Re: how to get the area of circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg74803] Re: how to get the area of circles*From*: "Valeri Astanoff" <astanoff at gmail.com>*Date*: Thu, 5 Apr 2007 04:19:00 -0400 (EDT)*References*: <euvlho$b9n$1@smc.vnet.net>

On 4 avr, 09:53, "doufunao" <gaoshan2... at gmail.com> wrote: > hi guys, > > I'm working on a project. I need to calculate the area of many circles > in a 2D space which may overlap each other. > It's quite complicated. I am not sure whether mathematica can do this. > Is there any software/lib/package available already? > thanks. Good day, Here is a solution using "Boole" : In[1]:= areaOfCircles[circles_List(*{{a1,b1,r1},{a2,b2,r2}...}*)]:= Module[{}, ixmin = Ordering[circles,1,#1[[1]] < #2[[1]]&]//First; xmin = circles[[ixmin,1]]-circles[[ixmin,3]]; ixmax = Ordering[circles,1,#1[[1]] > #2[[1]]&]//First; xmax = circles[[ixmax,1]]+circles[[ixmax,3]]; iymin = Ordering[circles,1,#1[[2]] < #2[[2]]&]//First; ymin = circles[[iymin,2]]-circles[[iymin,3]]; iymax = Ordering[circles,1,#1[[2]] > #2[[2]]&]//First; ymax = circles[[iymax,2]]+circles[[iymax,3]]; insideQ[{x_,y_},{a_,b_,r_}] := (x-a)^2+(y-b)^2 < r^2; NIntegrate[Boole[Or@@(insideQ[{x,y},#]& /@ circles)], {x,xmin,xmax},{y,ymin,ymax}] ]; In[2]:=circles={{-.5,1.5,9.7},{-1.8,4.3,5.8}, {3.5,4.0,1.7},{2.1,1.7,3.1},{1.4,5.9,1.9}}; In[3]:=areaOfCircles[circles]//Timing Out[3]={0.078Second,194.654} V.Astanoff