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Added circle circle intersection area #139

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Added circle circle intersection area #139

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Added circle circle intersection area
Chillee Nov 3, 2019
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Chillee Nov 4, 2019
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Chillee Nov 4, 2019
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21 changes: 21 additions & 0 deletions content/geometry/CircleCircleArea.h
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Original file line number Diff line number Diff line change
@@ -0,0 +1,21 @@
/**
* Author: Takanori MAEHARA, chilli
* Date: 2019-11-03
* License: CC0
* Source: https://github.com/spaghetti-source/algorithm/blob/master/geometry/_geom.cc#L729
* Description: Calculates the area of the intersection of 2 circles
* Status:
*/

template<class P>
double circleCircleArea(P c, double cr, P d, double dr) {
if (cr < dr) swap(c, d), swap(cr, dr);
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auto A = [&](double r, double h) {
return r*r*acos(h/r)-h*sqrt(r*r-h*h);
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@simonlindholm simonlindholm Nov 8, 2019

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The removal of the epsilons now means that r < h can happen due to numerical precision, I suspect (though I haven't tested). h = min(h, r); may be reasonable? h < 0 can likely also happen but doesn't seem like a problem.

};
auto l = (c - d).dist(), a = (l*l + cr*cr - dr*dr)/(2*l);
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@simonlindholm simonlindholm Nov 8, 2019

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double is clearer than auto

if (l - cr - dr >= 0) return 0; // far away
if (l - cr + dr <= 0) return M_PI*dr*dr;
if (l - cr >= 0) return A(cr, a) + A(dr, l-a);
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@simonlindholm simonlindholm Nov 8, 2019

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these inequalities can be simplified now without the epsilons

else return A(cr, a) + M_PI*dr*dr - A(dr, a-l);
}
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