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Rendering Equation
In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The various realistic rendering techniques in computer graphics attempt to solve this equation. The physical basis for the rendering equation is the law of conservation of energy. Assuming that ''L'' denotes radiance, we have that at each particular position and direction, the outgoing light (Lo) is the sum of the emitted light (Le) and the reflected light. The reflected light itself is the sum from all directions of the incoming light (Li) multiplied by the surface reflection and cosine of the incident angle. Equation form The rendering equation may be written in the form :L_(\mathbf x, \omega_, \lambda, t) = L_(\mathbf x, \omega_, \lambda, t) \ + \int_\Omeg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rendering Eq
Render, rendered, or rendering may refer to: Computing * Rendering (computer graphics), generating an image from a model by means of computer programs * Architectural rendering, creating two-dimensional images or animations showing the attributes of a proposed architectural design * Artistic rendering, creating, shading, and texturing of an image * Typesetting, composition of text for visual display * Rendering engine, the software that transforms (renders) data into a picture ** 3D rendering, generating image or motion picture from virtual 3D models ** Browser engine, component of a web browser that renders web pages ** High-dynamic-range rendering, allows preservation of details that may be lost due to limiting contrast ratios ** Non-photorealistic rendering, focuses on enabling a wide variety of expressive styles for digital art ** Scanline rendering, algorithm for visible surface determination ** Volume rendering, used to display a 2D projection of a 3D discretely sampled dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metropolis Light Transport
Metropolis light transport (MLT) is a global illumination application of a variant of the Monte Carlo method called the Metropolis–Hastings algorithm to the rendering equation for generating images from detailed physical descriptions of three-dimensional scenes. The procedure constructs paths from the eye to a light source using bidirectional path tracing, then constructs slight modifications to the path. Some careful statistical calculation (the Metropolis algorithm) is used to compute the appropriate distribution of brightness over the image. This procedure has the advantage, relative to bidirectional path tracing, that once a path has been found from light to eye, the algorithm can then explore nearby paths; thus difficult-to-find light paths can be explored more thoroughly with the same number of simulated photons. In short, the algorithm generates a path and stores the path's 'nodes' in a list. It can then modify the path by adding extra nodes and creating a new lig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon Mapping
In computer graphics, photon mapping is a two-pass global illumination rendering algorithm developed by Henrik Wann Jensen between 1995 and 2001Jensen, H. (1996). ''Global Illumination using Photon Maps''. nlineAvailable at: http://graphics.stanford.edu/~henrik/papers/ewr7/egwr96.pdf that approximately solves the rendering equation for integrating light radiance at a given point in space. Rays from the light source (like photons) and rays from the camera are traced independently until some termination criterion is met, then they are connected in a second step to produce a radiance value. The algorithm is used to realistically simulate the interaction of light with different types of objects (similar to other photorealistic rendering techniques). Specifically, it is capable of simulating the refraction of light through a transparent substance such as glass or water (including caustics), diffuse interreflection between illuminated objects, the subsurface scattering of light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Tracing
Path tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to a single point on the surface of an object. This illuminance is then reduced by a surface reflectance function ( BRDF) to determine how much of it will go towards the viewpoint camera. This integration procedure is repeated for every pixel in the output image. When combined with physically accurate models of surfaces, accurate models of real light sources (light bulbs), and optically correct cameras, path tracing can produce still images that are indistinguishable from photographs. Path tracing naturally simulates many effects that have to be specifically added to other methods (conventional ray tracing or scanline rendering), such as soft shadows, depth of field, motion blur, caustics, ambient occlusion, and indirect lighting. Impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiosity (3D Computer Graphics)
In 3D computer graphics, radiosity is an application of the finite element method to solving the rendering equation for scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms (such as path tracing), which handle all types of light paths, typical radiosity only account for paths (represented by the code "LD*E") which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye. Radiosity is a global illumination algorithm in the sense that the illumination arriving on a surface comes not just directly from the light sources, but also from other surfaces reflecting light. Radiosity is viewpoint independent, which increases the calculations involved, but makes them useful for all viewpoints. Radiosity methods were first developed in about 1950 in the engineering field of heat transfer. They were later refined specifically for the problem of rendering computer graphics in 1984 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Analysis
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Realistic Rendering
Global illumination (GI), or indirect illumination, is a group of algorithms used in 3D computer graphics that are meant to add more realistic lighting to 3D scenes. Such algorithms take into account not only the light that comes directly from a light source (''direct illumination''), but also subsequent cases in which light rays from the same source are reflected by other surfaces in the scene, whether reflective or not (''indirect illumination''). Theoretically, reflections, refractions, and shadows are all examples of global illumination, because when simulating them, one object affects the rendering of another (as opposed to an object being affected only by a direct source of light). In practice, however, only the simulation of diffuse inter-reflection or caustics is called global illumination. Algorithms Images rendered using global illumination algorithms often appear more photorealistic than those using only direct illumination algorithms. However, such images are com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Averaging
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average. Another universal property is monotonicity: if two lists of numbers ''A'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Motion Blur
Motion blur is the apparent streaking of moving objects in a photograph or a sequence of frames, such as a film or animation. It results when the image being recorded changes during the recording of a single exposure, due to rapid movement or long exposure. Usages / Effects of motion blur Photography When a camera creates an image, that image does not represent a single instant of time. Because of technological constraints or artistic requirements, the image may represent the scene over a period of time. Most often this exposure time is brief enough that the image captured by the camera appears to capture an instantaneous moment, but this is not always so, and a fast moving object or a longer exposure time may result in blurring artifacts which make this apparent. As objects in a scene move, an image of that scene must represent an integration of all positions of those objects, as well as the camera's viewpoint, over the period of exposure determined by the shutter speed. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trichromatic
Trichromacy or trichromatism is the possessing of three independent channels for conveying color information, derived from the three different types of cone cells in the eye. Organisms with trichromacy are called trichromats. The normal explanation of trichromacy is that the organism's retina contains three types of color receptors (called cone cells in vertebrates) with different absorption spectra. In actuality the number of such receptor types may be greater than three, since different types may be active at different light intensities. In vertebrates with three types of cone cells, at low light intensities the rod cells may contribute to color vision. Humans and other animals that are trichromats Humans and some other mammals have evolved trichromacy based partly on pigments inherited from early vertebrates. In fish and birds, for example, four pigments are used for vision. These extra cone receptor visual pigments detect energy of other wavelengths, sometimes including ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
