@InProceedings{SotoSánchezMedeFigu:2021:PeTiRe,
               author = "Soto S{\'a}nchez, Jos{\'e} Ezequiel and Medeiros e S{\'a}, Asla 
                         and de Figueiredo, Luiz Henrique",
          affiliation = "IMPA and {FGV / EMAp} and IMPA",
                title = "On periodic tilings with regular polygons",
            booktitle = "Proceedings...",
                 year = "2021",
               editor = "Paiva, Afonso and Menotti, David and Baranoski, Gladimir V. G. and 
                         Proen{\c{c}}a, Hugo Pedro and Junior, Antonio Lopes Apolinario 
                         and Papa, Jo{\~a}o Paulo and Pagliosa, Paulo and dos Santos, 
                         Thiago Oliveira and e S{\'a}, Asla Medeiros and da Silveira, 
                         Thiago Lopes Trugillo and Brazil, Emilio Vital and Ponti, Moacir 
                         A. and Fernandes, Leandro A. F. and Avila, Sandra",
         organization = "Conference on Graphics, Patterns and Images, 34. (SIBGRAPI)",
            publisher = "Sociedade Brasileira de Computa{\c{c}}{\~a}o",
              address = "Porto Alegre",
             keywords = "Tessellations, Symmetry, Geometric modeling, Procedural modeling, 
                         Combinatorial geometry.",
             abstract = "The thesis describes a simple integer-based computational 
                         representation for periodic tilings of regular polygons using 
                         complex numbers, which is now the state of the art for these 
                         objects. Several properties of this representation are discussed, 
                         including elegant and efficient strategies for acquisition, 
                         reconstruction, rendering, and automatic crystallographic 
                         classification by symmetry detection. The thesis also describes a 
                         novel strategy for the enumeration and generation of 
                         triangle-square tilings via equivalence with edge-labeled 
                         hexagonal graphs. The equivalence provide triangle-square tilings 
                         with an algebraic structure that allows an unfolding 
                         interpretation.",
  conference-location = "Gramado, RS, Brazil (virtual)",
      conference-year = "18-22 Oct. 2021",
             language = "en",
                  ibi = "8JMKD3MGPEW34M/45DJBDS",
                  url = "http://urlib.net/ibi/8JMKD3MGPEW34M/45DJBDS",
           targetfile = "OnPeriodicTilings_JEzequielSotoS.pdf",
        urlaccessdate = "2024, May 02"
}