nLab
barycenter

Barycenter of a simplex

Definition

If σ={v 0,,v q}K q\sigma = \{ v_0, \ldots, v_q\} \in K_q, the set of qq-simplices of a simplicial complex, KK, then its barycentre, b(σ)b(\sigma), is the point

b(σ)= 0iq1q+1v i|K|.b(\sigma) = \sum_{0\leq i \leq q}\frac{1}{q + 1} v_i \in |K|.

For the use of barycenters in the barycentric subdivision, see classical triangulation or

Revised on December 1, 2010 21:00:49 by Tim Porter (95.147.238.157)