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Register a new userProcedural Wang Tile Algorithm for Stochastic Wall Patterns
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Added by
Alexandre Derouet-Jourdan
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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The game and movie industries always face the challenge of reproducing materials. This problem is tackled by combining illumination models and various textures (painted or procedural patterns). Gnerating stochastic wall patterns is crucial in the creation of a wide range of backgrounds (castles, temples, ruins...). A specific Wang tile set was introduced previously to tackle this problem, in a non-procedural fashion. Long lines may appear as visual artifacts. We use this tile set in a new procedural algorithm to generate stochastic wall patterns. For this purpose, we introduce specific hash functions implementing a constrained Wang tiling. This technique makes possible the generation of boundless textures while giving control over the maximum line length. The algorithm is simple and easy to implement, and the wall structure we get from the tiles allows to achieve visuals that reproduce all the small details of artist painted walls.
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The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2015 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.
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