CVT_SIZE - Try to Prescribe CVT Cell Sizes

CVT_SIZE was yet another effort to compute a centroidal Voronoi tessellation (CVT) in which there were cells of specified size. Normally, given arbitrary initial data and a constant density, the CVT would comprise cells of roughly equal area. In this case, a modification was made to the CVT iteration, in an attempt to drive the algorithm towards cells of prescribed sizes. In this case, each cell generator was given a weight, and the "nearest neighbor" routine measured distance to each generator divided by this weight. It was thought that manipulating these weights would be an easy way to predictably change the sizes of individual cells.

At the moment, this approach has produced some interesting results, but we haven't been able to drive the code to produce the exact sizes we want. Also, we see that our current results depend somewhat haphazardly on the local geometry. But they do result in some rather pretty pictures!

Files you may copy include:

• cvt_size.f90, the source code.
• cvt_size_prb.f90, a sample problem.
• cvt_size_prb.out, sample problem output.
• cvt_1111133333.ps, results using 10 generators, 5 with weight 1, 5 with weight 3 (DELETED, TOO LARGE).
• cvt_123456789x.ps, results using 10 generators with weights 1 through 10 (DELETED, TOO LARGE).
• cvt_halfandhalf20.ps, results using 20 generators, half with weight 1, half with weight 4 (I think).

The list of routines includes:

• CVT_SIZE_ITERATION takes one step of the CVT size iteration.
• FIND_CLOSEST_SIZE finds the Voronoi cell generator closest to a point X.
• GENERATOR_INIT initializes the Voronoi cell generators.
• RANDOM_INITIALIZE initializes the FORTRAN 90 random number seed.
• REGION_SAMPLER returns a sample point in the physical region.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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