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