2001/08/01 by Alejo Hausner · 2 citations
Computer Science · Engineering · Mathematics · #Computer Graphics and Visualization Techniques #3D Shape Modeling and Analysis #Computational Geometry and Mesh Generation #Voronoi diagram #Tile #Centroidal Voronoi tessellation #Computer science #Computer graphics (images) #Square (algebra) #Hexagonal crystal system #Enhanced Data Rates for GSM Evolution #Hexagonal tiling #Graphics #Computer vision #Metric (unit) #Computer graphics #Diagram #Artificial intelligence #Geometry #Mathematics #Grid #Engineering
paper · doi:10.1145/383259.383327
openalex publication_date 2001/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
This paper presents a method for simulating decorative tile mosaics. Such mosaics are challenging because the square tiles that comprise them must be packed tightly and yet must follow orientations chosen by the artist. Based on an existing image and user-selected edge features, the method can both reproduce the image's colours and emphasize the selected edges by placing tiles that follow the edges. The method uses centroidal voronoi diagrams which normally arrange points in regular hexagonal grids. By measuring distances with an manhattan metric whose main axis is adjusted locally to follow the chosen direction field, the centroidal diagram can be adapted to place tiles in curving square grids instead. Computing the centroidal voronoi diagram is made possible by leveraging the z-buffer algorithm available in many graphics cards.