


Jo Simoens



Project descriptions

During his visit, Jo has been working on the following projects:
 Facebased subdivision on triangulations
In subdivision schemes for surface generation, the subdivision procedure
is applied to the coordinates of vertices in successively finer meshes.
The same procedure can be applied to other values associated to the
vertices, defining in the limit a continuous function on the subdivision
surface.
In some applications it seems more natural, though, to associate values
not to the vertices but to the faces in successively refined meshes.
Values associated to faces in a mesh live on the nodes of the
(graphtheoretical) dual of this mesh. Hence a facebased subdivision
scheme for quadrilateral or triangle meshes operates on the dual meshes of
quadrilateral or triangle meshes with subdivision connectivity. Facebased
subdivision schemes are often referred to as vertexsplit or dual
subdivision schemes, where facesplit or primal subdivision schemes are
vertexbased.
Subdivision schemes on the dual mesh of a quadrilateral mesh with
subdivision connectivity are knownthe DooSabin scheme is a wellknown
example. Because the dual mesh of a regular quadrilateral mesh is again
quadrilateral, the analysis of vertexbased and of facebased subdivision schemes in
this setting is very similar. In contrast, the dual mesh of a regular
triangle mesh consists of hexagons and is not translationinvariant.
We analyze subdivision on the hexagonal mesh
by reducing it to matrix subdivision on a translationinvariant mesh.


Publications

The following publications summarize some of the results of the
research work that Jo has participated in during his stay:
 Nira Dyn, David Levin, and Jo Simoens.
PrimalDual Repeated Averaging Subdivision on Triangulations.
In preparation.


