Abstract: From the view of the solution space of a system of linear equations, the recursion formula
is worked out on generalized barycentric coordinates (GBCs) from n -gons to n 1 -gons. Unlike
the classical way to construct GBCs, which based on geometric meaning of coordinate functions, a
new method is provided to construct GBCs for planar n -gons if a coordinate function is chosen
which satisfies constraint condition. To get the recursion formula, since a (n  1) -gons (n≥3) can
be seen as a n -gons plus one extra vertex, the extra vertex can be represented by affine linear
combination of the vertices of the n -gons. Hence the GBCs in (n 1) -gons can be rewritten by
homogeneous coordinates in n -gons. Conditions for the (n 1) th coordinate function are presented
to satisfy the requirement of GBCs.

Key words: barycentric coordinates, recursion, polygon