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Marching Tetrahedrons
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] |
Marching Tetrahedrons
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] |
Visualisation Diamond Cubic
Visualization or visualisation may refer to: *Visualization (graphics), the physical or imagining creation of images, diagrams, or animations to communicate a message * Data visualization, the graphic representation of data * Information visualization, the study of visual representations of abstract data * Music visualization, animated imagery based on a piece of music *Mental image, the experience of images without the relevant external stimuli * "Visualization", a song by Blank Banshee on the 2012 album ''Blank Banshee 0'' See also * Creative visualization (other) * Visualizer (other) * * * * Graphics * List of graphical methods, various forms of visualization * Guided imagery, a mind-body intervention by a trained practitioner * Illustration, a decoration, interpretation or visual explanation of a text, concept or process * Image, an artifact that depicts visual perception, such as a photograph or other picture * Infographics Infographics (a clipped co ... [...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] |
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] |
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] |
Manifold Dual Contouring
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isosurface
An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space; in other words, it is a level set of a continuous function whose domain is 3-space. The term ''isoline'' is also sometimes used for domains of more than 3 dimensions. Applications Isosurfaces are normally displayed using computer graphics, and are used as data visualization methods in computational fluid dynamics (CFD), allowing engineers to study features of a fluid flow (gas or liquid) around objects, such as aircraft wings. An isosurface may represent an individual shock wave in supersonic flight, or several isosurfaces may be generated showing a sequence of pressure values in the air flowing around a wing. Isosurfaces tend to be a popular form of visualization for volume datasets since they can be rendered by a simple polygonal model, which can be drawn on the screen very quic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Contouring
Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical number), a grammatical category used in some languages * Dual county, a Gaelic games county which in both Gaelic football and hurling * Dual diagnosis, a psychiatric diagnosis of co-occurrence of substance abuse and a mental problem * Dual fertilization, simultaneous application of a P-type and N-type fertilizer * Dual impedance, electrical circuits that are the dual of each other * Dual SIM cellphone supporting use of two SIMs * Aerochute International Dual a two-seat Australian powered parachute design Acronyms and other uses * Dual (brand), a manufacturer of Hifi equipment * DUAL (cognitive architecture), an artificial intelligence design model * DUAL algorithm, or diffusing update algorithm, used to update Internet protocol routing ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texture Splatting
In computer graphics, texture splatting is a method for combining different textures. It works by applying an alphamap (also called a "weightmap" or a "splat map") to the higher levels, thereby revealing the layers underneath where the alphamap is partially or completely transparent. The term was coined by Crawfis et al. Optimizations Since texture splatting is commonly used for terrain rendering in computer games, various optimizations are required. Because the underlying principle is for each texture to have its own alpha channel, large amounts of memory can easily be consumed. As a solution to this problem, multiple alpha maps can be combined into one texture using the red channel for one map, the blue for another, and so on. This effectively uses a single texture to supply alpha maps for four real-color textures. The alpha textures can also use a lower resolution than the color textures, and often the color textures can be tiled. Terrains can also be split into chunks where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texel (graphics)
In computer graphics, a texel, texture element, or texture pixel is the fundamental unit of a texture map. Textures are represented by arrays of texels representing the texture space, just as other images are represented by arrays of pixels. Texels can also be described by image regions that are obtained through simple procedures such as thresholding. Voronoi tesselation can be used to define their spatial relationships—divisions are made at the midpoints between the centroids of each texel and the centroids of every surrounding texel for the entire texture. This results in each texel centroid having a Voronoi polygon surrounding it, which consists of all points that are closer to its own texel centroid than any other centroid. Rendering When texturing a 3D surface or surfaces (a process known as texture mapping), the renderer maps texels to appropriate pixels in the geometric fragment (typically a triangle) in the output picture. On modern computers, this operation is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diamond Cubic
The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α-tin, the semiconductors silicon and germanium, and silicon–germanium alloys in any proportion. There are also crystals, such as the high-temperature form of cristobalite, which have a similar structure, with one kind of atom (such as silicon in cristobalite) at the positions of carbon atoms in diamond but with another kind of atom (such as oxygen) halfway between those (see :Minerals in space group 227). Although often called the diamond lattice, this structure is not a lattice in the technical sense of this word used in mathematics. Crystallographic structure Diamond's cubic structure is in the Fdm space group (space group 227), which follows the face-centered cubic Bravais lattice. The lattice describes the repeat pattern; for diamond cubic cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
