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'''Perlin noise''' is a [[computer graphics|computer-generated visual effect]] developed by [[Ken Perlin]], who won an [[Academy Award for Technical Achievement]] for inventing it. It can be used to simulate elements from nature, and is especially useful in circumstances where computer memory is limited.
 
==Uses==
[[Image:Perlin_noise.jpg|frame|Two-dimensional slice through 3D Perlin noise.]]
Perlin noise is a [[Procedural_generation|procedural]] [[Texture (computer graphics)|texture]] primitive, a type of [[gradient noise]] used by visual effects artists to increase the appearance of realism in [[computer graphics]]. The function has a [[pseudo-random]] appearance, yet all of its visual details are the same size (see image). This property allows it to be readily controllable; multiple scaled copies of Perlin noise can be inserted into mathematical expressions to create a great variety of [[procedural texture]]s. Synthetic textures using Perlin noise are often used in [[computer-generated imagery|CGI]] to make computer-generated visual elements – such as fire, smoke, or clouds – appear more natural, by imitating the controlled random appearance of textures of nature.
 
It is also frequently used to generate textures when memory is extremely limited, such as in [[Demo (computer programming)|demos]], and is increasingly finding use in [[graphics processing unit]]s for [[real-time graphics]] in [[computer game]]s.
 
==Development==
Perlin noise resulted from the work of [[Ken Perlin]], who developed it at [[Mathematical Applications Group, Inc.]] (MAGI) for [[Disney]]'s [[computer animated]] [[sci-fi]] motion picture ''[[Tron]]'' (1982). In 1997, he won an [[Academy Award for Technical Achievement]] from the [[Academy of Motion Picture Arts and Sciences]] for this contribution to CGI.<ref>Kerman, Phillip. ''Macromedia Flash 8 @work: Projects and Techniques to Get the Job Done.'' Sams Publishing. 2006. ISBN 9780672328282.</ref>
 
==Algorithm==
[[Image:Perlin.png|thumb|128px|Perlin noise rescaled and added into itself to create [[fractal noise]].]]
Perlin noise is most commonly implemented as a two-, three- or four-dimensional [[function (mathematics)|function]], but can be defined for any number of dimensions.  
 
Define an ''n''-dimensional grid. Each grid coordinate stores a gradient of unit length in ''n'' dimensions.  To sample, determine which grid cell you're in, and then compute the ''n''-dimensional vectors from the sample location to each grid coordinate of the cell. For each grid coordinate, calculate the [[dot product]]s of the corresponding distance and gradient vectors.  Finally, interpolate these dot products using a function that has zero first derivative (and possibly also second derivative) at both endpoints.
 
In 2001, [[Ken Perlin]] created [[simplex noise]], which is similar but uses a simpler space-filling grid, alleviating some problems with Perlin "classic noise", among them, computational complexity.
 
==Complexity==
When <math>n</math> is the number of dimensions, Perlin noise has complexity <math>O(2^n)</math>, while simplex noise has complexity <math>O(n^2)</math>.
 
==See also==
* [[Value noise]]
* [[Fractal landscape]]
* [[Simplex noise]]
* [[Simulation noise]]
* [[Wavelet noise]]
* [[Worley noise]]
* [[Gradient noise]]
 
== References ==
{{reflist}}
 
==External links==
* [http://www.noisemachine.com/talk1/ Making Noise] Ken Perlin talk on noise.
* [http://mrl.nyu.edu/~perlin/doc/oscar.html#noise Original source code] of Ken Perlin's 'coherent noise function'
* [http://webstaff.itn.liu.se/~stegu/TNM022-2005/perlinnoiselinks/perlin-noise-math-faq.html Matt Zucker's Perlin noise math FAQ ]
* [http://www.ddj.com/architect/222600097?pgno=4 Rob Farber's tutorial demonstrating Perlin noise generation and visualization on CUDA-enabled graphics processors]
* [http://www.xna-connection.com/post/Algorithme-de-Perlin-Noise-en-C French tutorial about implementing improved Perlin Noise in C#]
 
[[Category:Noise]]
[[Category:Special effects]]
[[Category:Fractals]]
[[Category:Computer graphics]]

Latest revision as of 01:56, 14 November 2014

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