(a) 5 faces, max K = 12, average K = 4.7
(b) 6 faces, max K = 4.5, average K = 3.6
(c) 20 faces, max K = 1.8, average K = 1.5
Figure 11: Parameterization of convex polyhedrons, per-
formed by the radial stretching toward the unit ball, with
a = 1. Each ﬁgure shows, from left to right, tetrahedral
mesh of domain and image. Highlighted areas are the 1-
rings of the vertices that reached maximal dilatation. Keep
in mind, that parameterization is applied on vertices and it
does not reﬁne meshes. Therefore the surface of the result-
ing image can deviate from being round.
ACKNOWLEDGEMENTS
Emil Saucan’s research was supported by Israel Sci-
ence Foundation Grants 221/07 and 93/11 and by Eu-
ropean Research Council under the European Com-
munity’s Seventh Framework Programme (FP7/2007-
2013) / ERC grant agreement n
o
[URI-306706].
The research of Y. Y. Zeevi is supported by the
Ollendorff Minerva Center for Vision and Image Sci-
ences.
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