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Octree
An octree is a tree data structure in which each internal node has exactly eight child node, children. Octrees are most often used to partition a three-dimensional space by recursive subdivision, recursively subdividing it into eight Octant (geometry), 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 octant (solid geometry), octants. In a point region (PR) octree (analogous to a point quadtree), the node stores an explicit Point (geometry), 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 (analogous to a region quadtree), the subdivision point is implicitly the center of the space the node represents. The root n ... [...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 standar ... [...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 sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadtree
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application, but the leaf cell represents a "unit of interesting spatial information". The subdivided regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. A similar partitioning is also known as a ''Q-tree''. All forms of quadtrees share some common features: * They decompose space into adaptable cells. * Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits. * The tree directory follows the spatial decomposition of the quadtree. A tree-pyramid (T-pyramid) is a "complete" tree; every node of the T-pyramid has four child nodes e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level Of Detail (computer Graphics)
In computer graphics, level of detail (LOD) refers to the complexity of a 3D model representation. LOD can be decreased as the model moves away from the viewer or according to other metrics such as object importance, viewpoint-relative speed or position. LOD techniques increase the efficiency of rendering (computer graphics), rendering by decreasing the workload on graphics pipeline stages, usually vertex transformations. The reduced visual quality of the model is often unnoticed because of the small effect on object appearance when distant or moving fast. Although most of the time LOD is applied to Geometry (computer graphics), geometry detail only, the basic concept can be generalized. Recently, LOD techniques also included shader management to keep control of pixel complexity. A form of level of detail management has been applied to texture maps for years, under the name of mipmapping, also providing higher rendering quality. It is commonplace to say that "an object has been '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
View Frustum Culling
In 3D computer graphics, hidden-surface determination (also known as shown-surface determination, hidden-surface removal (HSR), occlusion culling (OC) or visible-surface determination (VSD)) is the process of identifying what surfaces and parts of surfaces can be seen from a particular viewing angle. A hidden-surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics. The process of hidden-surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. When referring to line rendering it is known as hidden-line removal. Hidden-surface determination is necessary to render a scene correctly, so that one may not view features hidden behind the model itself, allowing only the naturally viewable portion of the graphic to be visible. Background Hidden-surface determination is a process that identifies which surfaces are not visible to the user (for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collision Detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of ''if'', ''when'' and ''where'' two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving) and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. Overview Collision detection is closely linked to calculating the distance between objects, as two objects (or more) intersect when the distance between them reaches zero or even becomes negative. Negative distance indicates that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for the co ... [...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), 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 (computer graphics), 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 Computer-aided design, CAD, collision detection in robotics and 3D video games, ray tracing (graphics), ray tracing, virtual landscape simulation, and other applications tha ... [...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. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Estimation
In statistics, a random vector is classically represented by a probability density function. In a set-membership approach or set estimation, is represented by a set to which is assumed to belong. This means that the Support (mathematics), support of the probability distribution function of is included inside . On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as Independence (probability theory), independence) and dealing with nonlinearity, 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 theory, estimation approach which considers that measurements are represented by a set (most of the time a box of where is the number of measurements) of the measurement space. If is the parameter vector a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Estimation
In control theory, a state observer, state estimator, or Luenberger observer 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. Typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Analysis
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical analysis, numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the constructio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
