shoelace formula

#include <vector>
#include <cmath>
#include <utility>

double shoelaceArea(const std::vector<std::pair<double, double>>& pts) {
    size_t n = pts.size();
    if (n < 3) return 0.0;

    double signedArea = 0.0;
    for (size_t i = 0; i < n; ++i) {
        const auto& [x_i, y_i]     = pts[i];
        const auto& [x_ip1, y_ip1] = pts[(i + 1) % n];  // wraps last -> first
        signedArea += x_i * y_ip1 - x_ip1 * y_i;         // this is 2 * triangle_{i,i+1}
    }
    signedArea *= 0.5;

    return std::fabs(signedArea);  // drop fabs() to keep the signed area (winding direction)
}

// usage
#include <iostream>

int main() {
	std::vector<std::pair<double, double>> square = {
		{0, 0}, {4, 0}, {4, 4}, {0, 4}
	};
	std::cout << shoelaceArea(square) << "\n"; // 16
}