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Smoothstep
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, video game engines, and machine learning. The function depends on three parameters, the input ''x'', the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge. The function receives a real number ''x'' as an argument. It returns 0 if ''x'' is less than or equal to the left edge and 1 if ''x'' is greater than or equal to the right edge. Otherwise, it smoothly interpolates, using Hermite interpolation, and returns a value between 0 and 1. The slope of the smoothstep function is zero at both edges. This is convenient for creating a sequence of transitions using smoothstep to interpolate each segment as an alternative to using more sophisticated or expensive interpolation techniques. In HLSL and GLSL, smoothstep implements the \operatorname_1(x), the cubic Hermite interpolation after clamping: :\operatorname(x) = S_1(x) = \begi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is any mathematical function whose graph of a function, graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula :\sigma(x) = \frac = \frac = 1 - \sigma(-x). Other sigmoid functions are given in the #Examples, Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of ''x'') and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (''y'' axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RenderMan Shading Language
Renderman Shading Language (abbreviated RSL) is a component of the RenderMan Interface Specification, and is used to define shaders. The language syntax is C-like. A shader written in RSL can be used without changes on any RenderMan-compliant renderer, such as Pixar's PhotoRealistic RenderMan, DNA Research's 3Delight, Sitexgraphics' Air or an open source solution such as Pixie or Aqsis. RenderMan Shading Language defines standalone functions and five types of shaders: surface, light, volume, imager and displacement shaders. An example of a surface shader that defines a metal surface is: surface metal (float Ka = 1; float Ks = 1; float roughness = 0.1;) Shaders express their work by reading and writing special variables such as Cs (surface color), N (normal at given point), and Ci (final surface color). The arguments to the shaders are global parameters that are attached to objects of the model (so one metal shader can be used for different metals and so on). Shaders have no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even And Odd Functions
In mathematics, an even function is a real function such that f(-x)=f(x) for every x in its domain. Similarly, an odd function is a function such that f(-x)=-f(x) for every x in its domain. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = x^n is even if ''n'' is an even integer, and it is odd if ''n'' is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an odd function. Early history The concept of even and odd functions appears to date back to the early 18th century, with Leonard Euler playing a significant role in their formalization. Euler introduced the concepts of even and odd functions (using La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ken Perlin
Kenneth 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. degree in Theoretical Mathematics from Harvard University (7/1979), a MS degree in computer science from the Courant Institute of Mathematical Sciences, New York University (6/1984), and a PhD degree in computer science from the same institution (2/1986). His research interests include graphics, animation, multimedia, and science education. He developed or was involved with the development of techniques such as Perlin noise, real-time interactive character animation, and computer-user interfaces. He is best known for the development of Perlin noise and Simplex noise, both of which are algorithms for realistic-looking Gradient noise. He is a collaborator of the World Building Institute. Awards In 1996, Perlin received ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clipping (signal Processing)
Clipping is a form of distortion that limits a signal once it exceeds a threshold. Clipping may occur when a signal is recorded by a sensor that has constraints on the range of data it can measure, it can occur when a signal is digitized, or it can occur any other time an analog or digital signal is transformed, particularly in the presence of gain or overshoot and undershoot. Clipping may be described as hard, in cases where the signal is strictly limited at the threshold, producing a flat cutoff; or it may be described as soft, in cases where the clipped signal continues to follow the original at a reduced gain. Hard clipping results in many high-frequency harmonics; soft clipping results in fewer higher-order harmonics and intermodulation distortion components. Audio In the frequency domain, clipping produces strong harmonics in the high-frequency range (as the clipped waveform comes closer to a square wave). The extra high-frequency weighting of the signal could ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of A Polynomial
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial. The term order has been used as a synonym of ''degree'' but, nowadays, may refer to several other concepts (see Order of a polynomial (other)). For example, the polynomial 7x^2y^3 + 4x - 9, which can also be written as 7x^2y^3 + 4x^1y^0 - 9x^0y^0, has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term. To determine the degree of a polynomial that is not in standard form, such as (x+1)^2 - (x-1)^2, one c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GLSL
OpenGL Shading Language (GLSL) is a high-level shading language with a syntax based on the C programming language. It was created by the OpenGL ARB (OpenGL Architecture Review Board) to give developers more direct control of the graphics pipeline without having to use ARB assembly language or hardware-specific languages. Background With advances in graphics cards, new features have been added to allow for increased flexibility in the rendering pipeline at the vertex and fragment level. Programmability at this level is achieved with the use of fragment and vertex shaders. Originally, this functionality was achieved by writing shaders in ARB assembly language – a complex and unintuitive task. The OpenGL ARB created the OpenGL Shading Language to provide a more intuitive method for programming the graphics processing unit while maintaining the open standards advantage that has driven OpenGL throughout its history. Originally introduced as an extension to OpenGL 1.4, G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HLSL
The High-Level Shader Language or High-Level Shading Language (HLSL) is a proprietary shading language developed by Microsoft for the Direct3D 9 API to augment the shader assembly language, and went on to become the required shading language for the unified shader model of Direct3D 10 and higher. HLSL is analogous to the GLSL shading language used with the OpenGL standard. It is very similar to the Nvidia Cg shading language, as it was developed alongside it. Early versions of the two languages were considered identical, only marketed differently. HLSL shaders can enable profound speed and detail increases as well as many special effects in both 2D and 3D computer graphics. HLSL programs come in six forms: pixel shaders (fragment in GLSL), vertex shaders, geometry shaders, compute shaders, tessellation shaders (Hull and Domain shaders), and ray tracing shaders (Ray Generation Shaders, Intersection Shaders, Any Hit/Closest Hit/Miss Shaders). A vertex shader is executed fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
