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Codeforces (Russian: Коудфорсес) is a website that hosts competitive programming contests. [1] It is maintained by a group of competitive programmers from ITMO University led by Mikhail Mirzayanov. [2] Since 2013, Codeforces claims to surpass Topcoder in terms of active contestants. [3] As of 2019, it has over 600,000 registered users ...
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
Given a rectilinear polygon (whose sides meet at right angles) R in the plane, a set S of points in R, and a set of identical squares, the goal is to find the largest number of non-overlapping squares that can be packed in points of S. Suppose that, for each point p in S, we put a square centered at p. Let G S be the intersection graph of these ...
In decision problem versions of the art gallery problem, one is given as input both a polygon and a number k, and must determine whether the polygon can be guarded with k or fewer guards. This problem is ∃ R {\displaystyle \exists \mathbb {R} } -complete , as is the version where the guards are restricted to the edges of the polygon. [ 10 ]
[2]: p. 1 They could also construct half of a given angle, a square whose area is twice that of another square, a square having the same area as a given polygon, and regular polygons of 3, 4, or 5 sides [2]: p. xi (or one with twice the number of sides of a given polygon [2]: pp. 49–50 ).
Once all sides of the clip polygon have been processed, the final generated list of vertices defines a new single polygon that is entirely visible. Note that if the subject polygon was concave at vertices outside the clipping polygon, the new polygon may have coincident (i.e., overlapping) edges – this is acceptable for rendering, but not for ...
A fractal landscape being rendered using the painter's algorithm on an Amiga. The painter's algorithm (also depth-sort algorithm and priority fill) is an algorithm for visible surface determination in 3D computer graphics that works on a polygon-by-polygon basis rather than a pixel-by-pixel, row by row, or area by area basis of other Hidden-Surface Removal algorithms.
The Weiler–Atherton is a polygon-clipping algorithm. It is used in areas like computer graphics and games development where clipping of polygons is needed. It allows clipping of a subject or candidate polygon by an arbitrarily shaped clipping polygon/area/region. It is generally applicable only in 2D.