72 lines
2.7 KiB
Text
72 lines
2.7 KiB
Text
local class point
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function __construct(public x, public y) end
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end
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local class circle
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function __construct(public x, public y, public r) end
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end
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local circles = {
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new circle( 1.6417233788, 1.6121789534, 0.0848270516),
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new circle(-1.4944608174, 1.2077959613, 1.1039549836),
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new circle( 0.6110294452, -0.6907087527, 0.9089162485),
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new circle( 0.3844862411, 0.2923344616, 0.2375743054),
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new circle(-0.2495892950, -0.3832854473, 1.0845181219),
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new circle( 1.7813504266, 1.6178237031, 0.8162655711),
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new circle(-0.1985249206, -0.8343333301, 0.0538864941),
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new circle(-1.7011985145, -0.1263820964, 0.4776976918),
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new circle(-0.4319462812, 1.4104420482, 0.7886291537),
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new circle( 0.2178372997, -0.9499557344, 0.0357871187),
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new circle(-0.6294854565, -1.3078893852, 0.7653357688),
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new circle( 1.7952608455, 0.6281269104, 0.2727652452),
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new circle( 1.4168575317, 1.0683357171, 1.1016025378),
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new circle( 1.4637371396, 0.9463877418, 1.1846214562),
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new circle(-0.5263668798, 1.7315156631, 1.4428514068),
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new circle(-1.2197352481, 0.9144146579, 1.0727263474),
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new circle(-0.1389358881, 0.1092805780, 0.7350208828),
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new circle( 1.5293954595, 0.0030278255, 1.2472867347),
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new circle(-0.5258728625, 1.3782633069, 1.3495508831),
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new circle(-0.1403562064, 0.2437382535, 1.3804956588),
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new circle( 0.8055826339, -0.0482092025, 0.3327165165),
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new circle(-0.6311979224, 0.7184578971, 0.2491045282),
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new circle( 1.4685857879, -0.8347049536, 1.3670667538),
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new circle(-0.6855727502, 1.6465021616, 1.0593087096),
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new circle( 0.0152957411, 0.0638919221, 0.9771215985)
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}
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local sq = |v| -> v * v
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local function area_scan(precision)
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local function sect(c, y)
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local dr = math.sqrt(sq(c.r) - sq(y - c.y))
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return new point(c.x - dr, c.x + dr)
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end
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local cm1 = circles:mapped(|c| -> c.y + c.r)
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local cm2 = circles:mapped(|c| -> c.y - c.r)
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local ys = {}
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table.move(cm1, 1, #cm1, 1, ys)
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table.move(cm2, 1, #cm2, #ys + 1, ys)
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local mins = math.floor(ys:min() / precision)
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local maxs = math.ceil (ys:max() / precision)
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local total = 0
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for x = mins, maxs do
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local y = x * precision
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local right = -1 / 0
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local points = circles:filtered(|c| -> math.abs(y - c.y) < c.r)
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:reorder()
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:map(|c| -> sect(c, y))
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:sort(|p1, p2| -> p1.x < p2.x)
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for points as p do
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if p.y > right then
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total += p.y - math.max(p.x, right)
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right = p.y
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end
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end
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end
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return total * precision
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end
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local p = 1e-5
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print($"Approximate area = {area_scan(p)}")
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