2023/10/23 by Haard Panchal, Ergün Akleman, Panchal, Haard +7
Engineering · #Advanced Materials and Mechanics #Architecture and Computational Design #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR)
paper · pdf · doi:10.48550/arxiv.2310.15361
openalex publication_date 2023/10/23 · openalex created_date 2023/10/26 · openalex updated_date 2026/07/28
In this paper, we present a new approach to obtain symmetric tiles with curved edges. Our approach is based on using higher-order Voronoi sites that are closed under wallpaper symmetries. The resulting Voronoi tessellations provide us with symmetric tiles with curved edges. We have developed a web application that provides real-time tile design. Our application can be found at https://voronoi.viz.tamu.edu. One of our key findings in this paper is that not all symmetry operations are useful for creating curved tiles. In particular, all symmetries that use mirror operation produce straight lines that are useless for creating new tiles. This result is interesting because it suggests that we need to avoid mirror transformations to produce unusual space-filling tiles in 2D and 3D using Voronoi tessellations.