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Oct-tree Hashing
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from ''oct'' (Greek root meaning "eight") + ''tree''. Octrees are often used in 3D graphics and 3D game engines. For spatial representation Each node in an octree subdivides the space it represents into eight octants. In a point region (PR) octree, the node stores an explicit three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix based (MX) octree, the subdivision point is implicitly the center of the space the node represents. The root node of a PR octree can represent infinite space; the root node of an MX octree must represent a finite bounded space so that the implicit centers are well-defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octree2
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from ''oct'' (Greek root meaning "eight") + ''tree''. Octrees are often used in 3D graphics and 3D game engines. For spatial representation Each node in an octree subdivides the space it represents into eight octants. In a point region (PR) octree, the node stores an explicit three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix based (MX) octree, the subdivision point is implicitly the center of the space the node represents. The root node of a PR octree can represent infinite space; the root node of an MX octree must represent a finite bounded space so that the implicit centers are well-define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Index
A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spatial databases allow the representation of simple geometric objects such as points, lines and polygons. Some spatial databases handle more complex structures such as 3D objects, topological coverages, linear networks, and triangulated irregular networks (TINs). While typical databases have developed to manage various numeric and character types of data, such databases require additional functionality to process spatial data types efficiently, and developers have often added ''geometry'' or ''feature'' data types. The Open Geospatial Consortium (OGC) developed the Simple Features specification (first released in 1997) and sets standards for adding spatial functionality to database systems. The '' SQL/MM Spatial'' ISO/IEC standard is a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Interval Hierarchy
A bounding interval hierarchy (BIH) is a partitioning data structure similar to that of bounding volume hierarchies or kd-trees. Bounding interval hierarchies can be used in high performance (or real-time) ray tracing and may be especially useful for dynamic scenes. The BIH was first presented under the name of SKD-Trees,Nam, Beomseok; Sussman, AlanA comparative study of spatial indexing techniques for multidimensional scientific datasets/ref> presented by Ooi et al., and BoxTrees,Zachmann, Gabriel{{Webarchive, url=https://web.archive.org/web/20070210140734/http://zach.in.tu-clausthal.de/papers/vrst02.html , date=2007-02-10 independently invented by Zachmann. Overview Bounding interval hierarchies (BIH) exhibit many of the properties of both bounding volume hierarchies (BVH) and kd-trees. Whereas the construction and storage of BIH is comparable to that of BVH, the traversal of BIH resemble that of kd-trees. Furthermore, BIH are also binary trees just like kd-trees (and in fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Space Partitioning
In computer science, binary space partitioning (BSP) is a method for space partitioning which recursively subdivides a Euclidean space into two convex sets by using hyperplanes as partitions. This process of subdividing gives rise to a representation of objects within the space in the form of a tree data structure known as a BSP tree. Binary space partitioning was developed in the context of 3D computer graphics in 1969. The structure of a BSP tree is useful in rendering because it can efficiently give spatial information about the objects in a scene, such as objects being ordered from front-to-back with respect to a viewer at a given location. Other applications of BSP include: performing geometrical operations with shapes (constructive solid geometry) in CAD, collision detection in robotics and 3D video games, ray tracing, and other applications that involve the handling of complex spatial scenes. Overview Binary space partitioning is a generic process of recursively dividi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Color Quantization
In computer graphics, color quantization or color image quantization is quantization applied to color spaces; it is a process that reduces the number of distinct colors used in an image, usually with the intention that the new image should be as visually similar as possible to the original image. Computer algorithms to perform color quantization on bitmaps have been studied since the 1970s. Color quantization is critical for displaying images with many colors on devices that can only display a limited number of colors, usually due to memory limitations, and enables efficient compression of certain types of images. The name "color quantization" is primarily used in computer graphics research literature; in applications, terms such as ''optimized palette generation'', ''optimal palette generation'', or ''decreasing color depth'' are used. Some of these are misleading, as the palettes generated by standard algorithms are not necessarily the best possible. Algorithms Most standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Estimation
In statistics, a random vector ''x'' is classically represented by a probability density function. In a set-membership approach or set estimation, ''x'' is represented by a set ''X'' to which ''x'' is assumed to belong. This means that the support of the probability distribution function of ''x'' is included inside ''X''. On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as independence) and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support. Set-membership estimation Set membership estimation (or ''set estimation'' for short) is an estimation approach which considers that measurements are represented by a set ''Y'' (most of the time a box of R''m'', where ''m'' is the number of measurements) of the measurement space. If ''p'' is the parameter vector and ''f'' is the model function, then t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Estimation
In control theory, a state observer or state estimator is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback. In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable, it is possible to fully reconstruct the system state from its output measurements using the state observer. Typical observer model Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Voxel Octree
A sparse voxel octree (SVO) is a 3D computer graphics rendering technique using a raycasting or sometimes a ray tracing approach into an octree data representation. The technique generally relies on generating and processing the hull of points (sparse voxels) which are visible, or may be visible, given the resolution and size of the screen. There are two main advantages to the technique. The first is that only pixels that will be displayed are computed, with the screen resolution limiting the level of detail required; this limits computational cost during rendering. The second is that interior voxels (those fully enclosed by other voxels) need not be included in the 3D data set; this limits the amount of 3D voxel data (and thus storage space) required for realistic, high-resolution digital models and/or environments. The basic advantage of octrees is that, as a hierarchical data structure, they need not be explored to their full depth. This means that a system can extract a smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Analysis
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unstructured Grid
An unstructured grid or irregular grid is a tessellation of a part of the Euclidean plane or Euclidean space by simple shapes, such as triangles or tetrahedra, in an irregular pattern. Grids of this type may be used in finite element analysis when the input to be analyzed has an irregular shape. Unlike structured grids, unstructured grids require a list of the connectivity which specifies the way a given set of vertices make up individual elements (see graph (data structure)). 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 triangulat ... is often used to convert an irregularly shaped polygon into an unstructured grid of triangles. In addition to triangles and tetrahedra, other commonly used elements in finite element simulation include quadrilateral (4-noded) and hexa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Multipole Method
__NOTOC__ The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the ''n''-body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a single source. The FMM has also been applied in accelerating the iterative solver in the method of moments (MOM) as applied to computational electromagnetics problems. The FMM was first introduced in this manner by Leslie Greengard and Vladimir Rokhlin Jr. and is based on the multipole expansion of the vector Helmholtz equation. By treating the interactions between far-away basis functions using the FMM, the corresponding matrix elements do not need to be explicitly stored, resulting in a significant reduction in required memory. If the FMM is then applied in a hierarchical manner, it can improve the complexity of matrix-vector products in an ite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
