RE: Fast help for circle problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg13334] RE: [mg13261] Fast help for circle problem*From*: "Jean-Marie THOMAS" <jmthomas at cybercable.tm.fr>*Date*: Mon, 20 Jul 1998 02:49:54 -0400*Sender*: owner-wri-mathgroup at wolfram.com

I wrote recently solutions to a similar problem: given a set of positive real numbers, representing the radii of circles, how can I draw these circles in such a way that they never overlap and keep as compact as possible. They are multiple solutions, depending on whether to keep the sorting order of the set of numbers. The constrain on compactness has been a prerequisite at the beginning of my work, but abandoning this constrain leads to other sets of solutions, with a fractal-like behaviour. Mail me if interested, I guess I can give you interesting tips and eventually computational geometry packages. Have a look at ftp://tea.fr.eu.org in the directory "mathematics". -----Original Message----- From: jmittag [mailto:jmittag at pc0932g1.bv.tu-berlin.de] To: mathgroup at smc.vnet.net Subject: [mg13334] [mg13261] Fast help for circle problem We are looking for a solution for the following problem: Given are 3 circles, each with center coordinates and radius. Circle 1 is touching circle 2 and circle 2 is touching circle 3 (without any intersection). As a special case circle 1 is also touching circle 3. We are looking for circle 4, which is touching circles 1 to 3. The equation for one circle "i" is as follows: (ri+r4)^2=(x4-xi)^2+(y4-yi)^2 with i = 1,2,3 We need a symbolic solution for x4, y4 and r4. Thanks in advance! Jens Mittag email: Jens.Mittag at tu-berlin.de