Loops and canonical polygonal schema
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française
Index
Description
Results
Publications
Description
canonical polygonal schema
A closed
orientable surface of genus g can be obtained by appropriate
identification
of pairs of edges of a 4g-gon (the polygonal schema). The identified
edges
form 2g loops on the surface, that are disjoint except for their common
end-point. These loops are generators of both the fundamental group and
the homology group of the surface. The inverse problem is concerned
with
finding a set of 2g loops on a triangulated surface, such that cutting
the surface along these loops yields a (canonical) polygonal schema. We
present two optimal algorithms for this inverse problem. Both
algorithms
have been implemented using the CGAL polyhedron data structure.
A control of smooth deformations with topological change on
a
polyhedral
mesh based on curves and loops
We propose
a method to model and control topological changes by a
smooth
deformation of a polyhedral mesh using curves and loops. As changing
the
genus of a surface is not a continuous transformation,the topological
change
is made when an intermediate shape between the two topologies has been
obtained. The creation and the deletion ofholes are studied. The
deletion
of a hole uses non null-homotopic loops to designate the hole to be
deleted.
A method computing two independent loops associated to a hole is
presented.
Results
canonical polygonal schema
Incremental method
Publications
- F. Lazarus and M.
Pocchiola and G.
Vegter
and A.
Verroust. Computing a canonical polygonal schema of an orientable
triangulated
surface. In .Seventeenth Annual ACM Symposium on COMPUTATIONAL
GEOMETRY,
Tufts University, Medford (Boston), June 2001 [pdf]
- A Verroust and M.
Finiasz.A control of
smooth deformations
with topological change on a polyhedral mesh based on curves and
loops. In Shape Modelling International 2002, Banff, Canada, May
2002. [pdf]
Contact
Email : Anne.Verroust(@)inria.fr
Adress : Inria
Paris-Rocquencourt - BP 105, 78153 Le Chesnay Cedex - FRANCE
Phone : (+33 1) 39 63 54 41
Fax : (+33 1) 39 63 59 95
Secretary : (+33 1) 39 63 53 74