Portraits of Orthogonal Matrices as a Base for Discrete Textile Ornament Patterns

Sergeev, A.; Sergeev, Mikhail; Vostrikov, Anton A.; Kurtyanik, Daniil

doi:10.1007/978-981-13-8303-8_12

Cited by 2 publications

(2 citation statements)

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“…Indeed, patterns are an essential part of aesthetics, that form more or less complex designs. Authors report that there are four kinds of symmetry [38][39][40][41]: translation, bilateral or reflection, rotation and glide reflection. A pattern can be described as the repetition of a motif, which can be symmetrical (whenever they have two or more identical parts) or asymmetrical (whenever it cannot be geometrically deconstructed in equal parts) [40][41][42].…”

Section: Symmetry and Silk Fabricsmentioning

confidence: 99%

“…A pattern can be described as the repetition of a motif, which can be symmetrical (whenever they have two or more identical parts) or asymmetrical (whenever it cannot be geometrically deconstructed in equal parts) [40][41][42]. Symmetrical patterns have a geometrical basis, and no matter how complex these patterns are, they will fall into one of the four kinds of transformations [38,39]. These are possible for a geometric object, depending on the set of geometric transforms available, and on what properties remain unchanged after a transformation.…”

Section: Symmetry and Silk Fabricsmentioning

confidence: 99%

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Applying Axial Symmetries to Historical Silk Fabrics: SILKNOW’s Virtual Loom

et al. 2020

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Symmetry is part of textile art in patterns and motifs that decorate fabrics, which are made by the interlacement of warp and wefts. Moreover, the 3D representation of fabrics have already been studied by some authors; however, they have not specifically dealt with preserving historical weaving techniques. In this paper, we present the SILKNOW’s Virtual Loom, a tool intended to document, preserve and reproduce silk historical weaving techniques from the 15th to the 19th centuries. We focus on the symmetry function and its contribution to art history, textile conservation, and modern design. We analyzed 2028 records from Garin 1820 datasets—a historical industry that still weaves with these techniques—and we reconstructed some historical designs that presented different types of defects. For those images (including fabrics and drawings) that had a symmetrical axis, we applied the symmetry functionality allowing to reconstruct missing parts. Thanks to these results, we were able to verify the usefulness of the Virtual Loom for conservation, analysis and new interpretative advantages, thanks to symmetry analysis applied to historical fabrics.

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Section: Symmetry and Silk Fabricsmentioning

confidence: 99%

Section: Symmetry and Silk Fabricsmentioning

confidence: 99%

Applying Axial Symmetries to Historical Silk Fabrics: SILKNOW’s Virtual Loom

et al. 2020

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Interrelation of Symmetry and Antisymmetry of Quasi-Orthogonal Cyclic Matrices with Prime Numbers

Sergeev

2023

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Quasi-orthogonal Hadamard matrices and Mersenne matrices with two and three values of the elements, used in digital data processing, are considered, as well as the basis of error-correcting codes and algorithms for transforming orthogonal images. Attention is paid to the structures of cyclic matrices with symmetries and antisymmetries. The connection between symmetry and antisymmetry of structures of cyclic Hadamard and Mersenne matrices on a orders equal to prime numbers, products of close primes, composite numbers, powers of a prime number is shown. Separately, orders equal to the degrees of the prime number 2 are distinguished, both the orders of Hadamard matrices and the basis of the composite orders of Mersenne matrices of block structures with two element values. It is shown that symmetric Hadamard matrices of cyclic and bicyclic structures, according to the extended Riser boundary, do not exist on orders above 32. Mersenne matrices of composite orders belonging to the sequence of Mersenne numbers 2k ‒ 1 nested in the sequence of orders of the main family of Mersenne matrices 4t ‒ 1 exist in a symmetric and antisymmetric form. For orders equal to the powers of a prime number, Mersenne matrices exist in the form of block-diagonal constructions with three element values. The value of prime power determines the number of blocks along the diagonal of the matrix on which the elements with the third value are located. The cyclic blocks are symmetrical and antisymmetric.

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Portraits of Orthogonal Matrices as a Base for Discrete Textile Ornament Patterns

Cited by 2 publications

References 5 publications

Applying Axial Symmetries to Historical Silk Fabrics: SILKNOW’s Virtual Loom

Applying Axial Symmetries to Historical Silk Fabrics: SILKNOW’s Virtual Loom

Interrelation of Symmetry and Antisymmetry of Quasi-Orthogonal Cyclic Matrices with Prime Numbers

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