One-to-one piecewise linear mappings over triangulations

@article{Floater2003OnetoonePL,
  title={One-to-one piecewise linear mappings over triangulations},
  author={Michael S. Floater},
  journal={Math. Comput.},
  year={2003},
  volume={72},
  pages={685-696}
}
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 oneto-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 RadóKneser-Choquet theorem for harmonic mappings, but is also… CONTINUE READING
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