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Breaking a polygon into monotone polygons. A simple polygon may be easily cut into monotone polygons in O(n log n) time. However, since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed for simple polygons in O(n) time with a complex algorithm. [6]
A polygonal chain is called monotone if there is a straight line L such that every line perpendicular to L intersects the chain at most once. Every nontrivial monotone polygonal chain is open. In comparison, a monotone polygon is a polygon (a closed chain) that can be partitioned into exactly two monotone chains. [2]
A monotone planar subdivision with some monotone chains highlighted. A (vertical) monotone chain is a path such that the y-coordinate never increases along the path. A simple polygon is (vertical) monotone if it is formed by two monotone chains, with the first and last vertices in common. It is possible to add some edges to a planar subdivision ...
A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can be triangulated in O(n) time. Assuming a given polygon is y-monotone, the greedy algorithm begins by walking on one chain of the polygon from top to bottom while adding ...
The polygonal wraps, weakly simple polygons that use each given point one or more times as a vertex, include all polygonalizations and are connected by local moves. [2] Another more general class of polygons, the surrounding polygons, are simple polygons that have some of the given points as vertices and enclose all of the points. They are ...
CRULP (Center for research for Urdu language processing) has been working on phonetic keyboard designs for URDU and other local languages of Pakistan. Their Urdu Phonetic Keyboard Layout v1.1 for Windows is widely used and considered as a standard for typing Urdu on Microsoft platform.
In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons.
Monotone preferences, a property of a consumer's preference ordering. Monotonicity (mechanism design), a property of a social choice function. Monotonicity criterion, a property of a voting system. Resource monotonicity, a property of resource allocation rules and bargaining systems.