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The time complexity of triangulation of an n-vertex polygon with holes has an Ω(n log n) lower bound, in algebraic computation tree models of computation. [1] It is possible to compute the number of distinct triangulations of a simple polygon in polynomial time using dynamic programming , and (based on this counting algorithm) to generate ...
For a hole-free polygon with vertices, a triangulation can be calculated in time (). For a polygon with holes , there is a lower bound of Ω ( n log n ) {\displaystyle \Omega (n\log n)} . A related problem is partitioning to triangles with a minimal total edge length, also called minimum-weight triangulation .
In geometry, a polygon with holes is an area-connected planar polygon with one external boundary and one or more interior boundaries (holes). [1] Polygons with holes can be dissected into multiple polygons by adding new edges, so they are not frequently needed. An ordinary polygon can be called simply-connected, while a polygon-with-holes is ...
Kooshesh & Moret (1992) gave a linear time algorithm by using Fisk's short proof and Bernard Chazelle's linear time plane triangulation algorithm. For simple polygons that do not contain holes, the existence of a constant factor approximation algorithm for vertex and edge guards was conjectured by Ghosh.
Since every tree with more than one vertex has at least two leaves, every triangulated polygon with more than one triangle has at least two ears. Thus, the two ears theorem is equivalent to the fact that every simple polygon has a triangulation. [2] Triangulation algorithms based on this principle have been called ear-clipping algorithms ...
Polygon triangulations may be found in linear time and form the basis of several important geometric algorithms, including a simple approximate solution to the art gallery problem. The constrained Delaunay triangulation is an adaptation of the Delaunay triangulation from point sets to polygons or, more generally, to planar straight-line graphs.
Paul Benos, Merle Benos, Yogi Fabe, Esmeralda Ramirez and Olivia Dionio sit at the Brooklyn Botanic Garden, wearing cherry blossom-colored outfits for the solar eclipse on April 8, 2024.
Three possible triangulations of the same polygon. The central triangulation has less weight (sum of perimeters). In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. [1]
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