic geometric art.
