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For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle: The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...
Many problems in the chemical and physical sciences can be related to packing problems where more than one size of sphere is available. Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing.
In the first variant, called bin-packing with size-increasing fragmentation (BP-SIF), each item may be fragmented; overhead units are added to the size of every fragment. In the second variant, called bin-packing with size-preserving fragmentation ( BP-SPF ) each item has a size and a cost; fragmenting an item increases its cost but does not ...
The set of all orthogonal matrices of size n with determinant +1 is a representation of a group known as the special orthogonal group SO(n), one example of which is the rotation group SO(3). The set of all orthogonal matrices of size n with determinant +1 or −1 is a representation of the (general) orthogonal group O(n).
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Colour indicates function value. The black dots are the locations of the prescribed data being interpolated. Note how the color samples are not radially symmetric. Bilinear interpolation on the same dataset as above. Derivatives of the surface are not continuous over the square boundaries. Nearest-neighbor interpolation on the same dataset as ...
This means a shared spatial vertex position can have different UV coordinates for each of its triangles, so adjacent triangles can be cut apart and positioned on different areas of the texture map. The UV mapping process at its simplest requires three steps: unwrapping the mesh, creating the texture, and applying the texture to a respective ...
The traditional flood-fill algorithm takes three parameters: a start node, a target color, and a replacement color. The algorithm looks for all nodes in the array that are connected to the start node by a path of the target color and changes them to the replacement color.