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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.
Cell is the intersection of all of these half-spaces, and hence it is a convex polygon. [6] When two cells in the Voronoi diagram share a boundary, it is a line segment , ray , or line, consisting of all the points in the plane that are equidistant to their two nearest sites.
The following pseudocode describes a basic implementation of the Bowyer-Watson algorithm. Its time complexity is ().Efficiency can be improved in a number of ways. For example, the triangle connectivity can be used to locate the triangles which contain the new point in their circumcircle, without having to check all of the triangles - by doing so we can decrease time complexity to ().
However, this polygon also has other ears that are not evident in this triangulation. In geometry , the two ears theorem states that every simple polygon with more than three vertices has at least two ears , vertices that can be removed from the polygon without introducing any crossings.
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 ...
The Greedy Triangulation is a method to compute a polygon triangulation or a Point set triangulation using a greedy schema, which adds edges one by one to the solution in strict increasing order by length, with the condition that an edge cannot cut a previously inserted edge.
A flip removes an edge between two triangles in the triangulation and then adds the other diagonal in the edge's enclosing quadrilateral, forming a different triangulation of the same point set. This problem is known to be NP-hard. However, the computational complexity of determining the flip distance between convex polygons, a special case of ...
The triangulation number is T = b 2 + bc + c 2. This number times the number of original faces expresses how many triangles the new polyhedron will have. This number times the number of original faces expresses how many triangles the new polyhedron will have.