On the injectivity of Wachspress and mean value mappings between convex polygons
The injectivity of Wachspress [cf. \textit{E. L. Wachspress}, A rational finite element basis (1975; Zbl 0322.65001)] and mean value mappings between planar convex polygons is investigated in this paper. Wachspress and mean value coordinates represent two generalizations of triangular barycentric coordinates to convex polygons and are used for construction of mappings between planar polygons. Mappings between planar polygons are widely used in image warping for deformation of the curve which is associated with the polygon. Therefore, the problem of injectivity is very important because it is necessary to ensure the same number of self-intersections on the original and deformed curve. The proof that Wachspress mappings are always injective is given and the examples of mean value mappings that are not injective when the polygons have five or more vertices are shown in this paper.
scientific article; zbMATH DE number 5675107
scientific article