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Steiner Point (computational Geometry)
In computational geometry, a Steiner point is a point that is not part of the input to a geometric optimization problem but is added during the solution of the problem, to create a better solution than would be possible from the original points alone. The name of these points comes from the Steiner tree problem, named after Jakob Steiner, in which the goal is to connect the input points by a network of minimum total length. If the input points alone are used as endpoints of the network edges, then the shortest network is their minimum spanning tree. However, shorter networks can often be obtained by adding Steiner points, and using both the new points and the input points as edge endpoints. Another problem that uses Steiner points is Steiner triangulation. The goal is to partition an input (such as a point set or polygon) into triangles, meeting edge-to-edge. Both input points and Steiner points may be used as triangle vertices. See also *Delaunay refinement References {{r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Points Example
Steiner may refer to: People *Steiner (surname) *Steiner Brothers, a professional wrestling tag team *Steiner Brothers (tap-dancing trio), a 1950s–1960s Canadian act Places *Steiner, Michigan, U.S. *Steiner, Mississippi, U.S. Math and science *Steiner's theorem, or parallel axis theorem *Steiner tree *Poncelet–Steiner theorem *Steiner surface *Steiner system, a type of block design *Steiner point (other) Other uses *Steiner House, in Vienna, Austria *Steiner Studios, a film and television production studio in New York City *Franz Steiner Verlag, a German publisher See also *Army Detachment Steiner, a temporary German military unit during the 1945 Battle of Berlin during World War II *Waldorf education, also called Steiner education {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Tree Problem
In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of settings, they all require an optimal interconnect for a given set of objects and a predefined objective function. One well-known variant, which is often used synonymously with the term Steiner tree problem, is the Steiner tree problem in graphs. Given an undirected graph with non-negative edge weights and a subset of vertices, usually referred to as terminals, the Steiner tree problem in graphs requires a tree of minimum weight that contains all terminals (but may include additional vertices) and minimizes the total weight of its edges. Further well-known variants are the ''Euclidean Steiner tree problem'' and the '' rectilinear minimum Steiner tree problem''. The Steiner tree problem in graphs can be seen as a generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of Niels Henrik Abel, then also staying at Berlin, founded his famous '' Journal'' (1826). After Steiner's publication (1832) of his ''Systematische Entwickelungen'' he received, through Carl Gustav Jacob Jacobi, who was then professor at Königsberg University, and earned an honorary degree there; and through the influence of Jacobi and of the brothers Alexander and Wilhelm von Humboldt a new chair of geometry was founded for him at Berlin (1834). This he occupied until his death in Bern on 1 April 1863. He was described by Thomas Hirst as follo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Spanning Tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ''Trends (journals), Trends'', the ''Current Opinion (Elsevier), Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services include digital tools for Data management platform, data management, instruction, research analytics, and assessment. Elsevier is part of the RELX Group, known until 2015 as Reed Elsevier, a publicly traded company. According to RELX reports, in 2022 Elsevier published more than 600,000 articles annually in over 2,800 journals. As of 2018, its archives contained over 17 million documents and 40,000 Ebook, e-books, with over one b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Triangulation
Steiner may refer to: People * Steiner (surname) * Steiner Brothers, a professional wrestling tag team * Steiner Brothers (tap-dancing trio), a 1950s–1960s Canadian act Places * Steiner, Michigan, U.S. * Steiner, Mississippi, U.S. Math and science * Steiner's theorem, or parallel axis theorem * Steiner tree * Poncelet–Steiner theorem * Steiner surface * Steiner system, a type of block design * Steiner point (other) Other uses * Steiner House, in Vienna, Austria * Steiner Studios, a film and television production studio in New York City * Franz Steiner Verlag, a German publisher See also * Army Detachment Steiner, a temporary German military unit during the 1945 Battle of Berlin during World War II *Waldorf education Waldorf education, also known as Steiner education, is based on the educational philosophy of Rudolf Steiner, the founder of anthroposophy. Its educational style is holistic, intended to develop pupils' intellectual, artistic, and practical sk ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Refinement
In mesh generation, Delaunay refinements are algorithms for mesh generation based on the principle of adding Steiner point (computational geometry), Steiner points to the geometry of an input to be meshed, in a way that causes the Delaunay triangulation or constrained Delaunay triangulation of the augmented input to meet the quality requirements of the meshing application. Delaunay refinement methods include methods by Chew and by Ruppert. Chew's second algorithm Chew's second algorithm takes a piecewise linear manifold, piecewise linear system (PLS) and returns a constrained Delaunay triangulation of only quality triangles where quality is defined by the minimum angle in a triangle. Developed by L. Paul Chew for meshing surfaces embedded in three-dimensional space, Chew's second algorithm has been adopted as a two-dimensional mesh generator due to practical advantages over Ruppert's algorithm in certain cases and is the default quality mesh generator implemented in the freely av ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
