March 31st, 2006, 7:31 pm
QuoteOriginally posted by: sevvostI wonder if you had a chance to take a look at the Fejes Tóth book mentioned earlier. I am not sure what is the problem you are trying to solve, so I don't know if his stuff is exactly relevant, but I think the book is a real pleasure to read. He devotes a considerable number of pages to precise estimations of circle packings for convex shapes - both same and different size circles. If that could be any help, I can quote some of his results.Managed to get the 1953 edition of the book. Amazing stuff.His circle packing might not be exactly what we need because I am not sure what happens at the edges of the bounding convex shape. The anti-aliasing effects might be too disruptive. A possibility is to fill in near the edges with smaller and smaller circles.The discete conformal mapping technique looks promising even though it is for circles. Of course, it is a good start.The general problem is to pack arbitrary shapes into an abritrary convex outer shape with packing as 'dense' as possible.Thanks for the reference.
Last edited by
Cuchulainn on March 30th, 2006, 10:00 pm, edited 1 time in total.