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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.
An ear of a polygon is defined as a triangle formed by three consecutive vertices ,, of the polygon, such that its edge lies entirely in the interior of the polygon. The two ears theorem states that every simple polygon that is not itself a triangle has at least two ears.
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 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 ().
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.
Golden Gate assembly involves digesting DNA sequences containing a type IIS restriction enzyme cut site and ligating them together. Golden Gate Cloning or Golden Gate assembly [1] is a molecular cloning method that allows a researcher to simultaneously and directionally assemble multiple DNA fragments into a single piece using Type IIS restriction enzymes and T4 DNA ligase. [2]
Repeated sequences (also known as repetitive elements, repeating units or repeats) are short or long patterns that occur in multiple copies throughout the genome.In many organisms, a significant fraction of the genomic DNA is repetitive, with over two-thirds of the sequence consisting of repetitive elements in humans. [1]
The triangulation of a parametrically defined surface is simply achieved by triangulating the area of definition (see second figure, depicting the Monkey Saddle). However, the triangles may vary in shape and extension in object space, posing a potential drawback.