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A series of geometric shapes enclosed by its minimum bounding rectangle. 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).
A sphere enclosed by its axis-aligned minimum bounding box (in 3 dimensions) In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie.
The key idea of the data structure is to group nearby objects and represent them with their minimum bounding rectangle in the next higher level of the tree; the "R" in R-tree is for rectangle. Since all objects lie within this bounding rectangle, a query that does not intersect the bounding rectangle also cannot intersect any of the contained ...
The minimum bounding box of a regular tetrahedron The minimal enclosing box of the regular tetrahedron is a cube, with side length 1/ √ 2 that of the tetrahedron; for instance, a regular tetrahedron with side length √ 2 fits into a unit cube , with the tetrahedron's vertices lying at the vertices (0,0,0), (0,1,1), (1,0,1) and (1,1,0) of the ...
The prioritized R-tree is essentially a hybrid between a k-dimensional tree and a R-tree in that it defines a given object's N-dimensional bounding volume (called Minimum Bounding Rectangles – MBR) as a point in N-dimensions, represented by the ordered pair of the rectangles.
Minimum bounding box (Smallest enclosing box, Smallest bounding box) 2-D case: Smallest bounding rectangle (Smallest enclosing rectangle) There are two common variants of this problem. In many areas of computer graphics, the bounding box (often abbreviated to bbox) is understood to be the smallest box delimited by sides parallel to coordinate ...
A bounding box or minimum bounding box (MBB) is a cuboid, or in 2-D a rectangle, containing the object. In dynamical simulation , bounding boxes are preferred to other shapes of bounding volume such as bounding spheres or cylinders for objects that are roughly cuboid in shape when the intersection test needs to be fairly accurate.
However, for the Hilbert curve this is much harder than for example the Z-order curve. Figure 2 shows one such ordering for a 4x4 grid (see curve H 2). For example, the point (0,0) on the H 2 curve has a Hilbert value of 0, while the point (1,1) has a Hilbert value of 2. The Hilbert value of a rectangle is defined as the Hilbert value of its ...