ABSTRACT
Barycentric mappings allow us to naturally warp a source polygon to a corresponding target polygon, or, more generally, to create mappings between closed curves or polyhedra. Unfortunately, bijectivity of such barycentric mappings can only be guaranteed for the special case of warping between convex polygons. In fact, for any barycentric coordinates, it is always possible to construct a pair of polygons such that the barycentric mapping is not bijective. For any choice of barycentric coordinates, it is possible to construct a source and a target polygon such that the barycentric mapping is not bijective. This chapter suggests that if source and target polygon are sufficiently close, the mapping is close to the identity and hence bijective. Therefore, by "splitting" the barycentric mapping from source to target polygon into a finite number of intermediate steps, where each step perturbs the vertices only slightly, it should be possible to obtain a bijective composite mapping.
