computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

, 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 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 nu ...

, named after

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 st ...

, 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 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. T ...

. 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.

References

{{reflist Computational geometry

See also

References