Total circles area

You are encouraged to solve this task according to the task description, using any language you may know.
 Example circles
 Example circles filtered
Given some partially overlapping circles on the plane, compute and show the total area covered by them, with four or six (or a little more) decimal digits of precision. The area covered by two or more disks needs to be counted only once.

One point of this Task is also to compare and discuss the relative merits of various solution strategies, their performance, precision and simplicity. This means keeping both slower and faster solutions for a language (like C) is welcome.

To allow a better comparison of the different implementations, solve the problem with this standard dataset, each line contains the x and y coordinates of the centers of the disks and their radii   (11 disks are fully contained inside other disks):

         xc              yc          radius
     1.6417233788   1.6121789534   0.0848270516
    -1.4944608174   1.2077959613   1.1039549836
     0.6110294452  -0.6907087527   0.9089162485
     0.3844862411   0.2923344616   0.2375743054
    -0.2495892950  -0.3832854473   1.0845181219
     1.7813504266   1.6178237031   0.8162655711
    -0.1985249206  -0.8343333301   0.0538864941
    -1.7011985145  -0.1263820964   0.4776976918
    -0.4319462812   1.4104420482   0.7886291537
     0.2178372997  -0.9499557344   0.0357871187
    -0.6294854565  -1.3078893852   0.7653357688
     1.7952608455   0.6281269104   0.2727652452
     1.4168575317   1.0683357171   1.1016025378
     1.4637371396   0.9463877418   1.1846214562
    -0.5263668798   1.7315156631   1.4428514068
    -1.2197352481   0.9144146579   1.0727263474
    -0.1389358881   0.1092805780   0.7350208828
     1.5293954595   0.0030278255   1.2472867347
    -0.5258728625   1.3782633069   1.3495508831
    -0.1403562064   0.2437382535   1.3804956588
     0.8055826339  -0.0482092025   0.3327165165
    -0.6311979224   0.7184578971   0.2491045282
     1.4685857879  -0.8347049536   1.3670667538
    -0.6855727502   1.6465021616   1.0593087096
     0.0152957411   0.0638919221   0.9771215985

The result is   21.56503660... .



Related task

   Circles of given radius through two points.


See also

 http://www.reddit.com/r/dailyprogrammer/comments/zff9o/9062012_challenge_96_difficult_water_droplets/
 http://stackoverflow.com/a/1667789/10562


import "/dynamic" for Tuple
import "/math" for Nums
 
var Circle = Tuple.create("Circle", ["x", "y", "r"])
 
var circles = [
    Circle.new( 1.6417233788,  1.6121789534, 0.0848270516),
    Circle.new(-1.4944608174,  1.2077959613, 1.1039549836),
    Circle.new( 0.6110294452, -0.6907087527, 0.9089162485),
    Circle.new( 0.3844862411,  0.2923344616, 0.2375743054),
    Circle.new(-0.2495892950, -0.3832854473, 1.0845181219),
    Circle.new( 1.7813504266,  1.6178237031, 0.8162655711),
    Circle.new(-0.1985249206, -0.8343333301, 0.0538864941),
    Circle.new(-1.7011985145, -0.1263820964, 0.4776976918),
    Circle.new(-0.4319462812,  1.4104420482, 0.7886291537),
    Circle.new( 0.2178372997, -0.9499557344, 0.0357871187),
    Circle.new(-0.6294854565, -1.3078893852, 0.7653357688),
    Circle.new( 1.7952608455,  0.6281269104, 0.2727652452),
    Circle.new( 1.4168575317,  1.0683357171, 1.1016025378),
    Circle.new( 1.4637371396,  0.9463877418, 1.1846214562),
    Circle.new(-0.5263668798,  1.7315156631, 1.4428514068),
    Circle.new(-1.2197352481,  0.9144146579, 1.0727263474),
    Circle.new(-0.1389358881,  0.1092805780, 0.7350208828),
    Circle.new( 1.5293954595,  0.0030278255, 1.2472867347),
    Circle.new(-0.5258728625,  1.3782633069, 1.3495508831),
    Circle.new(-0.1403562064,  0.2437382535, 1.3804956588),
    Circle.new( 0.8055826339, -0.0482092025, 0.3327165165),
    Circle.new(-0.6311979224,  0.7184578971, 0.2491045282),
    Circle.new( 1.4685857879, -0.8347049536, 1.3670667538),
    Circle.new(-0.6855727502,  1.6465021616, 1.0593087096),
    Circle.new( 0.0152957411,  0.0638919221, 0.9771215985)
]
 
var sq = Fn.new { |v| v * v }
 
var xMin = Nums.min(circles.map { |c| c.x - c.r })
var xMax = Nums.max(circles.map { |c| c.x + c.r })
var yMin = Nums.min(circles.map { |c| c.y - c.r }) 
var yMax = Nums.max(circles.map { |c| c.y + c.r })
var boxSide = 3000
var dx = (xMax - xMin) / boxSide
var dy = (yMax - yMin) / boxSide
var count = 0
for (r in 0...boxSide) {
    var y = yMin + r * dy
    for (c in 0...boxSide) {
        var x = xMin + c * dx
        var b = circles.any { |c| sq.call(x-c.x) + sq.call(y-c.y) <= sq.call(c.r) }
        if (b) count = count + 1
    }
}
System.print("Approximate area = %(count * dx * dy)")