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Polygon triangulation. In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. [ 1 ] [ 2 ] [ 3 ] Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology , but also in visual art .
If a simple polygon is triangulated, then a triple of consecutive vertices ,, forms an ear if is a convex vertex and none of its other neighbors in the triangulation lie in triangle . By testing all neighbors of all vertices, it is possible to find all the ears of a triangulated simple polygon in linear time . [ 4 ]
Two simple polygons (green and blue) and a self-intersecting polygon (red, in the lower right, not simple) 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.
Successive steps of triangulation refinement. A polygon with m vertices can be partitioned into m–2 triangles. Which can be shown by induction starting from a triangle. There are numerous algorithms to triangulate a polygon efficiently, the fastest having O(n) worst case time. Therefore, we can decompose each polygon of our subdivision in ...
Triangulation in a simple polygon. Triangulation means the partition of any planar object into a collection of triangles. For example, in polygon triangulation, a polygon is subdivided into multiple triangles that are attached edge-to-edge, with the property that their vertices coincide with the set of vertices of the polygon. [52]
A triangulation of the square that respects the gluings, like that shown below, also defines a triangulation of the torus. A two dimensional torus, represented as the gluing of a square via the map g, identifying its opposite sites; The projective plane admits a triangulation (see CW-complexes)
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity.
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