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Largest Empty Sphere
In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in ''d''-dimensional space whose interior does not overlap with any given obstacles. Two dimensions The largest empty circle problem is the problem of finding a circle of largest radius in Plane (geometry), the plane whose interior does not overlap with any given obstacles. A common special case is as follows. Given ''n'' points in the plane, find a largest circle centered within their convex hull and enclosing none of them. The problem may be solved using Voronoi diagrams in time complexity, optimal time \Theta(n\, \log\, n).Megan Schuster"The Largest Empty Circle Problem"/ref> See also *Bounding sphere *Farthest-first traversal *Largest empty rectangle References {{reflist Geometric algorithms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Espace Octaedrique Cubique Faces Centrees , a multi-purpose-vehicle
*eSpace, an Egyptian software company
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Espace may refer to: *ESPACE, a complexity class in computational complexity theory *Espace musique, a Canadian radio service *Espace 2, a Swiss radio station *Radio Espace, a French radio station *Espace Group, a French media company *Group Espace, a concrete art group *Renault Espace The Renault Espace () is a series of automobiles manufactured by Renault since 1984. For its first five generations, the Espace was a multi-purpose vehicle/MPV (M-segment), but it has been redesigned as a mid-size crossover SUV for its sixth ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plus Grand Cercle Vide Voronoi
Plus or PLUS may refer to: Mathematics * Addition * +, the mathematical sign Music * Plus (band), a Japanese pop boy band Albums and EPs * ''+'' (Ed Sheeran album), (pronounced "plus"), 2011 * ''Plus'' (Astrud Gilberto and James Last album), 1986 * ''Plus'' (Autechre album), 2020 * ''Plus'' (Cannonball Adderley Quintet album), 1961 * ''Plus'' (Martin Garrix EP), 2018 * ''Plus'' (Matt Nathanson EP), 2003 Companies * Plus (autonomous trucking) * Plus (British TV channel), run by Granada Sky Broadcasting * PLUS (Dutch supermarket) * Plus (German supermarket) * Plus (interbank network), Visa's ATM and debit card network * Plus (telecommunications Poland), a mobile phone brand * Plus Communication Sh.A, a cellphone company in Albania * Plus Development, a defunct American computer storage manufacturer * PLUS Expressways, concessionaire holder of majority of Malaysian expressways * PLUS Markets, a small stock exchange in London, UK Other uses * , the international call prefix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypersphere
In mathematics, an -sphere or hypersphere is an - dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer . The circle is considered 1-dimensional and the sphere 2-dimensional because a point within them has one and two degrees of freedom respectively. However, the typical embedding of the 1-dimensional circle is in 2-dimensional space, the 2-dimensional sphere is usually depicted embedded in 3-dimensional space, and a general -sphere is embedded in an -dimensional space. The term ''hyper''sphere is commonly used to distinguish spheres of dimension which are thus embedded in a space of dimension , which means that they cannot be easily visualized. The -sphere is the setting for -dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in -dimensional Euclidean space, an -sphere is the locus of points at equal distance (the ''radius'') from a given '' center'' point. Its interior, consisting of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane (geometry)
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement. A Euclidean plane with a chosen Cartesian coordinate system is called a '' Cartesian plane''. The set \mathbb^2 of the ordered pairs of real numbers (the real coordinate plane), equipped with the dot product, is often called ''the'' Euclidean plane or ''standard Euclidean plane'', since every Euclidean plane is isomorphic to it. History Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a Bounded set, bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its projective duality, dual problem of intersecting Half-space (geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. Simplest case In the simplest case, shown in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Sphere
In mathematics, given a non-empty set of objects of finite extension in d-dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is a d-dimensional solid sphere containing all of these objects. Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms with a high practical value in real-time computer graphics applications. In statistics and operations research, the objects are typically points, and generally the sphere of interest is the minimal bounding sphere, that is, the sphere with minimal radius among all bounding spheres. It may be proven that such a sphere is unique: If there are two of them, then the objects in question lie within their intersection. But an intersection of two non-coinciding spheres of equal radius is contained in a sphere of smaller radius. The problem of computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farthest-first Traversal
In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as far as possible from the set of previously-selected points. The same concept can also be applied to a finite set of geometric points, by restricting the selected points to belong to the set or equivalently by considering the finite metric space generated by these points. For a finite metric space or finite set of geometric points, the resulting sequence forms a permutation of the points, also known as the greedy permutation. Every prefix of a farthest-first traversal provides a set of points that is widely spaced and close to all remaining points. More precisely, no other set of equally many points can be spaced more than twice as widely, and no other set of equally many points can be less than half as far to its farthest remaining point. In part because of these properties, farthest- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Empty Rectangle
In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic formulation, in particular, depending on the measure of the "size", domain (type of obstacles), and the orientation of the rectangle. The problems of this kind arise e.g., in electronic design automation, in design and verification of physical layout of integrated circuits. A maximal empty rectangle is a rectangle which is not contained in another empty rectangle. Each side of a maximal empty rectangle abuts an obstacle (otherwise the side may be shifted outwards, increasing the empty rectangle). An application of this kind is enumeration of "maximal white rectangles" in image segmentation R&D of image processing and pattern recognition. In the contexts of man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
