Key points are not available for this paper at this time.
We call a piecewise linear mapping from a planar triangulation to the plane a convex combination mapping if the image of every interior vertex is a convex combination of the images of its neighbouring vertices. Such mappings satisfy a discrete maximum principle and we show that they are one-to-one if they map the boundary of the triangulation homeomorphically to a convex polygon. This result can be viewed as a discrete version of the Radó-Kneser-Choquet theorem for harmonic mappings, but is also closely related to Tutte’s theorem on barycentric mappings of planar graphs.
Michael S. Floater (2002) studied this question.