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  2. Polygon partition - Wikipedia

    en.wikipedia.org/wiki/Polygon_partition

    A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number of units or with units of smallest total side-length. Polygon partitioning is an important class of problems in computational geometry. There are many different polygon partition problems, depending on ...

  3. Space partitioning - Wikipedia

    en.wikipedia.org/wiki/Space_partitioning

    Storing objects in a space-partitioning data structure (k-d tree or BSP tree for example) makes it easy and fast to perform certain kinds of geometry queries—for example in determining whether a ray intersects an object, space partitioning can reduce the number of intersection test to just a few per primary ray, yielding a logarithmic time ...

  4. Dividing a square into similar rectangles - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_square_into...

    However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...

  5. Partition of a set - Wikipedia

    en.wikipedia.org/wiki/Partition_of_a_set

    (Note: this is the partition, not a member of the partition.) For any non-empty set X, P = { X} is a partition of X, called the trivial partition. Particularly, every singleton set {x} has exactly one partition, namely { {x} }. For any non-empty proper subset A of a set U, the set A together with its complement form a partition of U, namely ...

  6. Binary space partitioning - Wikipedia

    en.wikipedia.org/wiki/Binary_space_partitioning

    Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies one or more requirements. It can be seen as a generalization of other spatial tree structures such as k -d trees and quadtrees , one where hyperplanes that partition the space may have any orientation, rather than being ...

  7. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    For example, 4 can be partitioned in five distinct ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1.

  8. Octree - Wikipedia

    en.wikipedia.org/wiki/Octree

    Binary space partitioning; Bounding interval hierarchy; Cube 2: Sauerbraten, a 3D game engine in which geometry is almost entirely based on octrees; id Tech 6 is a 3D game engine that utilizes voxels stored in octrees; Irrlicht Engine, supports octree scene nodes; Klee's measure problem; Linear octree; OGRE, has an octree scene manager ...

  9. Voronoi diagram - Wikipedia

    en.wikipedia.org/wiki/Voronoi_diagram

    In the simplest case, shown in the first picture, we are given a finite set of points {, …} in the Euclidean plane.In this case each site is one of these given points, and its corresponding Voronoi cell consists of every point in the Euclidean plane for which is the nearest site: the distance to is less than or equal to the minimum distance to any other site .

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