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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 ...
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 straightforward to find the smallest enclosing box that has sides parallel to the coordinate axes; the difficult part of the problem is to ...
The total volume of the pieces, 27xyz, is less than the volume (x + y + z) 3 of the cube that they pack into. If one takes the cube root of both volumes, and divides by three, then the number obtained in this way from the total volume of the pieces is the geometric mean of x , y , and z , while the number obtained in the same way from the ...
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 spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non ...
The position of this cell is the extreme foreground of the 4th dimension beyond the position of the viewer's screen. 4-cube 3 4 virtual puzzle, rotated in the 4th dimension to show the colour of the hidden cell. 4-cube 3 4 virtual puzzle, rotated in normal 3D space. 4-cube 3 4 virtual puzzle, scrambled. 4-cube 2 4 virtual puzzle, one cubie is ...
The choice of the type of bounding volume for a given application is determined by a variety of factors: the computational cost of computing a bounding volume for an object, the cost of updating it in applications in which the objects can move or change shape or size, the cost of determining intersections, and the desired precision of the intersection test.
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.