Multiresolution mesh representations are a key tool used in computer
graphics to achieve real-time interaction with large and complex
object models. In a multiresolution modeling environment we are able to
deal with global shape and structural details of the same object
managing meshes of it at different level of refinement.
We then need tools to coarsen a given fine mesh as well as tools
for refining a coarse mesh.
We study refinement approaches that combine the advantages of subdivision
(arbitrary topology, local control and efficiency) with those of variational
design (high quality surfaces).
The basic idea behind this strategy, first proposed by Kobbelt
and named variational subdivision, is to apply, at each subdivision step,
a splitting operation to obtain a finer mesh followed by a smoothing operation
to update the vertex mesh locations in order to increase the overall smoothness.
In this research project the smoothing step is based on a geometric
diffusion and filtering approach related to mean curvature motion, which
have already been proved to be very promising for surface fairing
purposes.