An
affine combination of a
sequence of
vectors
v1,
v2, ...,
vn is given by
c1v1 + c2v2 + ... + cnvn
where
c1,
c2, ...,
cn are
real numbers with the restriction that
c1 +
c2 + ... +
cn = 1.
As an example, any affine combination of 3 points in 3-space lies on the plane defined by those three points. Any affine combination of 2 points in 3-space lies on the line defined by those two points.