Non-periodic Tiling of Procedural Noise Functions
Article No.: 32, Pages 1 - 15
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.
Supplementary Material
Supplemental movie, appendix, image and software files for, Non-periodic Tiling of Procedural Noise Functions
- Download
- 432.31 KB
References
[1]
Robert Berger. 1966. The undecidability of the domino problem. Memoirs of the American Mathematical Society 66 (1966), 1--72.
[2]
L. Blum, M. Blum, and M. Shub. 1986. A Simple Unpredictable Pseudo-Random Number Generator. SIAM J. Comput. 15, 2 (1986), 364--383.
[3]
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.
[4]
Robert L. Cook and Tony DeRose. 2005. Wavelet Noise. ACM Trans. Graph. 24, 3, 803--811.
[5]
Karel Culik, II. 1996. An Aperiodic Set of 13 Wang Tiles. Discrete Math. 160, 1-3 (Nov. 1996), 245--251.
[6]
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-matter
[7]
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.
[8]
Alexander Goldberg, Matthias Zwicker, and Frédo Durand. 2008. Anisotropic Noise. ACM Trans. Graph. 27, 3, Article 54, 8 pages.
[9]
Emmanuel Jeandel and Michael Rao. 2015. An aperiodic set of 11 Wang tiles. https://arxiv.org/pdf/1506.06492.pdf
[10]
Jarkko Kari. 1996. A Small Aperiodic Set of Wang Tiles. Discrete Math. 160, 1-3 (Nov. 1996), 259--264.
[11]
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.pdf
[12]
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.
[13]
Ares Lagae and Philip Dutré. 2005. A Procedural Object Distribution Function. ACM Transactions on Graphics 24, 4 (October 2005), 1442--1461.
[14]
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.
[15]
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.
[16]
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.
[17]
J. P. Lewis. 1989. Algorithms for Solid Noise Synthesis. SIGGRAPH Comput. Graph. 23, 3, 263--270.
[18]
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.
[19]
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.
[20]
NVIDIA. 2004. Improve Batching Using Texture Atlases. NVSDK 7.0 Whitepaper. http://download.nvidia.com/developer/NVTextureSuite/Atlas_Tools/Texture_Atlas_Whitepaper.pdf
[21]
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.
[22]
Roger Penrose. 1974. The role of aesthetics in pure and applied mathematical research. Bulletin of the Institute of Mathematics and its Applications 10 (1974).
[23]
Ken Perlin. 1985. An Image Synthesizer. SIGGRAPH Comput. Graph. 19, 3, 287--296.
[24]
Ken Perlin. 2002. Improving Noise. ACM Trans. Graph. 21, 3, 681--682.
[25]
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.pdf
[26]
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.
[27]
Hao Wang. 1961. Proving theorems by pattern recognition II. Bell Systems Technical Journal 40 (1961), 1--42.
[28]
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.
[29]
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.
[30]
Guillaume Werle and Benoit Martinez. 2017. Ghost Recon Wildlands, Terrain Technology and Tools. GDC Vault. https://www.gdcvault.com/play/1024029/-Ghost-Recon-Wildlands-Terrain
[31]
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.
Index Terms
- Non-periodic Tiling of Procedural Noise Functions
Recommendations
Procedural noise using sparse Gabor convolution
Noise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a ...
An alternative for Wang tiles: colored edges versus colored corners
In this article we revisit the concept of Wang tiles and introduce corner tiles, square tiles with colored corners. During past years, Wang tiles have become a valuable tool in computer graphics. Important applications of Wang tiles include texture ...
Wang Tiles for image and texture generation
We present a simple stochastic system for non-periodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of ...
Comments
Information & Contributors
Information
Published In
Copyright © 2018 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 24 August 2018
Published in PACMCGIT Volume 1, Issue 2
Check for updates
Author Tags
Qualifiers
- Research-article
- Research
- Refereed
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 226Total Downloads
- Downloads (Last 12 months)27
- Downloads (Last 6 weeks)0
Reflects downloads up to 27 Jul 2024
Other Metrics
Citations
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in