Let P i {\displaystyle {}P_{i}} , i ∈ I {\displaystyle {}i\in I} , be an affine basis in an affine space E {\displaystyle {}E} over the K {\displaystyle {}K} -vector space V {\displaystyle {}V} . Then the point P j {\displaystyle {}P_{j}} ( j = I {\displaystyle {}j=I} ) has the barycentric coordinates ( 0 , … , 0 , 1 , 0 , … , 0 ) {\displaystyle {}(0,\ldots ,0,1,0,\ldots ,0)} , where the 1 {\displaystyle {}1} is at the j {\displaystyle {}j} -th place ( I {\displaystyle {}I} being finite and ordered).
, 
,
be an
affine basis
in an
affine space
over the
-vector space
. Then the point 
(
)
has the
barycentric coordinates
, where the 
is at the 
-th place
(
being finite and ordered).
