from math import floor, ceil, sqrt

def area_scan(prec, circs):
    def sect((cx, cy, r), y):
        dr = sqrt(r ** 2 - (y - cy) ** 2)
        return (cx - dr, cx + dr)

    ys = [a[1] + a[2] for a in circs] + [a[1] - a[2] for a in circs]
    mins = int(floor(min(ys) / prec))
    maxs = int(ceil(max(ys) / prec))

    total = 0
    for y in (prec * x for x in xrange(mins, maxs + 1)):
        right = -float("inf")

        for (x0, x1) in sorted(sect((cx, cy, r), y)
                               for (cx, cy, r) in circs
                               if abs(y - cr) < r):
            if x1 <= right:
                continue
            total += x1 - max(x0, right)
            right = x1

    return total * prec

def main():
    circles = [
        ( 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)]

    p = 1e-3
    print "@stepsize", p, "area = %.4f" % area_scan(p, circles)

main()
