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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 ().
[4] [5] The run-time complexity of this problem crucially depends on whether the raw polygon is allowed to have holes. If the raw polygon is hole-free , then an optimal partition can be found in time O ( n 4 ) {\displaystyle O(n^{4})} , where n is the number of vertices of the polygon.
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.
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 ...
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]
Triangulation of an implicit surface of genus 3 Triangulation of a parametric surface (Monkey Saddle) Triangulation of a surface means a net of triangles, which covers a given surface partly or totally, or; the procedure of generating the points and triangles of such a net of triangles.
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 ...