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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.
The Perverse Triangle was first described in 1977 by Jay Haley [6] as a triangle where two people who are on different hierarchical or generational levels form a coalition against a third person (e.g., "a covert alliance between a parent and a child, who band together to undermine the other parent's power and authority".) [7] The perverse triangle concept has been widely discussed in ...
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.
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 ]
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.
Two cases of two interrelated geons, What does the reader imagine in each case? There are 4 essential properties of geons: View-invariance: Each geon can be distinguished from the others from almost any viewpoints except for “accidents” at highly restricted angles in which one geon projects an image that could be a different geon, as, for example, when an end-on view of a cylinder can be a ...
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
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.