Wachspress and mean value coordinates are two generalizations of triangular barycentric coordinates to convex polygons and have recently been used to construct mappings between polygons, with application to curve deformation and image warping. We show that Wachspress mappings between convex polygons are always injective but that mean value mappings can fail to be so in extreme cases.

We investigate the problem of finding orthogonal polygons that fold to plural incongruent orthogonal boxes. There are two known polygons that fold to produce two incongruent orthogonal boxes. In this paper, we show that there are infinite such polygons. We also show that there exists a tile that produces two incongruent orthogonal boxes.