Abstract
In this paper, we present a simple and intuitive approach for designing space filling tiles in 3D space. Our approach is inspired by “scutoids” — shapes that were recently reported to occur in epithelial cells due to topological changes between the extremal (apical and basal) surfaces of epithelia. Drawing from this discovery, we develop the theoretical and computational foundations leading to a generalized procedure for generating Delaunay Lofts — a new class of scutoid-like shapes. Given two extremal surfaces, both with Delaunay diagrams, Delaunay Lofts are shapes that result from Voronoi tessellation of all intermediate surfaces along the curves joining the vertices of Delaunay diagrams that defines the extremal tessellations. This, combined with the use of wallpaper symmetries allows for intuitive design of complex space filling regular and semi-regular tilings in 3D space.
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