geometry/polygon_area.hpp

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• Last update: 2023-06-01 23:47:10+09:00
• Include: #include "geometry/polygon_area.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A

Depends on

• geometry/point.hpp
• geometry/polygon.hpp

Required by

• geometry/all.hpp

Verified with

• verify/aoj_cgl/aoj_cgl_3_a.test.cpp
• verify/aoj_cgl/aoj_cgl_4_c.test.cpp

Code

#pragma once

#include "geometry/polygon.hpp"

// area of polygon
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
// return area * 2
template <typename T> T polygon_area2(const Polygon<T> &p) {
    int n = (int)p.size();
    assert(n >= 2);
    T ret = T(0);
    for (int i = 0; i < n - 1; i++) {
        ret += cross(p[i], p[i + 1]);
    }
    ret += cross(p[n - 1], p[0]);
    // counter clockwise: ret > 0
    // clockwise: ret < 0
    return ret;
}
template <typename T> T polygon_area(const Polygon<T> &p) { return polygon_area2(p) / T(2); }

#line 2 "geometry/polygon_area.hpp"

#line 2 "geometry/polygon.hpp"

#line 2 "geometry/point.hpp"

// point
template <typename T> struct Point {
    static T EPS;
    static constexpr T PI = 3.1415926535'8979323846'2643383279L;
    static void set_eps(const T &e) { EPS = e; }
    T x, y;
    Point(const T x = T(0), const T y = T(0)) : x(x), y(y) {}
    Point &operator+=(const Point &p) {
        x += p.x;
        y += p.y;
        return *this;
    }
    Point &operator-=(const Point &p) {
        x -= p.x;
        y -= p.y;
        return *this;
    }
    Point &operator*=(const Point &p) { return *this = Point(x * p.x - y * p.y, x * p.y + y * p.x); }
    Point &operator*=(const T &k) {
        x *= k;
        y *= k;
        return *this;
    }
    Point &operator/=(const Point &p) { return *this = Point(x * p.x + y * p.y, -x * p.y + y * p.x) / (p.x * p.x + p.y * p.y); }
    Point &operator/=(const T &k) {
        x /= k;
        y /= k;
        return *this;
    }

    Point operator+() const { return *this; }
    Point operator-() const { return Point(-x, -y); }

    friend Point operator+(const Point &a, const Point &b) { return Point(a) += b; }
    friend Point operator-(const Point &a, const Point &b) { return Point(a) -= b; }
    friend Point operator*(const Point &a, const Point &b) { return Point(a) *= b; }
    friend Point operator*(const Point &p, const T &k) { return Point(p) *= k; }
    friend Point operator/(const Point &a, const Point &b) { return Point(a) /= b; }
    friend Point operator/(const Point &p, const T &k) { return Point(p) /= k; }
    // for std::set, std::map, compare_arg, ...
    friend bool operator<(const Point &a, const Point &b) { return a.x == b.x ? a.y < b.y : a.x < b.x; }
    friend bool operator>(const Point &a, const Point &b) { return a.x == b.x ? a.y > b.y : a.x > b.x; }
    // I/O
    friend std::istream &operator>>(std::istream &is, Point &p) { return is >> p.x >> p.y; }
    friend std::ostream &operator<<(std::ostream &os, const Point &p) { return os << '(' << p.x << ' ' << p.y << ')'; }
};

// template
template <typename T> inline int sign(const T &x) { return x < -Point<T>::EPS ? -1 : (x > Point<T>::EPS ? 1 : 0); }
template <typename T> inline bool equal(const T &a, const T &b) { return sign(a - b) == 0; }
template <typename T> inline T radian_to_degree(const T &r) { return r * 180.0 / Point<T>::PI; }
template <typename T> inline T degree_to_radian(const T &d) { return d * Point<T>::PI / 180.0; }

// contain enum
constexpr int IN = 2;
constexpr int ON = 1;
constexpr int OUT = 0;

// equal (point and point)
template <typename T> inline bool equal(const Point<T> &a, const Point<T> &b) { return equal(a.x, b.x) and equal(a.y, b.y); }
// inner product
template <typename T> inline T dot(const Point<T> &a, const Point<T> &b) { return a.x * b.x + a.y * b.y; }
// outer product
template <typename T> inline T cross(const Point<T> &a, const Point<T> &b) { return a.x * b.y - a.y * b.x; }
// rotate Point p counterclockwise by theta radian
template <typename T> inline Point<T> rotate(const Point<T> &p, const T &theta) { return p * Point<T>(std::cos(theta), std::sin(theta)); }
// compare (x, y)
template <typename T> inline bool compare_x(const Point<T> &a, const Point<T> &b) { return equal(a.x, b.x) ? sign(a.y - b.y) < 0 : sign(a.x - b.x) < 0; }
// compare (y, x)
template <typename T> inline bool compare_y(const Point<T> &a, const Point<T> &b) { return equal(a.y, b.y) ? sign(a.x - b.x) < 0 : sign(a.y - b.y) < 0; }
// compare by (arg(p), norm(p)) [0, 360)
template <typename T> inline bool compare_arg(const Point<T> &a, const Point<T> &b) {
    // https://ngtkana.hatenablog.com/entry/2021/11/13/202103
    assert(!equal(a, Point<T>(0, 0)));
    assert(!equal(b, Point<T>(0, 0)));
    if ((Point<T>(0, 0) < Point<T>(a.y, a.x)) == (Point<T>(0, 0) < Point<T>(b.y, b.x))) {
        return (a.x * b.y == a.y * b.x) ? norm(a) < norm(b) : a.x * b.y > a.y * b.x;
    } else {
        return Point<T>(a.y, a.x) > Point<T>(b.y, b.x);
    }
}
// |p| ^ 2
template <typename T> inline T norm(const Point<T> &p) { return p.x * p.x + p.y * p.y; }
// |p|
template <typename T> inline T abs(const Point<T> &p) { return std::sqrt(norm(p)); }
// arg
template <typename T> inline T arg(const Point<T> &p) { return std::atan2(p.y, p.x); }
// polar
template <typename T> inline Point<T> polar(const T &rho, const T &theta = T(0)) { return rotate(Point<T>(rho, 0), theta); }
// EPS
template <> double Point<double>::EPS = 1e-9;
template <> long double Point<long double>::EPS = 1e-12;
template <> long long Point<long long>::EPS = 0;
template <> __int128_t Point<__int128_t>::EPS = 0;
// change EPS
// using Double = double;
// using Pt = Point<Double>;
// Point<Double>::set_eps(new_eps);
#line 4 "geometry/polygon.hpp"

// polygon
template <typename T> using Polygon = std::vector<Point<T>>;
template <typename T> std::istream &operator>>(std::istream &is, Polygon<T> &p) {
    for (auto &&pi : p) is >> pi;
    return is;
}
template <typename T> std::ostream &operator<<(std::ostream &os, const Polygon<T> &p) {
    for (auto &&pi : p) os << pi << " -> ";
    return os;
}
#line 4 "geometry/polygon_area.hpp"

// area of polygon
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
// return area * 2
template <typename T> T polygon_area2(const Polygon<T> &p) {
    int n = (int)p.size();
    assert(n >= 2);
    T ret = T(0);
    for (int i = 0; i < n - 1; i++) {
        ret += cross(p[i], p[i + 1]);
    }
    ret += cross(p[n - 1], p[0]);
    // counter clockwise: ret > 0
    // clockwise: ret < 0
    return ret;
}
template <typename T> T polygon_area(const Polygon<T> &p) { return polygon_area2(p) / T(2); }

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