Barycentric coordinates

From Citizendium
Revision as of 17:00, 16 July 2024 by Suggestion Bot (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
This article is developing and not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In geometry, barycentric coordinates form a homogeneous coordinate system based on a reference simplex. The location of a point with respect to this system is given by the masses (by definition positive) which would need to be placed at the reference points in order to have the given point as barycentre. However, for a point outside the simplex some coordinates must be negative.

In an affine space or vector space of dimension n we take n+1 points in general position (no k+1 of them lie in an affine subspace of dimension less than k) as a simplex of reference. The barycentric coordinates of a point x are an (n+1)-tuple such that

and at least one of does not vanish. The coordinates are not affected by scaling, and it may be convenient to take , in which case they are called areal coordinates.