We show that four well-known kinds of generalized barycentric coordinates in convex polygons share a simple monotonicity property: the coordinate function associated with a vertex is increasing along any line from the polygon boundary to that vertex. This shows that the coordinate functions have no local extrema and that their contours are single curves connecting pairs of points on the two edges adjacent to the vertex.
['Michael S. Floater']
On the monotonicity of generalized barycentric coordinates on convex polygons