Total circles area: Difference between revisions
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{{out}}
area = 21.5650366037 at 5637290 scanlines
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <vector>
struct Pair_X {
double x1;
double x2;
bool operator <(const Pair_X& pair_x) const {
return x1 < pair_x.x1;
}
};
struct Circle {
double centre_x;
double centre_y;
double radius;
};
const std::vector<Circle> circles = {
Circle( 1.6417233788, 1.6121789534, 0.0848270516),
Circle(-1.4944608174, 1.2077959613, 1.1039549836),
Circle( 0.6110294452, -0.6907087527, 0.9089162485),
Circle( 0.3844862411, 0.2923344616, 0.2375743054),
Circle(-0.2495892950, -0.3832854473, 1.0845181219),
Circle( 1.7813504266, 1.6178237031, 0.8162655711),
Circle(-0.1985249206, -0.8343333301, 0.0538864941),
Circle(-1.7011985145, -0.1263820964, 0.4776976918),
Circle(-0.4319462812, 1.4104420482, 0.7886291537),
Circle( 0.2178372997, -0.9499557344, 0.0357871187),
Circle(-0.6294854565, -1.3078893852, 0.7653357688),
Circle( 1.7952608455, 0.6281269104, 0.2727652452),
Circle( 1.4168575317, 1.0683357171, 1.1016025378),
Circle( 1.4637371396, 0.9463877418, 1.1846214562),
Circle(-0.5263668798, 1.7315156631, 1.4428514068),
Circle(-1.2197352481, 0.9144146579, 1.0727263474),
Circle(-0.1389358881, 0.1092805780, 0.7350208828),
Circle( 1.5293954595, 0.0030278255, 1.2472867347),
Circle(-0.5258728625, 1.3782633069, 1.3495508831),
Circle(-0.1403562064, 0.2437382535, 1.3804956588),
Circle( 0.8055826339, -0.0482092025, 0.3327165165),
Circle(-0.6311979224, 0.7184578971, 0.2491045282),
Circle( 1.4685857879, -0.8347049536, 1.3670667538),
Circle(-0.6855727502, 1.6465021616, 1.0593087096),
Circle( 0.0152957411, 0.0638919221, 0.9771215985)
};
Pair_X horizontal_section(const Circle& circle, const double& y) {
const double value = circle.radius * circle.radius - ( y - circle.centre_y ) * ( y - circle.centre_y );
double delta_x = std::sqrt(value);
return Pair_X(circle.centre_x - delta_x, circle.centre_x + delta_x);
}
double area_scan(const double& precision) {
std::vector<double> y_values;
for ( const Circle& circle : circles ) {
y_values.emplace_back(circle.centre_y + circle.radius);
}
for ( const Circle& circle : circles ) {
y_values.emplace_back(circle.centre_y - circle.radius);
}
const double min = *min_element(y_values.begin(), y_values.end());
const double max = *max_element(y_values.begin(), y_values.end());
const int64_t mins = std::floor(min / precision);
const int64_t maxs = std::ceil(max / precision);
double total_area = 0.0;
for ( int64_t x = mins; x <= maxs; ++x ) {
double y = x * precision;
double right = -DBL_MAX;
std::vector<Pair_X> pairs_x;
for ( const Circle& circle : circles ) {
if ( std::fabs(y - circle.centre_y) < circle.radius ) {
pairs_x.emplace_back(horizontal_section(circle, y));
}
}
std::sort(pairs_x.begin(), pairs_x.end());
for ( const Pair_X& pair_x : pairs_x ) {
if ( pair_x.x2 > right ) {
total_area += pair_x.x2 - std::max(pair_x.x1, right);
right = pair_x.x2;
}
}
}
return total_area * precision;
}
int main() {
double precision = 0.00001;
std::cout << "Approximate area = " << std::setprecision(9) << area_scan(precision);
}
</syntaxhighlight>
{{ out }}
<pre>
Approximate area = 21.5650366
</pre>
=={{header|D}}==
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