{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:10Z","timestamp":1760060230194,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:00:00Z","timestamp":1755043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Research and Development Programs of Zhejiang Province","award":["2024C01210"],"award-info":[{"award-number":["2024C01210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the context of the deep integration of digital art and geometric computing, this paper proposes a digital art pattern generation method with arbitrary quadrilateral tiling. The aim is to break through the limitations of traditional fixed tiling templates in terms of adaptability to irregular tiling shapes, controllability of local deformations, and naturalness of boundary transitions. By decoupling the topological stability of quadrilaterals from deformation parameters and combining the Coons surface interpolation method, a smooth invariant mapping for the fundamental region of arbitrary quadrilaterals is constructed, solving the seamless splicing problem of irregular fundamental region. This method supports real-time editing of quadrilateral shape and colors the fundamental region based on the dynamical system model to generate periodic seamless patterns with global symmetry and controllable local details. Experiments show that the proposed method can be adapted to any quadrilateral structure, from regular rectangles to non-convex polygons. By adjusting the interpolation parameters and dynamical system functions, the symmetry, texture complexity, and visual rhythm of the patterns can be flexibly regulated. The algorithm achieves efficient computation under GPU parallel optimization (with an average generation time of 0.25 s per pattern), providing a new solution for the pattern generation and personalized design of digital art patterns.<\/jats:p>","DOI":"10.3390\/sym17081315","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T13:30:38Z","timestamp":1755091838000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Digital Art Pattern Generation with Arbitrary Quadrilateral Tilings"],"prefix":"10.3390","volume":"17","author":[{"given":"Chenzhi","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianlaier","family":"Bao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diqing","family":"Qian","sequence":"additional","affiliation":[{"name":"Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9518-7063","authenticated-orcid":false,"given":"Yao","family":"Jin","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3638048","article-title":"Creation of Dihedral Escher-like Tilings Based on As-Rigid-As-Possible Deformation","volume":"43","author":"Nagata","year":"2024","journal-title":"ACM Trans. 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