One-to-one piecewise linear mappings over triangulations

  title={One-to-one piecewise linear mappings over triangulations},
  author={Michael S. Floater},
  journal={Math. Comput.},
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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Publications referenced by this paper.
Showing 1-10 of 20 references

How to Draw a Graph

View 7 Excerpts
Highly Influenced

Sur un type de transformation analytique généralisant la représentation conforme et définé au moyen de fonctions harmoniques

G. Choquet
Bull. Sci. Math. 69 • 1945
View 5 Excerpts
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Aufgabe 41

T. Radó
Jahresber. Deutsch. Math.-Verien. 35 • 1926
View 5 Excerpts
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Lösung der Aufgabe 41

H. Kneser
Jahresber. Deutsch. Math.-Verien. 35 • 1926
View 6 Excerpts
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Matrix iterative analysis

R. S. Varga
Springer, New York • 2000
View 1 Excerpt

Finite elements

D. Braess
Cambridge University Press, Cambridge • 1997
View 1 Excerpt

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