Perlin noise is a type ofgradient noise developed byKen Perlin in 1982. It has many uses, including but not limited to:procedurally generating terrain, applyingpseudo-random changes to a variable, and assisting in the creation ofimage textures. It is most commonly implemented in two, three, or fourdimensions, but can be defined for any number of dimensions.
Ken Perlin developed Perlin noise in 1982 as a result of his frustration with the "machine-like" look ofcomputer-generated imagery (CGI) at the time.[1] He formally described his findings in aSIGGRAPH paper in 1985 called "An Image Synthesizer".[2] He developed it after working onDisney'scomputer animatedsci-fi motion pictureTron (1982) for the animation companyMathematical Applications Group (MAGI).[3] In 1997, Perlin was awarded anAcademy Award for Technical Achievement for creating the algorithm, the citation for which read:[4][5][6][7]
To Ken Perlin for the development of Perlin Noise, a technique used to produce natural appearingtextures on computer generated surfaces for motion picture visual effects.The development of Perlin Noise has allowed computer graphics artists to better represent the complexity of natural phenomena in visual effects for the motion picture industry.
Perlin did not apply for any patents on the algorithm, but in 2001 he was granted a patent for the use of 3D+ implementations ofsimplex noise fortexture synthesis. Simplex noise has the same purpose, but uses a simpler space-filling grid. Simplex noise alleviates some of the problems with Perlin's "classic noise", among them computational complexity and visually-significant directional artifacts.[8]
Perlin noise is aprocedural texture primitive, a type ofgradient noise used by visual effects artists to increase the appearance of realism incomputer graphics.[9] The function has apseudo-random appearance, yet all of its visual details are the same size.[citation needed] 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 textures. Synthetic textures using Perlin noise are often used in CGI to make computer-generated visual elements – such as object surfaces, fire, smoke, or clouds – appear more natural, by imitating the controlled random appearance of textures in nature.[9]
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It is also frequently used to generate textures when memory is extremely limited, such as indemos.[10] Its successors, such asfractal noise andsimplex noise, have become nearly ubiquitous ingraphics processing units both forreal-time graphics and for non-real-time procedural textures in all kinds of computer graphics.
It is frequently used in video games to makeprocedurally generated terrain that looks natural. The success is in part due to the hierarchical structuring of Perlin noise that mimics naturally occurring hierarchical structures, and therefore also has found to be useful in environmental science applications.[11]
Perlin noise is most commonly implemented as a two-, three- or four-dimensionalfunction, but can be defined for any number of dimensions. An implementation typically involves three steps: defining a grid of random gradient vectors, computing thedot product between the gradient vectors and their offsets, and interpolation between these values.[7]
Define ann-dimensional grid where each grid intersection has associated with it a fixed randomn-dimensional unit-length gradient vector, except in the one dimensional case where the gradients are random scalars between −1 and 1.
For working out the value of any candidate point, first find the unique grid cell in which the point lies. Then, identify the2n corners of that cell and their associated gradient vectors. Next, for each corner, calculate an offset vector. An offset vector is a displacement vector from that corner to the candidate point.
For each corner, we take thedot product between its gradient vector and the offset vector to the candidate point. This dot product will be zero if the candidate point is exactly at the grid corner.
For a point in a two-dimensional grid, this will require the computation of four offset vectors and dot products, while in three dimensions it will require eight offset vectors and eight dot products. In general, the algorithm hasO(2n)complexity inn dimensions.
The final step is interpolation between the2n dot products. Interpolation is performed using a function that has zero firstderivative (and possibly also second derivative) at the2n grid nodes. Therefore, at points close to the grid nodes, the output will approximate the dot product of the gradient vector of the node and the offset vector to the node. This means that the noise function will pass through 0 at every node, giving Perlin noise its characteristic look.
Ifn = 1, an example of a function that interpolates between valuea0 at grid node 0 and valuea1 at grid node 1 is
where thesmoothstep function was used.
Noise functions for use in computer graphics typically produce values in the range[–1.0, 1.0] and can be scaled accordingly.
In Ken Perlin's original implementation he used a simple hashing scheme to determine what gradient vector is associated with each grid intersection.[12] A pre-computed permutation table is used to turn a given grid coordinate into a random number. The original implementation worked on a 256 node grid and so included the following permutation table:
intpermutation[]={151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,88,237,149,56,87,174,20,125,136,171,168,68,175,74,165,71,134,139,48,27,166,77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,102,143,54,65,25,63,161,1,216,80,73,209,76,132,187,208,89,18,169,200,196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226,250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,223,183,170,213,119,248,152,2,44,154,163,70,221,153,101,155,167,43,172,9,129,22,39,253,19,98,108,110,79,113,224,232,178,185,112,104,218,246,97,228,251,34,242,193,238,210,144,12,191,179,162,241,81,51,145,235,249,14,239,107,49,192,214,31,181,199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180};
This specific permutation is not absolutely required, though it does require a randomized array of the integers 0 to 255. If creating a new permutation table, care should be taken to ensure uniform distribution of the values.[13]
To get a gradient vector using the permutation table the coordinates of a grid point are looked up sequentially in the permutation table adding the value of each coordinate to the permutation of the previous coordinate. So for example the original implementation did this in 3D as follows:
// Values above 255 were handled by repeating the permutation table twice.staticfinalintp[]=newint[512];static{for(inti=0;i<256;i++)p[256+i]=p[i]=permutation[i];}inthash=p[p[p[X]+Y]+Z];
The algorithm then looks at the bottom 4 bits of the hash output to pick 1 of 12 gradient vectors for that grid point.
For each evaluation of the noise function, the dot product of the position and gradient vectors must be evaluated at each node of the containing grid cell. Perlin noise therefore scales with complexityO(2n) forn dimensions.[14] Alternatives to Perlin noise producing similar results with improved complexity scaling includesimplex noise andOpenSimplex noise.
{{cite web}}: CS1 maint: bot: original URL status unknown (link) of Ken Perlin's 'coherent noise function'