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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 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 ().
The two base-pair complementary chains of the DNA molecule allow replication of the genetic instructions. The "specific pairing" is a key feature of the Watson and Crick model of DNA, the pairing of nucleotide subunits. [5] In DNA, the amount of guanine is equal to cytosine and the amount of adenine is equal to thymine. The A:T and C:G pairs ...
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.
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.
That is, if MWT(i,j) denotes the weight of the minimum-weight triangulation of the polygon below edge ij, then the overall algorithm performs the following steps: For each possible value of i, from n − 1 down to 1, do: For each possible value of j, from i + 1 to n, do: If ij is an edge of the polygon, set MWT(i,j) = length(ij)
The concept of a triangulation may also be generalized somewhat to subdivisions into shapes related to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles—polygons that, like triangles, have exactly three convex vertices. As in point set triangulations ...
Methods for folding most regular polygons up to and including the regular 19-gon have been developed. [36] A regular n-gon can be constructed by paper folding if and only if n is a product of distinct Pierpont primes, powers of two, and powers of three.