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In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. [1] That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the ...
Download as PDF; Printable version; ... Minimum relevant variables in linear system; Minimum-weight triangulation; Q.
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 Delaunay triangulation of a set of points in the plane contains the Gabriel graph, the nearest neighbor graph and the minimal spanning tree of . Triangulations have a number of applications, and there is an interest to find the "good" triangulations of a given point set under some criteria as, for instance minimum-weight triangulations .
For a hole-free polygon with vertices, a triangulation can be calculated in time (). For a polygon with holes , there is a lower bound of Ω ( n log n ) {\displaystyle \Omega (n\log n)} . A related problem is partitioning to triangles with a minimal total edge length, also called minimum-weight triangulation .
The minimum weight is a concept used in various branches of mathematics and computer science related to measurement. Minimum Hamming weight, a concept in coding theory; Minimum weight spanning tree; Minimum-weight triangulation, a topic in computational geometry and computer science
A point-set triangulation, i.e., a triangulation of a discrete set of points , is a subdivision of the convex hull of the points into simplices such that any two simplices intersect in a common face of any dimension or not at all and such that the set of vertices of the simplices are contained in . [1]
There are two versions of the problem: in the optimization problem associated with Steiner trees, the task is to find a minimum-weight Steiner tree; in the decision problem the edge weights are integers and the task is to determine whether a Steiner tree exists whose total weight does not exceed a predefined natural number k.