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OpenSimplex Noise
OpenSimplex noise is an n-dimensional (up to 4D) gradient noise function that was developed in order to overcome the patent-related issues surrounding simplex noise, while likewise avoiding the visually-significant directional artifacts characteristic of Perlin noise. The algorithm shares numerous similarities with simplex noise, but has two primary differences: * Whereas simplex noise starts with a hypercubic honeycomb and squashes it down the main diagonal in order to form its grid structure,Ken Perlin, Noise hardware. In Real-Time Shading SIGGRAPH Course Notes (2001), Olano M., (Ed.)(pdf)/ref> OpenSimplex noise instead swaps the skew and inverse-skew factors and uses a stretched hypercubic honeycomb. The stretched hypercubic honeycomb becomes a simplectic honeycomb after subdivision. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composition In 3D Generated With The Opensimplex Noise
Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include visuals and digital space *Composition (music), an original piece of music and its creation *Composition (visual arts), the plan, placement or arrangement of the elements of art in a work * ''Composition'' (Peeters), a 1921 painting by Jozef Peeters *Composition studies, the professional field of writing instruction * ''Compositions'' (album), an album by Anita Baker *Digital compositing, the practice of digitally piecing together a video Computer science *Function composition (computer science), an act or mechanism to combine simple functions to build more complicated ones *Object composition, combining simpler data types into more complex data types, or function calls into calling functions History *Composition of 1867, Austro-Hungarian/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Noise
Gradient noise is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different, and often confused with value noise. This method consists of a creation of a lattice of random (or typically pseudorandom) gradients, dot products of which are then interpolated to obtain values in between the lattices. An artifact of some implementations of this noise is that the returned value at the lattice points is 0. Unlike the value noise, gradient noise has more energy in the high frequencies. The first known implementation of a gradient noise function was Perlin noise, credited to Ken Perlin, who published the description of it in 1985. David Ebert, Kent Musgrave, Darwyn Peachey, Ken Perlin, and Worley. Texturing and Modeling: A Procedural Approach'' Academic Press, October 1994. Later developments were Simplex noise and OpenSimplex noise OpenSimplex noise is an n-dimensional (up to 4D) gradient noise function that was developed in orde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplex Noise
Simplex noise is the result of an ''n''-dimensional noise function comparable to Perlin noise ("classic" noise) but with fewer directional artifacts and, in higher dimensions, a lower computational overhead. Ken Perlin designed the algorithm in 2001 to address the limitations of his classic noise function, especially in higher dimensions. The advantages of simplex noise over Perlin noise: * Simplex noise has lower computational complexity and requires fewer multiplications. * Simplex noise scales to higher dimensions (4D, 5D) with much less computational cost: the complexity is O(n^2) for n dimensions instead of the O(n\,2^n) of classic noise. * Simplex noise has no noticeable directional artifacts (is visually isotropic), though noise generated for different dimensions is visually distinct (e.g. 2D noise has a different look than 2D slices of 3D noise, and it looks increasingly worse for higher dimensions). * Simplex noise has a well-defined and continuous gradient (almost) ever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perlin Noise
Perlin noise is a type of gradient noise developed by Ken Perlin. History Ken Perlin developed Perlin noise in 1983 as a result of his frustration with the "machine-like" look of computer-generated imagery (CGI) at the time. He formally described his findings in a SIGGRAPH paper in 1985 called ''An Image Synthesizer''. He developed it after working on Disney's computer animated sci-fi motion picture ''Tron'' (1982) for the animation company Mathematical Applications Group (MAGI). In 1997, Perlin was awarded an Academy Award for Technical Achievement for creating the algorithm, the citation for which read: Perlin did not apply for any patents on the algorithm, but in 2001 he was granted a patent for the use of 3D+ implementations of simplex noise for texture 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-significan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercubic Honeycomb
In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in -dimensional spaces with the Schläfli symbols and containing the symmetry of Coxeter group (or ) for . The tessellation is constructed from 4 -hypercubes per ridge. The vertex figure is a cross-polytope The hypercubic honeycombs are self-dual. Coxeter named this family as for an -dimensional honeycomb. Wythoff construction classes by dimension A Wythoff construction is a method for constructing a uniform polyhedron or plane tiling. The two general forms of the hypercube honeycombs are the ''regular'' form with identical hypercubic facets and one ''semiregular'', with alternating hypercube facets, like a checkerboard. A third form is generated by an expansion operation applied to the regular form, creating facets in place of all lower-dimensional elements. For example, an ''expanded cubic honeycomb'' has cubic cells centered on the original cubes, on the original faces, on the ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplectic Honeycomb
In geometry, the simplectic honeycomb (or -simplex honeycomb) is a dimensional infinite series of honeycombs, based on the _n affine Coxeter group symmetry. It is represented by a Coxeter-Dynkin diagram as a cyclic graph of nodes with one node ringed. It is composed of -simplex facets, along with all rectified -simplices. It can be thought of as an -dimensional hypercubic honeycomb that has been subdivided along all hyperplanes x+y+\cdots\in\mathbb, then stretched along its main diagonal until the simplices on the ends of the hypercubes become regular. The vertex figure of an -''simplex honeycomb'' is an expanded -simplex. In 2 dimensions, the honeycomb represents the triangular tiling, with Coxeter graph filling the plane with alternately colored triangles. In 3 dimensions it represents the tetrahedral-octahedral honeycomb, with Coxeter graph filling space with alternately tetrahedral and octahedral cells. In 4 dimensions it is called the 5-cell honeycomb, with Coxeter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ). The triangular tiling can also be called a kishextille by a kis operation that adds a center point and triangles to replace the faces of a hextille. It is one of three regular tilings of the plane. The other two are the square tiling and the hexagonal tiling. Uniform colorings There are 9 distinct uniform colorings of a triangular tiling. (Naming the colors by indices on the 6 triangles around a vertex: 111111, 111112, 111212, 111213, 111222, 112122, 121212, 121213, 121314) Three of them can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetragonal Disphenoid Honeycomb
The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells. Cells are face-transitive with 4 identical isosceles triangle faces. John Horton Conway calls it an ''oblate tetrahedrille'' or shortened to ''obtetrahedrille''. Symmetry of Things, Table 21.1. Prime Architectonic and Catopric tilings of space, p. 293, 295. A cell can be seen as 1/12 of a translational cube, with its vertices centered on two faces and two edges. Four of its edges belong to 6 cells, and two edges belong to 4 cells. : The tetrahedral disphenoid honeycomb is the dual of the uniform bitruncated cubic honeycomb. Its vertices form the A / D lattice, which is also known as the body-centered cubic lattice. Geometry This honeycomb's vertex figure is a tetrakis cube: 24 disphenoids meet at each vertex. The union of these 24 disphenoids forms a rhombic dodecahedron. Each edge of the tessellation is s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedral-octahedral Honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway calls this honeycomb a tetroctahedrille, and its dual a dodecahedrille. R. Buckminster Fuller combines the two words octahedron and tetrahedron into octet truss, a rhombohedron consisting of one octahedron (or two square pyramids) and two opposite tetrahedra. It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex. It is edge-transitive with 2 tetrahedra and 2 octahedra alternating on each edge. It is part of an infinite family of uniform honeycombs called alternated hypercubic honeycombs, formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value Noise
Value noise is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different from, and often confused with gradient noise, examples of which are Perlin noise and Simplex noise. This method consists of the creation of a lattice of points which are assigned random values. The noise function then returns the interpolated number based on the values of the surrounding lattice points. For many applications, multiple octaves of this noise can be generated and then summed together, just as can be done with Perlin noise and Simplex noise, in order to create a form of fractal noise Pink noise or noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or .... External links * - an explanation and implementation of Value Noise, mislabeled as Perlin noise. Lesson ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worley Noise
Worley noise is a noise function introduced by Steven Worley in 1996. In computer graphics it is used to create procedural textures, i.e. textures that are created automatically with arbitrary precision and do not have to be drawn by hand. Worley noise comes close to simulating textures of stone, water, or biological cells. Basic algorithm The algorithm chooses random points in space (2- or 3-dimensional) and then for every location in space takes the distances d''n'' to the ''n''th-closest point (e.g. the second-closest point) and uses combinations of those to control color information (note that d''n+1'' > d''n''). More precisely: * Randomly distribute feature points in space organised as grid cells. In practice this is done on the fly without storage (as a ''procedural noise''). The original method considered a variable number of seed points per cell so as to mimic a Poisson distribution, but many implementations just put one. * At run time, extract the distances d''n'' from th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
