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Mesh 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] |
Example Finite Element Mesh, For Illustrating The Concept
Example may refer to: * '' exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, example.edu, second-level domain names reserved for use in documentation as examples * HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * ''Example'' (album), a 1995 album by American rock band For Squirrels See also * * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample The Eixample (; ) is a district of Barcelona between the old city (Ciutat Vella) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Methods 1
Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: * Algebraic data type, a datatype in computer programming each of whose values is data from other datatypes wrapped in one of the constructors of the datatype * Algebraic numbers, a complex number that is a root of a non-zero polynomial in one variable with integer coefficients * Algebraic functions, functions satisfying certain polynomials * Algebraic element, an element of a field extension which is a root of some polynomial over the base field * Algebraic extension, a field extension such that every element is an algebraic element over the base field * Algebraic definition, a definition in mathematical logic which is given using only equalities between terms * Algebraic structure, a set with one or more finitary operations defined on it * Algebraic, the order of ent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Computing
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance increases must largely come from increasing the number of processors (or cores) on a die, rather than m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetragonal Trapezohedron
In geometry, a tetragonal trapezohedron, or deltohedron, is the second in an infinite series of trapezohedra, which are dual to the antiprisms. It has eight faces, which are congruent kites, and is dual to the square antiprism. In mesh generation This shape has been used as a test case for hexahedral mesh generation,..... simplifying an earlier test case posited by mathematician Robert Schneiders in the form of a square pyramid with its boundary subdivided into 16 quadrilaterals. In this context the tetragonal trapezohedron has also been called the cubical octahedron, quadrilateral octahedron, or octagonal spindle, because it has eight quadrilateral faces and is uniquely defined as a combinatorial polyhedron by that property. Adding four cuboids to a mesh for the cubical octahedron would also give a mesh for Schneiders' pyramid. As a simply-connected polyhedron with an even number of quadrilateral faces, the cubical octahedron can be decomposed into topological cuboids with curv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Polycube
upAll 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total A puzzle involving arranging nine L tricubes into a 3×3 cube A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes. Enumerating polycubes A chiral pentacube Like polyominoes, polycubes can be enumerated in two ways, depending on whether chiral pairs of polycubes are counted as one polycube or two. For example, 6 tetracubes have mirror symmetry and one is chiral, giving a count of 7 or 8 tetracubes respectively. Unlike polyominoes, polycubes are usually counted with mirror pairs distinguished, because one cannot turn a polycube over to reflect it as one can a polyomino give ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Graph
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space , forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8 × 8 square grid". The term lattice graph has also been given in the literature to various other kinds of graphs with some regular structure, such as the Cartesian product of a number of complete graphs. Square grid graph A common type of a lattice graph (known under different names, such as square grid graph) is the graph whose vertices correspond to the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruppert's Algorithm
In mesh generation, Delaunay refinement are algorithms for mesh generation based on the principle of adding Steiner points to the geometry of an input to be meshed, in a way that causes the Delaunay triangulation or constrained Delaunay triangulation of the augmented input to meet the quality requirements of the meshing application. Delaunay refinement methods include methods by Chew and by Ruppert. Chew's second algorithm Chew's second algorithm takes a piecewise linear system (PLS) and returns a constrained Delaunay triangulation of only quality triangles where quality is defined by the minimum angle in a triangle. Developed by L. Paul Chew for meshing surfaces embedded in three-dimensional space, Chew's second algorithm has been adopted as a two-dimensional mesh generator due to practical advantages over Ruppert's algorithm in certain cases and is the default quality mesh generator implemented in the freely available Triangle package. Chew's second algorithm is guaranteed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
