\indent Generalized barycentric coordinate functions allow for novel, flexible finite element methods accommodating polygonal element geometries. The Sobolev-norm error estimates associated to such methods, however, require varying levels of geometric criteria on the polygons, depending on the definition of the coordinate functions. In this talk, I will discuss these criteria for a variety of coordinate definitions and discuss the practical tradeoffs between enforcing geometric constraints and computing finite element basis functions over polygons.