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Wang Tiles for Image and Texture Generation Michael Cohen Microsoft Research Jonathan Shade University of Washington and WildTangent Stefan Hiller University.

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Presentation on theme: "Wang Tiles for Image and Texture Generation Michael Cohen Microsoft Research Jonathan Shade University of Washington and WildTangent Stefan Hiller University."— Presentation transcript:

1 Wang Tiles for Image and Texture Generation Michael Cohen Microsoft Research Jonathan Shade University of Washington and WildTangent Stefan Hiller University of Constance Oliver Deussen University of Constance

2 Wang Tiles Rules –Tilings are assembled by matching like edges –Tiles cannot be rotated In 1961 Wang asserted that no aperiodic set of tiles exists, i.e., a set that –COULD tile the plane –could NOT tile it periodically He was wrong, but still got to keep his name on them Aperiodic sets can be used to –Simulate Turing machines –Act as life forms in science fiction (Wangs Carpets by Greg Egan)

3 Wang Tiles – not new to CG Jos Stam –Showed the use of aperiodic tile sets for texture assembly

4 Wang Tiles – not new to CG Jos Stam –Showed the use of aperiodic tile sets for texture assembly Neyret and Cani –Used triangular tiles with coded edges to assure continuous texture

5 Wang Tiles Mirrored Wang Tiles

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7 We introduce non-periodic tilings –set can trivially tile the plane periodically –simple stochastic algorithm non-periodic aperiodic non-periodic

8 2 colors = 8 tiles 3 colors = 18 tiles C colors ? Wang Tiles 2 x C 2

9 Why Wang Tiles? Once you fill a set of Wang Tiles with stuff You can create as much of that stuff as you want for almost free. Free stuff! Demo

10 Wang Tiles for Texture Synthesis

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15 Demo

16 Wang Tiles for Texture Synthesis

17 Wang Tiles: the corner problem ?

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19 A better solution? Lefebvre and Neyret, I3D 2003

20 Poisson Disc Distributions Wang Tiles for Distributions

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30 3D Wang Tiles Volumetric tiles filled with 3D texture In this example, 2.5D Layered Depth Image samples

31 3D Wang Tiles Hierarchical View Dependent

32 3D Wang Tiles

33 Wang Tiles Simple stochastic assembly: non-periodic Texture synthesis Distribution synthesis The corner problem Some 3D applications Free stuff!

34 Wang Tiles THANK YOU Don Mitchell Alex Colburn Reviewers


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