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Muqarnas is an exemplar case of the EPE method. Figure 6 shows an example of this method with a simple design. Fig.6: Square-based, Islamic geometric design was employed to generate the muqarnas-like form shown above through the manipulation of the z-coordinate of the points on different geometric patterns.

Figure 6 Muqarnas is an exemplar case of the EPE method. Figure 6 shows an example of this method with a simple design. Fig.6: Square-based, Islamic geometric design was employed to generate the muqarnas-like form shown above through the manipulation of the z-coordinate of the points on different geometric patterns.

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Muqarnas, a vaulting decorative component, shows some of the earliest attempts to employ Islamic geometric design to generate a three-dimensional composition from two-dimensional design blueprints, as shown in the Topkapi and the Tashkent Scroll (figure 2) (Necipoglu, 1996). Karbandi is another possible employment of geometric designs to derive forms beyond flat surfaces, such as the ribbed dome that exists at the Great Mosque of Cordoba (figure 3). Unlike Mugarnas, the geometry is curved as if it is being projected into a round surface (Mohammadi et al., 2018). Fig.1: Contemporary examples of IGP on non-flat surfaces. Left: Cambridge Mosque (Image credit: Wikimedia). Right: Louver Abu Dhabi (Image credit: authors).
Muqarnas, a vaulting decorative component, shows some of the earliest attempts to employ Islamic geometric design to generate a three-dimensional composition from two-dimensional design blueprints, as shown in the Topkapi and the Tashkent Scroll (figure 2) (Necipoglu, 1996). Karbandi is another possible employment of geometric designs to derive forms beyond flat surfaces, such as the ribbed dome that exists at the Great Mosque of Cordoba (figure 3). Unlike Mugarnas, the geometry is curved as if it is being projected into a round surface (Mohammadi et al., 2018). Fig.1: Contemporary examples of IGP on non-flat surfaces. Left: Cambridge Mosque (Image credit: Wikimedia). Right: Louver Abu Dhabi (Image credit: authors).
Fig.2: Left: page from the Topkapi scroll showing a 2D blueprint of a Mugarnas (Image credit: Wikimedia). Right: Mugarnas in the Iwan of the Shah Mosque in Isfahan, Iran (Image credit: Wikimedia).
Fig.2: Left: page from the Topkapi scroll showing a 2D blueprint of a Mugarnas (Image credit: Wikimedia). Right: Mugarnas in the Iwan of the Shah Mosque in Isfahan, Iran (Image credit: Wikimedia).
Fig.3: The interior part of the dome of the Great Mosque of Cordoba (Image credit: Wikimedia).
Fig.3: The interior part of the dome of the Great Mosque of Cordoba (Image credit: Wikimedia).
Fig.4: Historical examples of the employment of Islamic geometric patterns on non-flat surfaces. Left: the dome of the Karatay Madrasa (Image credit: Wikimedia). Right: the dome of the Sultan Qaytbay Funerary Complex (Image credit: Wikimedia).
Fig.4: Historical examples of the employment of Islamic geometric patterns on non-flat surfaces. Left: the dome of the Karatay Madrasa (Image credit: Wikimedia). Right: the dome of the Sultan Qaytbay Funerary Complex (Image credit: Wikimedia).
Fig. 5: shows the possible designs that can be derived from the same polylines by changing the employed symmetry (from top to bottom: rosettes, periodic, or quasi-periodic structural order). Rosettes patterns are formed by applying rotational symmetry to a particular geometric composition around a specified axis. This type of patterns can have several axes that goes from 1 to oo (Shubnikov 1974). Rosettes patterns have two types: cyclic and dihedral; cyclic is formed by applying rotations to the geometric compositions, while dihedral includes using reflection geometry in addition to the rotational symmetry.
Fig. 5: shows the possible designs that can be derived from the same polylines by changing the employed symmetry (from top to bottom: rosettes, periodic, or quasi-periodic structural order). Rosettes patterns are formed by applying rotational symmetry to a particular geometric composition around a specified axis. This type of patterns can have several axes that goes from 1 to oo (Shubnikov 1974). Rosettes patterns have two types: cyclic and dihedral; cyclic is formed by applying rotations to the geometric compositions, while dihedral includes using reflection geometry in addition to the rotational symmetry.
7ig.7: Left: shows example of a projected 2D Islamic Geometric Design on a curved surface. Right: tiling the derived form with the original 2D Geometric Design.
7ig.7: Left: shows example of a projected 2D Islamic Geometric Design on a curved surface. Right: tiling the derived form with the original 2D Geometric Design.
The Islamic geometric designs parameters are the symmetry type, points count, poin coordinates, and polyline intersections, all of which can explore the latent design space of a 2D Islamic geometric designs. The migration method parameters differ based on the employed method. For instance, the parameters in the Euclidean Point Extrusion are the Z-coordinates of the points and the shape of point connections. However, the parameters in the Curve Projection and Curve Mapping are primarily based on the shape of the HS. When combined, the two sets o parameters allow exploring the latent design space of Islamic geometric designs on a non-fla surface (figure 10). Fig.8: Curves Mapping method applied to a dome-like HS. Top: shows the process of unrolling the equivalent surface, inserting the desired design within, and mapping back the design to the hemisphere. Bottom left: perspective view illuminates the distortion occurring at the bottom edge of the HS when using the Curve Projection method. Bottom right: using Curves Mapping to fit a design into the hemisphere.
The Islamic geometric designs parameters are the symmetry type, points count, poin coordinates, and polyline intersections, all of which can explore the latent design space of a 2D Islamic geometric designs. The migration method parameters differ based on the employed method. For instance, the parameters in the Euclidean Point Extrusion are the Z-coordinates of the points and the shape of point connections. However, the parameters in the Curve Projection and Curve Mapping are primarily based on the shape of the HS. When combined, the two sets o parameters allow exploring the latent design space of Islamic geometric designs on a non-fla surface (figure 10). Fig.8: Curves Mapping method applied to a dome-like HS. Top: shows the process of unrolling the equivalent surface, inserting the desired design within, and mapping back the design to the hemisphere. Bottom left: perspective view illuminates the distortion occurring at the bottom edge of the HS when using the Curve Projection method. Bottom right: using Curves Mapping to fit a design into the hemisphere.
Fig.9: Computational process for exploring the latent design space of Islamic geometric design on non- flat surfaces.
Fig.9: Computational process for exploring the latent design space of Islamic geometric design on non- flat surfaces.
Fig.10: Design variations were created using a fourfold Islamic geometric design and the Curve Projection method.
Fig.10: Design variations were created using a fourfold Islamic geometric design and the Curve Projection method.
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Geometric Design
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