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Minimum-weight Triangulation
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. 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 sum of the perimeters of the triangles. The problem is NP-hard for point set inputs, but may be approximated to any desired degree of accuracy. For polygon inputs, it may be solved exactly in polynomial time. The minimum weight triangulation has also sometimes been called the optimal triangulation. History The problem of minimum weight triangulation of a point set was posed by , who suggested its application to the construction of triangulated irregular network models of land countours, and used a greedy heuristic to approximate it. conjectured that the minimum weight triangulation always coincided with the Delaunay triangulation, but this was q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Convex Polygon Triangulations
Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope, a polytope with a convex set of points ** Convex metric space, a generalization of the convexity notion in abstract metric spaces * Convex function, when the line segment between any two points on the graph of the function lies above or on the graph * Convex conjugate, of a function * Convexity (algebraic geometry), a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich Moduli space, moduli spaces Economics and finance * Convexity (finance), second derivatives in financial modeling generally * Convexity in economics * Bond convexity, a measure of the sensitivity of the duration of a bond to changes in interest rates * Convex preferences, an individual's ordering of various outcomes Other use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
