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A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that ...
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is ...
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 corresponding problem in n-dimensional space, the smallest bounding sphere problem, is to compute the smallest n-sphere that contains all of a given set of points. [1] The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857. [2]
The relation between the two geometries, Euclidean and projective, [4]: 133 shows that mathematical objects are not given to us with their structure. [ 4 ] : 21 Rather, each mathematical theory describes its objects by some of their properties, precisely those that are put as axioms at the foundations of the theory.
An object of C 3v symmetry under one of the 3-fold axes gives rise under the action of T d to an orbit consisting of four such objects, and T d corresponds to the set of permutations of these four objects. T d is a normal subgroup of O h. See also the isometries of the regular tetrahedron. T h, (3*2) [3 +,4] 2/m 3, m 3 order 24: pyritohedral ...
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders with diameters on the same order of magnitude as the spheres, such packings result in what are called columnar structures .
Two perpendicular coordinate axes are given which cross each other at the origin. They are usually labeled x and y . Relative to these axes, the position of any point in two-dimensional space is given by an ordered pair of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal ...