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\u0627\u0644\u0646\u062A\u0627\u0626\u062C \u0627\u0644\u0625\u064A\u062C\u0627\u0628\u064A\u0629 \u0627\u0644\u0632\u0627\u0626\u0641\u0629 \u0627\u0644\u0646\u0627\u062A\u062C\u0629 \u0639\u0646 \u0627\u062E\u062A\u0628\u0627\u0631 \u00AB\u0627\u0644\u0645\u0633\u062A\u0637\u064A\u0644\u0627\u062A \u0627\u0644\u0645\u062A\u062F\u0627\u062E\u0644\u0629\u00BB. \u062A\u0639\u062F \u0646\u0638\u0645 \u0627\u0644\u0627\u0633\u062A\u0639\u0644\u0627\u0645\u0627\u062A \u0627\u0644\u062D\u064A\u0632\u064A\u0629 \u0627\u0644\u0645\u0648\u062C\u0632\u0629 \u0648\u0627\u0644\u062A\u0645\u062B\u064A\u0644 \u0627\u0644\u0628\u064A\u0627\u0646\u064A (c-squares) \u0625\u062D\u062F\u0649 \u0627\u0644\u0637\u0631\u0642 \u0644\u0645\u0639\u0627\u0644\u062C\u0629 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060C \u0648\u0645\u0634\u0643\u0644\u0629 \u0631\u0642\u0639 \u0627\u0644\u0628\u064A\u0627\u0646\u0627\u062A \u0639\u0644\u0649 \u0648\u062C\u0647 \u0627\u0644\u062E\u0635\u0648\u0635. \u062A\u0639\u062F \u0643\u0630\u0644\u0643 \u0645\u0633\u062A\u0637\u064A\u0644\u0627\u062A \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0635\u063A\u0631\u0649 \u0645\u0642\u0648\u0645\u064B\u0627 \u0623\u0633\u0627\u0633\u064A\u064B\u0627 \u0641\u064A \u0646\u0638\u0645 \u0627\u0644\u0634\u062C\u0631\u0629 \u0630\u0627\u062A \u0627\u0644\u0634\u0643\u0644 R (R-tree) \u0641\u064A \u0627\u0644\u0641\u0647\u0631\u0633\u0629 \u0627\u0644\u062D\u064A\u0632\u064A\u0629."@ar . . . "1092238686"^^ . "\u6700\u5C0F\u5916\u63A5\u77E9\u5F62"@zh . . . . "Das minimal umgebende Rechteck (MUR) (Englisch: minimum bounding rectangle, MBR, auch bounding box und envelope) bezeichnet das kleinstm\u00F6gliche achsenparallele Rechteck, das eine vorgegebene Menge von Objekten umschlie\u00DFt. Auch wenn der Begriff scheinbar eine Zweidimensionalit\u00E4t impliziert, so spricht man auch in anderen Dimensionen von einem minimal umgebenden (Hyper-)Rechteck. Mathematisch gesehen handelt es sich um einen sehr einfachen H\u00FCllenoperator. Daf\u00FCr muss man auch die gesamte Ebene als Grenzfall eines Rechtecks zulassen."@de . "\u6700\u5C0F\u5916\u63A5\u77E9\u5F62 (minimum bounding rectangle, MBR)\uFF0C\u4E5F\u6709\u8BD1\u4E3A\u6700\u5C0F\u8FB9\u754C\u77E9\u5F62\uFF0C\u6700\u5C0F\u5305\u542B\u77E9\u5F62\uFF0C\u6216\u6700\u5C0F\u5916\u5305\u77E9\u5F62\u3002\u662F\u6307\u4EE5\u4E8C\u7EF4\u5750\u6807\u8868\u793A\u7684\u82E5\u5E72\u4E8C\u7EF4\u5F62\u72B6\uFF08\u4F8B\u5982\u70B9\u3001\u76F4\u7EBF\u3001\u591A\u8FB9\u5F62\uFF09\u7684\u6700\u5927\u8303\u56F4\uFF0C\u5373\u4EE5\u7ED9\u5B9A\u7684\u4E8C\u7EF4\u5F62\u72B6\u5404\u9876\u70B9\u4E2D\u7684\u6700\u5927\u6A2A\u5750\u6807\u3001\u6700\u5C0F\u6A2A\u5750\u6807\u3001\u6700\u5927\u7EB5\u5750\u6807\u3001\u6700\u5C0F\u7EB5\u5750\u6807\u5B9A\u4E0B\u8FB9\u754C\u7684\u77E9\u5F62\u3002\u8FD9\u6837\u7684\u4E00\u4E2A\u77E9\u5F62\u5305\u542B\u7ED9\u5B9A\u7684\u4E8C\u7EF4\u5F62\u72B6\uFF0C\u4E14\u8FB9\u4E0E\u5750\u6807\u8F74\u5E73\u884C\u3002\u6700\u5C0F\u5916\u63A5\u77E9\u5F62\u662F\u7684\u4E8C\u7EF4\u5F62\u5F0F\u3002"@zh . . . . . "In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its x-y coordinate system; in other words min(x), max(x), min(y), max(y). The MBR is a 2-dimensional case of the minimum bounding box. MBRs are frequently used as an indication of the general position of a geographic feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes. The degree to which an \"overlapping rectangles\" query based on MBRs will be satisfactory (in other words, produce a low number of \"false positive\" hits) will depend on the extent to which individual spatial objects occupy (fill) their associated MBR. If the MBR is full or nearly so (for example, a mapsheet aligned with axes of latitude and longitude will normally entirely fill its associated MBR in the same coordinate space), then the \"overlapping rectangles\" test will be entirely reliable for that and similar spatial objects. On the other hand, if the MBR describes a dataset consisting of a diagonal line, or a small number of disjunct points (patchy data), then most of the MBR will be empty and an \"overlapping rectangles\" test will produce a high number of false positives. One system that attempts to deal with this problem, particularly for patchy data, is c-squares. MBRs are also an essential prerequisite for the R-tree method of spatial indexing."@en . . "Minimum bounding rectangle"@en . . . . "Das minimal umgebende Rechteck (MUR) (Englisch: minimum bounding rectangle, MBR, auch bounding box und envelope) bezeichnet das kleinstm\u00F6gliche achsenparallele Rechteck, das eine vorgegebene Menge von Objekten umschlie\u00DFt. Auch wenn der Begriff scheinbar eine Zweidimensionalit\u00E4t impliziert, so spricht man auch in anderen Dimensionen von einem minimal umgebenden (Hyper-)Rechteck. Mathematisch gesehen handelt es sich um einen sehr einfachen H\u00FCllenoperator. Daf\u00FCr muss man auch die gesamte Ebene als Grenzfall eines Rechtecks zulassen. Der Begriff kommt aus der Informatik und findet dort Anwendung unter anderem bei der Datenspeicherung in Indexstrukturen (insbesondere im R-Baum), bei der Approximation von komplexen Objekten wie Polygonen und in der Computergrafik (siehe Bounding Volume) und in Geoinformationssystemen, da f\u00FCr Computer Rechtecke schneller zu verarbeiten sind als komplexe Objekte. W\u00E4hrend in der Computergrafik auch rotierte Rechtecke als \u201Ebounding box\u201C auftreten k\u00F6nnen, so werden im Allgemeinen nur achsenparallele Quader als MBR zugelassen."@de . . "\u0645\u0633\u062A\u0637\u064A\u0644 \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0623\u0635\u063A\u0631 (MBR)\u060C \u0648\u0627\u0644\u0630\u064A \u064A\u064F\u0639\u0631\u0641 \u0623\u064A\u0636\u064B\u0627 \u0628\u0627\u0633\u0645 \u0645\u0631\u0628\u0639 \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0623\u0648 \u0627\u0644\u0645\u0638\u0631\u0648\u0641 \u0647\u0648 \u0623\u0642\u0635\u0649 \u0627\u0645\u062A\u062F\u0627\u062F\u0627\u062A \u0644\u0634\u0643\u0644 \u062B\u0646\u0627\u0626\u064A \u0627\u0644\u0623\u0628\u0639\u0627\u062F (\u0645\u062B\u0644 \u0646\u0642\u0637\u0629 \u0648\u062E\u0637 \u0645\u0633\u062A\u0642\u064A\u0645 \u0648\u0645\u0636\u0644\u0639)\u060C \u0623\u0648 \u0645\u062C\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u062F\u0627\u062E\u0644 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A \u062B\u0646\u0627\u0626\u064A \u0627\u0644\u0623\u0628\u0639\u0627\u062F (\u0633 \u0648\u0635) \u0627\u0644\u062E\u0627\u0635 \u0628\u0647\u0627\u060C \u0623\u064A \u0628\u0645\u0639\u0646\u0649 \u0622\u062E\u0631\u060C \u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 (\u0633) \u0648\u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0635\u063A\u0631\u0649 (\u0633) \u0648\u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 (\u0635) \u0648\u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0635\u063A\u0631\u0649 (\u0635). \u0648\u064A\u0639\u062F \u0645\u0633\u062A\u0637\u064A\u0644 \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0623\u0635\u063A\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062C \u062B\u0646\u0627\u0626\u064A \u0627\u0644\u0623\u0628\u0639\u0627\u062F \u0645\u0646 \u0635\u0646\u062F\u0648\u0642 \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0623\u0635\u063A\u0631. \u062A\u0633\u062A\u062E\u062F\u0645 \u0645\u0633\u062A\u0637\u064A\u0644\u0627\u062A \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0635\u063A\u0631\u0649 \u0643\u062B\u064A\u0631\u064B\u0627 \u0641\u064A \u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0639\u0627\u0645 \u0644\u0623\u064A\u0629 \u062E\u0627\u0635\u064A\u0629 \u0623\u0648 \u0645\u062C\u0645\u0648\u0639\u0629 \u0628\u064A\u0627\u0646\u0627\u062A \u0647\u0646\u062F\u0633\u064A\u0629\u060C \u0645\u0646 \u0623\u062C\u0644 \u0623\u063A\u0631\u0627\u0636 \u0627\u0644\u0625\u0638\u0647\u0627\u0631\u060C \u0623\u0648 \u0627\u0644\u0627\u0633\u062A\u0639\u0644\u0627\u0645\u0627\u062A \u0627\u0644\u062D\u064A\u0632\u064A\u0629 \u0627\u0644\u062A\u0642\u0631\u064A\u0628\u064A\u0629 \u0627\u0644\u0623\u0648\u0644\u064A\u0629\u060C \u0623\u0648 \u0627\u0644\u0641\u0647\u0631\u0633\u0629 \u0627\u0644\u062D\u064A\u0632\u064A\u0629."@ar . . . . . . . "4799"^^ . "7416713"^^ . . . . . . . "Rectangle \u00E0 limite minimum"@fr . . . . "\u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0438\u0439 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0438\u0439 \u043F\u0440\u044F\u043C\u043E\u043A\u0443\u0442\u043D\u0438\u043A (\u0430\u043D\u0433\u043B. minimum bounding rectangle, MBR), \u0442\u0430\u043A\u043E\u0436 \u0432\u0456\u0434\u043E\u043C\u0438\u0439 \u044F\u043A \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0430 \u043A\u043E\u0440\u043E\u0431\u043A\u0430 (\u0430\u043D\u0433\u043B. bounding box) \u0447\u0438 \u043A\u043E\u043D\u0432\u0435\u0440\u0442 (\u0430\u043D\u0433\u043B. envelope), \u0446\u0435 \u0432\u0438\u0440\u0430\u0436\u0435\u043D\u043D\u044F \u043C\u0430\u043A\u0441\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u043F\u0440\u043E\u0442\u044F\u0436\u043D\u043E\u0441\u0442\u0456 \u0434\u0432\u043E\u0432\u0438\u043C\u0456\u0440\u043D\u043E\u0433\u043E \u043E\u0431'\u0454\u043A\u0442\u0430 (\u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434 \u0442\u043E\u0447\u043A\u0438, \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0430, \u043C\u043D\u043E\u0433\u043E\u043A\u0443\u0442\u043D\u0438\u043A\u0430) \u0447\u0438 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432 \u0432 \u0457\u0445 2-\u0432\u0438\u043C\u0456\u0440\u043D\u0456\u0439 (x, y) \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0442\u043E\u0431\u0442\u043E \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F min(x), max(x), min(y), max(y). MBR - \u0446\u0435 \u0434\u0432\u043E\u0432\u0438\u043C\u0456\u0440\u043D\u0438\u0439 \u0432\u0438\u043F\u0430\u0434\u043E\u043A \u043C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u043E\u0457 \u043A\u043E\u0440\u043E\u0431\u043A\u0438. \u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0456 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0456 \u043F\u0440\u044F\u043C\u043E\u043A\u0443\u0442\u043D\u0438\u043A\u0438 \u0447\u0430\u0441\u0442\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u044E\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0432\u043A\u0430\u0437\u0443\u0432\u0430\u043D\u043D\u044F \u043F\u0440\u0438\u0431\u043B\u0438\u0437\u043D\u043E\u0457 \u043F\u043E\u0437\u0438\u0446\u0456\u0457 \u043E\u0431'\u0454\u043A\u0442\u0430 \u0447\u0438 \u043D\u0430\u0431\u043E\u0440\u0443 \u0434\u0430\u043D\u0438\u0445, \u0434\u043B\u044F \u0437\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u043D\u044F, \u043F\u0440\u0438\u0431\u043B\u0438\u0437\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u043E\u0432\u043E\u0433\u043E \u0437\u0430\u043F\u0438\u0442\u0443, \u0447\u0438 \u0437 \u043C\u0435\u0442\u043E\u044E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u043E\u0432\u043E\u0433\u043E \u0456\u043D\u0434\u0435\u043A\u0441\u0443\u0432\u0430\u043D\u043D\u044F."@uk . . . . . . . . . . . . "\u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0438\u0439 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0438\u0439 \u043F\u0440\u044F\u043C\u043E\u043A\u0443\u0442\u043D\u0438\u043A (\u0430\u043D\u0433\u043B. minimum bounding rectangle, MBR), \u0442\u0430\u043A\u043E\u0436 \u0432\u0456\u0434\u043E\u043C\u0438\u0439 \u044F\u043A \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0430 \u043A\u043E\u0440\u043E\u0431\u043A\u0430 (\u0430\u043D\u0433\u043B. bounding box) \u0447\u0438 \u043A\u043E\u043D\u0432\u0435\u0440\u0442 (\u0430\u043D\u0433\u043B. envelope), \u0446\u0435 \u0432\u0438\u0440\u0430\u0436\u0435\u043D\u043D\u044F \u043C\u0430\u043A\u0441\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u043F\u0440\u043E\u0442\u044F\u0436\u043D\u043E\u0441\u0442\u0456 \u0434\u0432\u043E\u0432\u0438\u043C\u0456\u0440\u043D\u043E\u0433\u043E \u043E\u0431'\u0454\u043A\u0442\u0430 (\u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434 \u0442\u043E\u0447\u043A\u0438, \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0430, \u043C\u043D\u043E\u0433\u043E\u043A\u0443\u0442\u043D\u0438\u043A\u0430) \u0447\u0438 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432 \u0432 \u0457\u0445 2-\u0432\u0438\u043C\u0456\u0440\u043D\u0456\u0439 (x, y) \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0442\u043E\u0431\u0442\u043E \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F min(x), max(x), min(y), max(y). MBR - \u0446\u0435 \u0434\u0432\u043E\u0432\u0438\u043C\u0456\u0440\u043D\u0438\u0439 \u0432\u0438\u043F\u0430\u0434\u043E\u043A \u043C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u043E\u0457 \u043A\u043E\u0440\u043E\u0431\u043A\u0438."@uk . . . "Minimal umgebendes Rechteck"@de . . . . . . . "Le Rectangle \u00E0 limite minimum (\u00AB minimum bounding rectangle (MBR) \u00BB), connu aussi sous le nom de boite limite ou enveloppe, est l'expression de l'extension maximum d'un objet bi-dimensionnel (i.e. point, ligne, polygone) dans un syst\u00E8me de coordonn\u00E9es (x,y), soit min(x), max(x), min(y), max(y).En fouille de donn\u00E9es spatiales ou en Analyse spatiale, les Rectangles \u00E0 limite minimum sont fr\u00E9quemment utilis\u00E9s comme indication de la position g\u00E9n\u00E9rale d'un objet g\u00E9ographique, pour un affichage, une requ\u00EAte spatiale en premi\u00E8re approximation, ou dans un but d'indexation spatial."@fr . . . . . . . . . "Le Rectangle \u00E0 limite minimum (\u00AB minimum bounding rectangle (MBR) \u00BB), connu aussi sous le nom de boite limite ou enveloppe, est l'expression de l'extension maximum d'un objet bi-dimensionnel (i.e. point, ligne, polygone) dans un syst\u00E8me de coordonn\u00E9es (x,y), soit min(x), max(x), min(y), max(y).En fouille de donn\u00E9es spatiales ou en Analyse spatiale, les Rectangles \u00E0 limite minimum sont fr\u00E9quemment utilis\u00E9s comme indication de la position g\u00E9n\u00E9rale d'un objet g\u00E9ographique, pour un affichage, une requ\u00EAte spatiale en premi\u00E8re approximation, ou dans un but d'indexation spatial."@fr . . . . . . . . "In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its x-y coordinate system; in other words min(x), max(x), min(y), max(y). The MBR is a 2-dimensional case of the minimum bounding box. MBRs are frequently used as an indication of the general position of a geographic feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes."@en . . . "\u0645\u0633\u062A\u0637\u064A\u0644 \u0627\u0644\u0625\u062D\u0627\u0637\u0629 \u0627\u0644\u0623\u0635\u063A\u0631"@ar . . "\u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0438\u0439 \u043E\u0431\u043C\u0435\u0436\u0443\u0432\u0430\u043B\u044C\u043D\u0438\u0439 \u043F\u0440\u044F\u043C\u043E\u043A\u0443\u0442\u043D\u0438\u043A"@uk . . . . "\u6700\u5C0F\u5916\u63A5\u77E9\u5F62 (minimum bounding rectangle, MBR)\uFF0C\u4E5F\u6709\u8BD1\u4E3A\u6700\u5C0F\u8FB9\u754C\u77E9\u5F62\uFF0C\u6700\u5C0F\u5305\u542B\u77E9\u5F62\uFF0C\u6216\u6700\u5C0F\u5916\u5305\u77E9\u5F62\u3002\u662F\u6307\u4EE5\u4E8C\u7EF4\u5750\u6807\u8868\u793A\u7684\u82E5\u5E72\u4E8C\u7EF4\u5F62\u72B6\uFF08\u4F8B\u5982\u70B9\u3001\u76F4\u7EBF\u3001\u591A\u8FB9\u5F62\uFF09\u7684\u6700\u5927\u8303\u56F4\uFF0C\u5373\u4EE5\u7ED9\u5B9A\u7684\u4E8C\u7EF4\u5F62\u72B6\u5404\u9876\u70B9\u4E2D\u7684\u6700\u5927\u6A2A\u5750\u6807\u3001\u6700\u5C0F\u6A2A\u5750\u6807\u3001\u6700\u5927\u7EB5\u5750\u6807\u3001\u6700\u5C0F\u7EB5\u5750\u6807\u5B9A\u4E0B\u8FB9\u754C\u7684\u77E9\u5F62\u3002\u8FD9\u6837\u7684\u4E00\u4E2A\u77E9\u5F62\u5305\u542B\u7ED9\u5B9A\u7684\u4E8C\u7EF4\u5F62\u72B6\uFF0C\u4E14\u8FB9\u4E0E\u5750\u6807\u8F74\u5E73\u884C\u3002\u6700\u5C0F\u5916\u63A5\u77E9\u5F62\u662F\u7684\u4E8C\u7EF4\u5F62\u5F0F\u3002"@zh . . . .