geometry/polygon-area.hpp

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• Last update: 2026-08-30 15:33:14+09:00
• Include: #include "geometry/polygon-area.hpp"

Depends on

• geometry/base.hpp
• geometry/cross.hpp

Required by

• 幾何ライブラリ (geometry/geometry.hpp)

Verified with

• test/mytest/geometry/geometry.test.cpp

Code

#pragma once

#include <vector>

#include "cross.hpp"

namespace geometry {
    // 多角形の面積を求める
    inline D PolygonArea(const std::vector<Point> &p) {
        D res = 0;
        int n = p.size();
        for(int i = 0; i < n - 1; i++) res += cross(p[i], p[i + 1]);
        res += cross(p[n - 1], p[0]);
        return res * 0.5;
    }
} // namespace geometry

#line 2 "geometry/polygon-area.hpp"

#include <vector>

#line 2 "geometry/cross.hpp"

#line 2 "geometry/base.hpp"

#include <cmath>
#include <complex>

namespace geometry {
    // Point : 複素数型を位置ベクトルとして扱う
    // 実軸(real)をx軸、挙軸(imag)をy軸として見る
    using D = long double;
    using Point = std::complex<D>;
    const D EPS = 1e-7;
    const D PI = std::acos(D(-1));

    inline bool equal(const D &a, const D &b) { return std::fabs(a - b) < EPS; }
} // namespace geometry
#line 4 "geometry/cross.hpp"

namespace geometry {
    // 外積(cross product) : a×b = |a||b|sinΘ
    inline D cross(const Point &a, const Point &b) {
        return (a.real() * b.imag() - a.imag() * b.real());
    }
} // namespace geometry
#line 6 "geometry/polygon-area.hpp"

namespace geometry {
    // 多角形の面積を求める
    inline D PolygonArea(const std::vector<Point> &p) {
        D res = 0;
        int n = p.size();
        for(int i = 0; i < n - 1; i++) res += cross(p[i], p[i + 1]);
        res += cross(p[n - 1], p[0]);
        return res * 0.5;
    }
} // namespace geometry

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