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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 ...
Packing identical rectangles in a rectangle: The problem of packing multiple instances of a single rectangle of size (l,w), allowing for 90° rotation, in a bigger rectangle of size (L,W) has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. For example, it is possible to pack 147 rectangles of size (137 ...
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.
Sphere packing finds practical application in the stacking of cannonballs.. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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. The benefit is ...
To form an A-B-A-B-... hexagonal close packing of spheres, the coordinate points of the lattice will be the spheres' centers. Suppose, the goal is to fill a box with spheres according to HCP. The box would be placed on the x-y-z coordinate space. First form a row of spheres. The centers will all lie on a straight line.
In geometry, sphere packing in a cube is a three-dimensional sphere packing problem with the objective of packing spheres inside a cube. It is the three-dimensional equivalent of the circle packing in a square problem in two dimensions. The problem consists of determining the optimal packing of a given number of spheres inside the cube.
The potential energy in this model is given as = {, < < +,,, where L is the length of the box, x c is the location of the center of the box and x is the position of the particle within the box. Simple cases include the centered box ( x c = 0) and the shifted box ( x c = L /2) (pictured).