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Caustic (optics)
In optics, a caustic or caustic network is the Envelope (mathematics), envelope of Ray (optics), light rays which have been Reflection (physics), reflected or refraction, refracted by a curved surface or object, or the Projection (mathematics), projection of that envelope of rays on another surface. The caustic is a curve or Surface (mathematics), surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light. In some cases caustics can be seen as patches of light or their bright edges, shapes which often have cusp (singularity), cusp singularities. Explanation Concentration of light, especially sunlight, can burn. The word ''caustic'', in fact, comes from the Greek καυστός, burnt, via the Latin ''causticus'', burning. A common situation where caustics are visible is when light shines on a drinking glass. The glass casts a shadow, but also produces a curved region of bright light. In ideal circumstances ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rainbow
A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew. Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground, and centered on a line from the Sun to the observer's eye. In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it. In a double rainbow, a second arc is seen outside the primary arc, and has the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Distribution
In probability theory and statistics, the Poisson distribution () is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. It can also be used for the number of events in other types of intervals than time, and in dimension greater than 1 (e.g., number of events in a given area or volume). The Poisson distribution is named after French mathematician Siméon Denis Poisson. It plays an important role for discrete-stable distributions. Under a Poisson distribution with the expectation of ''λ'' events in a given interval, the probability of ''k'' events in the same interval is: :\frac . For instance, consider a call center which receives an average of ''λ ='' 3 calls per minute at all times of day. If the calls are independent, receiving one does not change the probability of when the next on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the Mean#Mean of a probability distribution, mean or expected value, expectation of the distribution (and also its median and mode (statistics), mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural science, natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by graphics hardware, computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as Computer-generated imagery, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, Sprite (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, sound source reconstruction, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects. Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They can be found in system identification, optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, slope stability analys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texture Mapping
Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV Space). Semantic Texture mapping can both refer to the task of unwrapping a 3D model, the abstract that a 3D model has textures applied to it and the related algorithm of the 3D software. Texture map refers to a Raster graphics also called image, texture. If the texture stores a specific property it's also referred to as color map, roughness map, etc. The coordinate space which converts from the 3D space of a 3D model into a 2D space so that it can sample from the Texture map is called: UV Space, UV Coordinates, Texture Space. Algorithm A simplified explanation of how an algorithm could work to render an image: # For each pixel we trace the coordinates of the screen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physically Based Rendering
Physically based rendering (PBR) is a computer graphics approach that seeks to render images in a way that models the lights and surfaces with optics in the real world. It is often referred to as "Physically Based Lighting" or "Physically Based Shading". Many PBR pipelines aim to achieve photorealism. Feasible and quick approximations of the bidirectional reflectance distribution function and rendering equation are of mathematical importance in this field. Photogrammetry may be used to help discover and encode accurate optical properties of materials. PBR principles may be implemented in real-time applications using Shaders or offline applications using ray tracing or path tracing. History Starting in the 1980s, a number of rendering researchers worked on establishing a solid theoretical basis for rendering, including physical correctness. Much of this work was done at the Cornell University Program of Computer Graphics; a 1997 paper from that lab describes the work done at Cor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volumetric Path Tracing
Volumetric path tracing is a method for rendering images in computer graphics which was first introduced by Lafortune and Willems. This method enhances the rendering of the lighting in a scene by extending the path tracing method with the effect of light scattering. It is used for photorealistic effects of participating media like fire, explosions, smoke, clouds, fog or soft shadows. Like in the path tracing method, a ray is followed backwards, beginning from the eye, until reaching the light source. In volumetric path tracing, scattering events can occur along with ray tracing. When a light ray hits a surface, a certain amount gets scattered into the media. Description The algorithm is based on the volumetric rendering equation, which extends the rendering equation with a scattering term. It is composed of an absorption, out-scattering, emission and an in-scattering part. The absorption and out-scattering together form the extinction term. The in-scattering is the most expensive p ... [...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] |
Ray Tracing (graphics)
In 3D computer graphics, ray tracing is a technique for modeling Light transport theory, light transport for use in a wide variety of Rendering (computer graphics), rendering algorithms for generating digital image, digital images. On a spectrum of Computation time, computational cost and visual fidelity, ray tracing-based rendering techniques, such as ray casting, #Recursive ray tracing algorithm, recursive ray tracing, Distributed ray tracing, distribution ray tracing, photon mapping and path tracing, are generally slower and higher fidelity than scanline rendering methods. Thus, ray tracing was first deployed in applications where taking a relatively long time to render could be tolerated, such as still computer-generated imagery, CGI images, and film and television visual effects (VFX), but was less suited to real-time computer graphics, real-time applications such as video games, where Frame rate, speed is critical in rendering each Film frame, frame. Since 2018, however, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Rendering
In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field. A typical 3D data set is a group of 2D slice images acquired by a CT, MRI, or MicroCT scanner. Usually these are acquired in a regular pattern (e.g., one slice for each millimeter of depth) and usually have a regular number of image pixels in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling the immediate area surrounding the voxel. To render a 2D projection of the 3D data set, one first needs to define a camera in space relative to the volume. Also, one needs to define the opacity and color of every voxel. This is usually defined using an RGBA (for red, green, blue, alpha) transfer function that defines the RGBA value for every possible voxel value. For example, a volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
