geometry/polygon_contain.hpp

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• Last update: 2024-03-24 14:28:32+09:00
• Include: #include "geometry/polygon_contain.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C

Depends on

• geometry/ccw.hpp
• geometry/is_intersect_sp.hpp
• geometry/line.hpp
• geometry/point.hpp
• geometry/polygon.hpp
• geometry/segment.hpp

Required by

• geometry/all.hpp

Verified with

• verify/aoj_cgl/aoj_cgl_3_c.test.cpp

Code

#pragma once

#include "geometry/polygon.hpp"
#include "geometry/is_intersect_sp.hpp"

// polygon contain point -> 2 (IN)
// polygon cross point -> 1 (ON)
// otherwise -> 0 (OUT)
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C
template <typename T> int polygon_contain(const Polygon<T> &q, const Point<T> &p) {
    bool x = false;
    int n = (int)q.size();
    for (int i = 0; i < n - 1; i++) {
        if (is_intersect_sp(Segment(q[i], q[i + 1]), p)) return ON;
        Point a = q[i] - p, b = q[i + 1] - p;
        if (a.y > b.y) std::swap(a, b);
        // a.y < b.y
        // check each point's y is 0 at most 1 times
        if (sign(a.y) <= 0 and sign(b.y) > 0 and sign(cross(a, b)) > 0) x = !x;
    }
    {
        if (is_intersect_sp(Segment(q[n - 1], q[0]), p)) return ON;
        Point a = q[n - 1] - p, b = q[0] - p;
        if (a.y > b.y) std::swap(a, b);
        if (sign(a.y) <= 0 and sign(b.y) > 0 and sign(cross(a, b)) > 0) x = !x;
    }
    return (x ? IN : OUT);
}

#line 2 "geometry/polygon_contain.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 2 "geometry/is_intersect_sp.hpp"

#line 2 "geometry/segment.hpp"

#line 2 "geometry/line.hpp"

#line 4 "geometry/line.hpp"

// line
template <typename T> struct Line {
    Point<T> a, b;

    Line() = default;

    Line(const Point<T> &a, const Point<T> &b) : a(a), b(b) {}

    // Ax + By = C
    Line(const T &A, const T &B, const T &C) {
        assert(!(equal(A, T(0)) and equal(B, T(0))));
        if (equal(A, T(0))) {
            a = Point<T>(T(0), C / B), b = Point<T>(T(1), C / B);
        } else if (equal(B, T(0))) {
            a = Point<T>(C / A, T(0)), b = Point<T>(C / A, T(1));
        } else if (equal(C, T(0))) {
            a = Point<T>(T(0), T(0)), b = Point<T>(T(1), B / A);
        } else {
            a = Point<T>(T(0), C / B), b = Point<T>(C / A, T(0));
        }
    }

    friend std::istream &operator>>(std::istream &is, Line &p) { return is >> p.a >> p.b; }
    friend std::ostream &operator<<(std::ostream &os, const Line &p) { return os << p.a << "->" << p.b; }
};
#line 4 "geometry/segment.hpp"

// segment
template <typename T> struct Segment : Line<T> {
    Segment() = default;

    Segment(const Point<T> &a, const Point<T> &b) : Line<T>(a, b) {}
};
#line 2 "geometry/ccw.hpp"

#line 4 "geometry/ccw.hpp"

// counter clockwise
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
constexpr int COUNTER_CLOCKWISE = 1;  // a-b-c counter clockwise
constexpr int CLOCKWISE = -1;         // a-b-c clockwise
constexpr int ONLINE_BACK = 2;        // c-a-b line
constexpr int ONLINE_FRONT = -2;      // a-b-c line
constexpr int ON_SEGMENT = 0;         // a-c-b line
template <typename T> int ccw(const Point<T> &a, Point<T> b, Point<T> c) {
    b = b - a, c = c - a;
    if (sign(cross(b, c)) == 1) return COUNTER_CLOCKWISE;
    if (sign(cross(b, c)) == -1) return CLOCKWISE;
    if (sign(dot(b, c)) == -1) return ONLINE_BACK;
    if (norm(b) < norm(c)) return ONLINE_FRONT;
    return ON_SEGMENT;
}
#line 5 "geometry/is_intersect_sp.hpp"

// intersection (segment and point)
// ccw(a, b, c) == ON_SEGMENT -> a - c - b
template <typename T> inline bool is_intersect_sp(const Segment<T> &s, const Point<T> &p) { return ccw(s.a, s.b, p) == ON_SEGMENT or sign(norm(s.a - p)) == 0 or sign(norm(s.b - p)) == 0; }
#line 5 "geometry/polygon_contain.hpp"

// polygon contain point -> 2 (IN)
// polygon cross point -> 1 (ON)
// otherwise -> 0 (OUT)
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C
template <typename T> int polygon_contain(const Polygon<T> &q, const Point<T> &p) {
    bool x = false;
    int n = (int)q.size();
    for (int i = 0; i < n - 1; i++) {
        if (is_intersect_sp(Segment(q[i], q[i + 1]), p)) return ON;
        Point a = q[i] - p, b = q[i + 1] - p;
        if (a.y > b.y) std::swap(a, b);
        // a.y < b.y
        // check each point's y is 0 at most 1 times
        if (sign(a.y) <= 0 and sign(b.y) > 0 and sign(cross(a, b)) > 0) x = !x;
    }
    {
        if (is_intersect_sp(Segment(q[n - 1], q[0]), p)) return ON;
        Point a = q[n - 1] - p, b = q[0] - p;
        if (a.y > b.y) std::swap(a, b);
        if (sign(a.y) <= 0 and sign(b.y) > 0 and sign(cross(a, b)) > 0) x = !x;
    }
    return (x ? IN : OUT);
}

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