nLab barycenter

Barycenter of a simplex

Definition

If $\sigma =\left\{{v}_{0},\dots ,{v}_{q}\right\}\in {K}_{q}$, the set of $q$-simplices of a simplicial complex, $K$, then its barycentre, $b\left(\sigma \right)$, is the point

$b\left(\sigma \right)=\sum _{0\le i\le q}\frac{1}{q+1}{v}_{i}\in \mid K\mid .$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)