# barycentric coordinates

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## barycentric coordinates

(ba-ră-**sen**-trik) See barycenter.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Barycentric Coordinates

the coordinates of a point *M* on a plane in relation to three basis points *A*_{1}, *A*_{2}, and *A*_{3} (not lying on the same line) of this plane—three numbers *m*_{1}, *m*_{2}, and *m*_{3} (which satisfy the condition *m*_{1} + *m*_{2} + *m*_{3} = 1), such that the point *M* represents the center of gravity of the system of three material points with masses *m*_{1}, *m*_{2}, and *m*_{3} located at the points *A*_{1}, *A*_{2}, and *A*_{3} respectively. (Here it is necessary to consider that the masses *m*_{1}, *m*_{2}, and *m*_{3} can be both positive and negative.) Barycentric coordinates in space are defined analogously. Barycentric coordinates are used in certain branches of mathematics and its applications.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

## barycentric coordinates

[‚bar·ə′sen·trik kō′ȯrd·ən‚əts] (mathematics)

The coefficients in the representation of a point in a simplex as a linear combination of the vertices of the simplex.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.