Abstract
Procedural noise functions have many applications in computer graphics, ranging from texture synthesis to atmospheric effect simulation or to landscape geometry specification. Noise can either be precomputed and stored into a texture, or evaluated directly at application runtime. This choice offers a tradeoff between image variance, memory consumption and performance.
Advanced tiling algorithms can be used to decrease visual repetition. Wang tiles allow a plane to be tiled in a non-periodic way, using a relatively small set of textures. Tiles can be arranged in a single texture map to enable the GPU to use hardware filtering.
In this paper, we present modifications to several popular procedural noise functions that directly produce texture maps containing the smallest complete Wang tile set. The findings presented in this paper enable non-periodic tiling of these noise functions and textures based on them, both at runtime and as a preprocessing step. These findings also allow decreasing repetition of noise-based effects in computer-generated images at a small performance cost, while maintaining or even reducing the memory consumption.
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- Robert Berger. 1966. The undecidability of the domino problem. Memoirs of the American Mathematical Society 66 (1966), 1--72.Google Scholar
- L. Blum, M. Blum, and M. Shub. 1986. A Simple Unpredictable Pseudo-Random Number Generator. SIAM J. Comput. 15, 2 (1986), 364--383. Google Scholar
Digital Library
- Michael F. Cohen, Jonathan Shade, Stefan Hiller, and Oliver Deussen. 2003. Wang Tiles for Image and Texture Generation. ACM Trans. Graph. 22, 3, 287--294. Google Scholar
Digital Library
- Robert L. Cook and Tony DeRose. 2005. Wavelet Noise. ACM Trans. Graph. 24, 3, 803--811. Google Scholar
Digital Library
- Karel Culik, II. 1996. An Aperiodic Set of 13 Wang Tiles. Discrete Math. 160, 1-3 (Nov. 1996), 245--251. Google Scholar
Digital Library
- Sebastien Deguy, Rogelio Olguin, and Brad Smith. 2016. Texturing Uncharted 4: a Matter of Substance. GDC Vault. https://www.gdcvault.com/play/1023488/Texturing-Uncharted-4-a-matterGoogle Scholar
- Alexei A. Efros and William T. Freeman. 2001. Image Quilting for Texture Synthesis and Transfer. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '01). ACM, New York, NY, USA, 341--346. Google Scholar
Digital Library
- Alexander Goldberg, Matthias Zwicker, and Frédo Durand. 2008. Anisotropic Noise. ACM Trans. Graph. 27, 3, Article 54, 8 pages. Google Scholar
Digital Library
- Emmanuel Jeandel and Michael Rao. 2015. An aperiodic set of 11 Wang tiles. https://arxiv.org/pdf/1506.06492.pdfGoogle Scholar
- Jarkko Kari. 1996. A Small Aperiodic Set of Wang Tiles. Discrete Math. 160, 1-3 (Nov. 1996), 259--264. Google Scholar
Digital Library
- Andrew Kensler, Aaron Knoll, and Peter Shirley. 2008. Better Gradient Noise. SCI Institute Technical Report No. UUSCI-2008-001. https://www.cs.utah.edu/~aek/research/noise.pdfGoogle Scholar
- Johannes Kopf, Daniel Cohen-Or, Oliver Deussen, and Dani Lischinski. 2006. Recursive Wang Tiles for Real-time Blue Noise. ACM Trans. Graph. 25, 3 (July 2006), 509--518. Google Scholar
Digital Library
- Ares Lagae and Philip Dutré. 2005. A Procedural Object Distribution Function. ACM Transactions on Graphics 24, 4 (October 2005), 1442--1461. Google Scholar
Digital Library
- Ares Lagae and Philip Dutré. 2006. An Alternative for Wang Tiles: Colored Edges Versus Colored Corners. ACM Trans. Graph. 25, 4 (Oct. 2006), 1442--1459. Google Scholar
Digital Library
- Ares Lagae, Sylvain Lefebvre, Rob Cook, Tony DeRose, George Drettakis, David S. Ebert, John P. Lewis, Ken Perlin, and Matthias Zwicker. 2010. State of the Art in Procedural Noise Functions. In EG 2010 - State of the Art Reports, Helwig Hauser and Erik Reinhard (Eds.). Eurographics, Eurographics Association, Norrkoping, Sweden.Google Scholar
- Ares Lagae, Sylvain Lefebvre, George Drettakis, and Philip Dutré. 2009. Procedural Noise Using Sparse Gabor Convolution. ACM Trans. Graph. 28, 3, Article 54, 10 pages. Google Scholar
Digital Library
- J. P. Lewis. 1989. Algorithms for Solid Noise Synthesis. SIGGRAPH Comput. Graph. 23, 3, 263--270. Google Scholar
Digital Library
- Joel McCormack, Ronald Perry, Keith I. Farkas, and Norman P. Jouppi. 1999. Feline: Fast Elliptical Lines for Anisotropic Texture Mapping. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 243--250. Google Scholar
Digital Library
- Fabrice Neyret and Marie-Paule Cani. 1999. Pattern-based Texturing Revisited. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 235--242. Google Scholar
Digital Library
- NVIDIA. 2004. Improve Batching Using Texture Atlases. NVSDK 7.0 Whitepaper. http://download.nvidia.com/developer/NVTextureSuite/Atlas_Tools/Texture_Atlas_Whitepaper.pdfGoogle Scholar
- Marc Olano. 2005. Modified Noise for Evaluation on Graphics Hardware. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS '05). ACM, New York, NY, USA, 105--110. Google Scholar
Digital Library
- Roger Penrose. 1974. The role of aesthetics in pure and applied mathematical research. Bulletin of the Institute of Mathematics and its Applications 10 (1974).Google Scholar
- Ken Perlin. 1985. An Image Synthesizer. SIGGRAPH Comput. Graph. 19, 3, 287--296. Google Scholar
Digital Library
- Ken Perlin. 2002. Improving Noise. ACM Trans. Graph. 21, 3, 681--682. Google Scholar
Digital Library
- Jos Stam. 1997. Aperiodic texture mapping. Tech. rep., R046. European Research Consortium for Informatics and Mathematics (ERCIM). http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/R046.pdfGoogle Scholar
- Stanley Tzeng and Li-Yi Wei. 2008. Parallel White Noise Generation on a GPU via Cryptographic Hash. In Proceedings of the 2008 Symposium on Interactive 3D Graphics and Games (I3D '08). ACM, New York, NY, USA, 79--87. Google Scholar
Digital Library
- Hao Wang. 1961. Proving theorems by pattern recognition II. Bell Systems Technical Journal 40 (1961), 1--42.Google Scholar
Cross Ref
- Li-Yi Wei. 2004. Tile-based Texture Mapping on Graphics Hardware. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS '04). ACM, New York, NY, USA, 55--63. Google Scholar
Digital Library
- Li-Yi Wei and Marc Levoy. 2000. Fast Texture Synthesis Using Tree-structured Vector Quantization. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '00). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 479--488. Google Scholar
Digital Library
- Guillaume Werle and Benoit Martinez. 2017. Ghost Recon Wildlands, Terrain Technology and Tools. GDC Vault. https://www.gdcvault.com/play/1024029/-Ghost-Recon-Wildlands-TerrainGoogle Scholar
- Steven Worley. 1996. A Cellular Texture Basis Function. In Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '96). ACM, New York, NY, USA, 291--294. Google Scholar
Digital Library
Index Terms
Non-periodic Tiling of Procedural Noise Functions
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