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["Adil Mughal" <>]

Dear Dr. A Fabi,

The SMVP has been shown to have an exact correspondence with a 2D foam in equilibrium (see http://front.math.ucdavis.edu/9701.0006). My project is to find the arrangement of N bubbles that will minimise the total perimeter of the foam. See attached image for an example of 19 bubbles constrained by a circular boundary - this image has been produced by using the Surface evlover algorithm (by Dr. Simon Cox (University of Aberystwyth)). The surface evolver algorithm is inefficient at sampling the configuration space and so a systems with large N cannot be successfully optimised. Thus I propose to incorporate a SMVP algorithm into a simulated annealing code. The energy of the system contains two terms - 1) the total perimeter between cells 2) the deviation in area for a given cell from the average cell area. Both the perimeter and the area of each cell must be computed. At each Monte Carlo step the configuration can be changed by moving the points which produce the SMVP. A new state will be accepted/rejected according to the standard Boltzmann statistics. Thus dynamically adding/removing points will also greatly reduce the amount of time required to compute the energy of the state after each Monte Carlo move. 

I am currently unemployed although I have just finished my PhD at the University of Manchester (U.K.). This project is part of a proposal I am writing for an EPSRC fellowship in theoretical physics. If successful I will then be based at the University of Aberystwyth.

Should you have any further thoughts on this project I would be most grateful to receive your opinion.

Yours

Adil Mughal

On 8/28/07, Andreas Fabri <> wrote:

Adil Mughal wrote:
> Dear Experts,
>
> Can you please tell me if it is possible to generate a sectional
> multiplicative Voronoi diagram (SMVP) with CGAL before I start making
> the big effort to read/install the libraries/manuals.
>
> I see that the section on Apollonius graphs seems to be describing a an
> additively weighted Voronoi diagram ( i.e. a sectional Voronoi diagram)
> - a SMVP has an additional weighting factor multiplying the distance
> between a point and its source.
>
> If CGAL does not have this feature - can it be encoded easily? Are there
> plans to write this code.
>
> Yours
>
> Adil Mughal


There exists such code at one of the CGAL project partners, but it
is not integrated in the library yet.

What functionality are you looking for, that is do you insert/remove
points, do you run nearest site queries on it for query points, or
do you need to traverse the Voronoi cells and edges?
Finally, what is your affiliation?

andreas

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