## Optimisation of Restricted Voronoï Diagrams

This presentation will describe the optimisation of Restricted Voronoï Diagrams.

Such a structure is meant to partition a mesh between a set of sample points,

associating each point of the mesh to its nearest sample. With this tool, many

applications can be derived in sampling optimisation and mesh generation. I will

first describe how to optimize objective functions defined on Restricted Voronoï

Diagrams, and especially how to compute their gradient. I will then show how to

use these results to optimise a sampling of a general function defined on a

mesh. Finally, I will show how a distance between two meshes can be viewed as

an objective function on a Restricted Voronoï Diagram, and optimized to obtain a

surface fitting algorithm.

More material on the results I will be presenting can be found on my personal

web page : http://alice.loria.fr/~nivoliev in my PhD (French), and two of my

publications (Sampling Functions on a Mesh [...] and Fitting Polynomial Surfaces

[...]).