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Total circles area: Difference between revisions
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<pre>Approximated area: 21.561559772</pre>
Scanline conversion:
<lang python>from math import floor, ceil, sqrt
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)]
def area_scan(prec, circs):
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))
def sect((cx, cy, r), y):
dr = sqrt(r ** 2 - (y - cy) ** 2)
return (cx - dr, cx + dr)
total = 0
for y in [prec * x for x in range(mins, maxs + 1)]:
right = -float("inf")
for (x0, x1) in sorted([sect((cx, cy, r), y)
for (cx, cy, r) in circs
if cy - r < y and y < cy + r ]):
if x1 <= right: continue
total += x1 - max(x0, right)
right = x1
return total * prec
p = 1e-3
print "@stepsize", p, "area = %.4f" % area_scan(p, circles)</lang>
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