arXiv subjects

Alexandre Derouet-Jourdan

Publications and source records attributed to Alexandre Derouet-Jourdan.

3 recordsLinked to original sources

arXiv2017

Procedural Wang Tile Algorithm for Stochastic Wall Patterns

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.

cs.GR↗

arXiv2017

A linear algorithm for Brick Wang tiling

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.

cs.DM↗

arXiv2017

Dappled tiling

We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds of tiles. We give an efficient algorithm to turn any tiling into one satisfying the condition, and discuss its applications in texturing.

cs.DM↗