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Marching Cubes
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels). The applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D modelling with what is usually called metaballs or other metasurfaces. The marching cubes algorithm is meant to be used for 3-D; the 2-D version of this algorithm is called the marching squares algorithm. History The algorithm was developed by William E. Lorensen (1946-2019) and Harvey E. Cline as a result of their research for General Electric. At General Electric they worked on a way to efficiently visualize data from CT and MRI devices. The premise of the algorithm is to divide the input volume into a discrete set of cubes. By assuming linear reconstruction filte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable energy, digital industry, additive manufacturing and venture capital and finance, but has since divested from several areas, now primarily consisting of the first four segments. In 2020, GE ranked among the Fortune 500 as the 33rd largest firm in the United States by gross revenue. In 2011, GE ranked among the Fortune 20 as the 14th most profitable company, but later very severely underperformed the market (by about 75%) as its profitability collapsed. Two employees of GE – Irving Langmuir (1932) and Ivar Giaever (1973) – have been awarded the Nobel Prize. On November 9, 2021, the company announced it would divide itself into three investment-grade public companies. On July 18, 2022, GE unveiled the brand names of the companies it will ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics Algorithms
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Tetrahedra
Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations. It was originally introduced in 1991. While the original marching cubes algorithm was protected by a software patent, marching tetrahedrons offered an alternative algorithm that did not require a patent license. More than 20 years have passed from the patent filing date (June 5, 1985), and the marching cubes algorithm can now be used freely. Optionally, the minor improvements of marching tetrahedrons may be used to correct the aforementioned ambiguity in some configurations. In ''marching tetrahedra'', each cube is split into six irregular tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the cube, we now h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image-based Meshing
Image-based meshing is the automated process of creating computer models for computational fluid dynamics (CFD) and finite element analysis (FEA) from 3D image data (such as magnetic resonance imaging (MRI), computed tomography (CT) or microtomography). Although a wide range of mesh generation techniques are currently available, these were usually developed to generate models from computer-aided design (CAD), and therefore have difficulties meshing from 3D imaging data. Mesh generation from 3D imaging data Meshing from 3D imaging data presents a number of challenges but also unique opportunities for presenting a more realistic and accurate geometrical description of the computational domain. There are generally two ways of meshing from 3D imaging data: CAD-based approach The majority of approaches used to date still follow the traditional CAD route by using an intermediary step of surface reconstruction which is then followed by a traditional CAD-based meshing algorithm. CAD-based ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Tetrahedra
Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations. It was originally introduced in 1991. While the original marching cubes algorithm was protected by a software patent, marching tetrahedrons offered an alternative algorithm that did not require a patent license. More than 20 years have passed from the patent filing date (June 5, 1985), and the marching cubes algorithm can now be used freely. Optionally, the minor improvements of marching tetrahedrons may be used to correct the aforementioned ambiguity in some configurations. In ''marching tetrahedra'', each cube is split into six irregular tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the cube, we now h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illumination Model
{{Short description, none This article lists common shading algorithms used in computer graphics. Interpolation techniques These techniques can be combined with any illumination model: * Flat shading * Gouraud shading * Phong shading Illumination models Realistic The illumination models listed here attempt to model the perceived brightness of a surface or a component of the brightness in a way that looks realistic. Some take physical aspects into consideration, like for example the Fresnel equations, microfacets, the rendering equation and subsurface scattering. Diffuse reflection Light that is reflected on a non-metallic and/or a very rough surface gives rise to a diffuse reflection. Models that describe the perceived brightness due to diffuse reflection include: * Lambert * Oren–Nayar (Rough opaque diffuse surfaces) * Minnaert Specular reflection Light that is reflected on a relatively smooth surface gives rise to a specular reflection. This kind of reflection is especial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. Linear interpolation between two known points If the two known points are given by the coordinates (x_0,y_0) and (x_1,y_1), the linear interpolant is the straight line between these points. For a value in the interval (x_0, x_1), the value along the straight line is given from the equation of slopes \frac = \frac, which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with . Solving this equation for , which is the unknown value at , gives \begin y &= y_0 + (x-x_0)\frac \\ &= \frac + \frac\\ &= \frac \\ &= \frac, \end which is the formula for linear interpolation in the interval (x_0,x_1). Outside this interval, the formula is identical to linear extrapolation. This formula can also be understood as a weighted average. The weights are inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Decider
In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, but can also be considered an algorithm in its own right. Principle The algorithm first divides the scalar field into uniform cubes. It draws topologically correct contours on the sides (interface) of the cubes. These contours can then be connected to polygons and triangulated. The triangles of all cubes form the isosurfaces and are thus the output of the algorithm. Sometimes there is more than one way to connect adjacent constructs. This algorithm describes a method for resolving these ambiguous configurations in a consistent manner. Ambiguous cases often occur if diagonally opposing points are found on the same side of the isoline, but on a different side to the other points in the square (for 2D systems) or cube (fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Triangulation
Triangulation of a surface means * a ''net'' of triangles, which covers a given surface partly or totally, ''or'' * the ''procedure'' of generating the points and triangles of such a net of triangles. Approaches This article describes the generation of a net of triangles. In literature there are contributions which deal with the optimization of a given net. Surface triangulations are important for * visualizing surfaces and * the application of finite element methods. The triangulation of a ''parametrically'' defined surface is simply achieved by triangulating the area of definition (see second figure, depicting the Monkey Saddle). However, the triangles may vary in shape and extension in object space, posing a potential drawback. This can be minimized through adaptive methods that consider step width while triangulating the parameter area. To triangulate an ''implicit surface'' (defined by one or more equations) is more difficult. There exist essentially two methods. * On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
