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Types Of Mesh
A mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes are commonly used to compute solutions of partial differential equations and render computer graphics, and to analyze geographical and cartographic data. A mesh partitions space into ''elements'' (or ''cells'' or ''zones'') over which the equations can be solved, which then approximates the solution over the larger domain. Element boundaries may be constrained to lie on internal or external boundaries within a model. Higher-quality (better-shaped) elements have better numerical properties, where what constitutes a "better" element depends on the general governing equations and the particular solution to the model instance. Common cell shapes Two-dimensional There are two types of two-dimensional cell shapes that are commonly used. These are the triangle and the quadrilateral. Computationally poor elements will have sharp internal angles or short edges or both. Triangle This cell shape cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Polygon Mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedron, polyhedral object's surface. It simplifies Rendering (computer graphics), rendering, as in a wire-frame model. The face (geometry), faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygon, convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygon, concave polygons, or even Polygon with holes, polygons with holes. The study of Polygon (computer graphics), polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes includes Boolean logic (Constructive solid geometry), Subdivision surfaces, smoothing, and Level of detail (computer graphics), simplification. Algorithms also exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Curvilinear Grid
A regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be conveniently expressed as finite differences, structured grids mainly appear in finite difference methods. Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods. Each cell in the grid can be addressed by index (i, j) in two dimensions or (i, j, k) in three dimensions, and each vertex has coordinates (i\cdot dx, j\cdot dy) in 2D or (i\cdot dx, j\cdot dy, k\cdot dz) in 3D for some real numbers ''dx'', ''dy'', and ''dz'' representing the grid spacing. Related grids A Cartesian grid is a special case where the elements are un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Principles Of Grid Generation
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine (have small elements) in areas that are important for the subsequent calculations. Meshes are used for rendering to a computer screen and for physical simulation such as finite element analysis or computational fluid dynamics. Meshes are composed of simple cells like triangles because, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mesh Generation
Mesh generation is the practice of creating a polygon mesh, mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine (have small elements) in areas that are important for the subsequent calculations. Meshes are used for rendering (computer graphics), rendering to a computer screen and for physical simulation such as finite element analysis or computational fluid dynamics. Meshes are compo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Aspect Ratio
The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape format, landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal Fraction (mathematics), fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: * Graphic / image ** Aspect ratio (image), Image aspect ratio ** Display aspect ratio ** Pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Multidimensional
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or Mathematical object, object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), line has a One-dimensional space, dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A Surface (mathematics), surface, such as the Boundary (mathematics), boundary of a Cylinder (geometry), cylinder or sphere, has a Two-dimensional space, dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the Euclidean plane, plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Aspect Ratio Grid
Aspect or Aspects may refer to: Companies * Aspect Capital, a London-based investment manager * Aspect Co., a Japanese video game company * Aspect Software, an American call center technology and customer experience company Literature * ''Aspect'' (magazine), a biannual DVD magazine showcasing new media art * ''Aspects'' (novel), a fantasy novel by John M. Ford Music * Aspects (band), a hip hop group from Bristol, England, UK * ''Aspects'' (Benny Carter album), a 1959 album * ''Aspects'' (The Eleventh House album), a 1976 album by Larry Coryell and The Eleventh House ** "Aspects" , the title track of the album Other uses * Alain Aspect (born 1947), French physicist and Nobel laureate * Aspect (computer programming), a feature linked to many parts of a program but not necessarily the primary function of the program * Aspect (geography), the compass direction that a slope faces * Aspect (religion), a particular manifestation of a deity * Astrological aspect, an angle the plane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Smooth And Large Jump
Smooth may refer to: Mathematics * Smooth function, a function that is infinitely differentiable; used in calculus and topology * Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions * Smooth algebraic variety, an algebraic variety with no singular points * Smooth number, a number whose prime factors are all less than a certain value; used in applications of number theory * Smoothsort, a sorting algorithm * "Analysis of the Jane Curve", an applied mathematics article by Norbert Schappacher referring to a surface that is infinitely smooth. Arts and entertainment Music * Smooth (singer), Juanita Stokes, American singer, rapper and actress * ''Smooth'' (Smooth album), 1995 * Smooth (Gerald Albright album), 1994 * "Smooth" (Florida Georgia Line song), 2017 * "Smooth" (iiO song), 2004 * "Smooth" (Santana song), featuring Rob Thomas, 1999 * "Smooth", a mashup by Neil Cicierega from ''Mouth Moods'', 2017 Other media * ''Smooth'' (magaz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Convergence (mathematics)
In mathematics, a series (mathematics), series is the summation, sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence (a_1, a_2, a_3, \ldots) defines a series (mathematics), series that is denoted :S=a_1 + a_2 + a_3 + \cdots=\sum_^\infty a_k. The th partial sum is the sum of the first terms of the sequence; that is, :S_n = a_1 +a_2 + \cdots + a_n = \sum_^n a_k. A series is convergent (or converges) if and only if the sequence (S_1, S_2, S_3, \dots) of its partial sums tends to a limit of a sequence, limit; that means that, when adding one a_k after the other ''in the order given by the indices'', one gets partial sums that become closer and closer to a given number. More precisely, a series converges, if and only if there exists a number \ell such that for every arbitrarily small positive number \varepsilon, there is a (sufficiently large) integer N such that for all n \ge N, :\left , S_n - \ell \right , 1 produce a convergent series: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
