Schnyder woods for higher genus triangulated surfaces with ...

Luca Castelli Aleardi, Eric Fusy and Thomas Lewiner 14
w
S in
S in
S in
w
w w a
F 2
F 2
w a
S out S out S out
u v
S out v 0 0 u v 0
u
u a
v 1
v 1
S in v 1
S in
S out
S in
S out
Figure 12: This pictures illustrate how the double orientation of special edges can contribute to the additional (trivial) faces to maps T 0
(or T 1 ): in this pictures the double orientation of (u, w) adds a face F 2 to the map T 1 . Depending on its coloration, (u, w) can (or not) be
included on the boundary of F 2
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Preprint MAT. 18/08, communicated on September 1 st , 2008 to the Department of Mathematics, Pontifícia Universidade Católica — Rio de Janeiro, Brazil.