Gradient noiseGradient 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, 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.
Function (mathematics)Association of one output to each inputIn mathematics, a function from a setX to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
Vertex arrangementIn geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a square vertex arrangement is understood to mean four points in a plane, equal distance and angles from a center point. Two polytopes share the same vertex arrangement if they share the same 0-skeleton. A group of polytopes that shares a vertex arrangement is called an army.
SimplexIn geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension.
Perlin noisePerlin noise is a type of gradient noise developed by Ken Perlin in 1982. It has many uses, including but not limited to: procedurally generating terrain, applying pseudo-random changes to a variable, and assisting in the creation of image textures. It is most commonly implemented in two, three, or four dimensions, but can be defined for any number of dimensions.
GradientMultivariate derivative (mathematics)The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function. The values of the function are represented in greyscale and increase in value from white (low) to dark (high).
Ken PerlinKenneth H. Perlin is a professor in the Department of Computer Science at New York University, founding director of the Media Research Lab at NYU, director of the Future Reality Lab at NYU, and the director of the Games for Learning Institute. He holds a BA.Schläfli orthoschemeIn geometry, a Schläfli orthoscheme is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined by a sequence of edges ( v 0 v 1 ) , ( v 1 v 2 ) , … , ( v d − 1 v d ) {\displaystyle (v_{0}v_{1}),(v_{1}v_{2}),\dots ,(v_{d-1}v_{d})\,} that are mutually orthogonal.Hypercubic honeycombIn geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group Rn (or B~n−1) for n ≥ 3. The tessellation is constructed from 4 n-hypercubes per ridge. The vertex figure is a cross-polytope {3...3,4}. The hypercubic honeycombs are self-dual. Coxeter named this family as δn+1 for an n-dimensional honeycomb.
Tetragonal disphenoid honeycombThe 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. A cell can be seen as 1/12 of a translational cube, with its vertices centered on two faces and two edges.
Equilateral triangleShape with three equal sidesAn equilateral triangle is a triangle with three sides of equal length and three equal angles. It is a regular polygon, occasionally known as the regular triangle. It is a special case of an isosceles triangle by modern definition. Its internal angle is 60 degrees or π/3 radians. Its perimeter is three times the side length. Its area is a quarter of the square root of three multiplied with its squared side length.
IsotropyIn physics and geometry, isotropy (from Ancient Greek (ísos)'equal' and (trópos)'turn, way') is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix or , hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction.*As an Amazon Associate I earn from qualifying purchases.