(definition)

**Definition:**
(1) A point that is not part of the input set of points, for instance, a point computed to construct a *Steiner tree*. (2) A point with a particular geometric relation to a triangle.

*Note:
Also called a Steiner vertex. *

Consider the three points of a triangle. The shortest tree connecting all three, called the *Steiner tree*, branches out from a fourth point in the middle. That middle point, which was not given initially and must be computed in order to build the shortest tree, is a Steiner point.

* From Algorithms and Theory of Computation Handbook, page 19-27, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.*

Author: CRC-A

Named for Jakob Steiner. See the following for the geometric (classical) definition of a Steiner Point.

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If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

HTML page formatted Mon Feb 2 13:10:40 2015.

Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "Steiner point", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/steinerpoint.html