geometry/base_arbitary.hpp

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• Last update: 2023-05-17 22:41:14+09:00
• Include: #include "geometry/base_arbitary.hpp"

Depends on

• テンプレート (template/template.hpp)

Verified with

• test/geometry/base_rational.test.cpp

Code

#pragma once

#include "../template/template.hpp"

namespace lib {

template <typename T> struct Vec {
    T x, y;
    Vec(T _x = T(0), T _y = T(0)) : x(_x), y(_y) {}
    Vec& operator*=(const T& a) {
        x *= a;
        y *= a;
        return *this;
    }
    Vec& operator/=(const T& a) {
        x /= a;
        y /= a;
        return *this;
    }
    Vec& operator+=(const Vec& rhs) {
        x += rhs.x;
        y += rhs.y;
        return *this;
    }
    Vec& operator-=(const Vec& rhs) {
        x -= rhs.x;
        y -= rhs.y;
        return *this;
    }
    friend bool operator==(const Vec& lhs, const Vec& rhs) {
        return lhs.x == rhs.x && lhs.y == rhs.y;
    }
    friend bool operator!=(const Vec& lhs, const Vec& rhs) {
        return lhs.x != rhs.x || lhs.y != rhs.y;
    }
    friend Vec operator+(const Vec& lhs, const Vec& rhs) {
        return Vec(lhs) += rhs;
    }
    friend Vec operator-(const Vec& lhs, const Vec& rhs) {
        return Vec(lhs) -= rhs;
    }
    friend Vec operator*(const Vec& lhs, const T& rhs) {
        return Vec(lhs) *= rhs;
    }
    friend Vec operator*(const T& rhs, const Vec& lhs) {
        return Vec(lhs) *= rhs;
    }
    friend Vec operator/(const Vec& lhs, const T& rhs) {
        return Vec(lhs) /= rhs;
    }
    friend Vec operator/(const T& rhs, const Vec& lhs) {
        return Vec(lhs) /= rhs;
    }
};

template <typename T> T dot(const Vec<T>& a, const Vec<T>& b) {
    return a.x * b.x + a.y * b.y;
}

// cross > 0 : counter clockwise a -> b
template <typename T> T cross(const Vec<T>& a, const Vec<T>& b) {
    return a.x * b.y - a.y * b.x;
}

template <typename T> ld abs(const Vec<T>& a) {
    return sqrtl(a.x * a.x + a.y * a.y);
}

template <typename T> T norm(const Vec<T>& a) {
    return a.x * a.x + a.y * a.y;
}

template <typename T> struct Line { Vec<T> p, q; };

template <typename T> int intersection(const Line<T>& a, const Line<T>& b) {
    if (cross(a.p - a.q, b.p - b.q) == 0) {
        if (cross(a.p - b.p, a.q - b.p) == 0) return 2;
        return 0;
    }
    return 1;
}

// intersection == 1 (cross(a.p-a.q,b.p-b.q) != 0)
template <typename T> Vec<T> cross_point(const Line<T>& a, const Line<T>& b) {
    Vec<T> va = a.p - a.q, vb = b.p - b.q;
    Vec<T> ba = b.p - a.q;
    T alpha = cross(ba, vb) / cross(va, vb);
    return alpha * a.p + (1 - alpha) * a.q;
}

}  // namespace lib

#line 2 "geometry/base_arbitary.hpp"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 4 "geometry/base_arbitary.hpp"

namespace lib {

template <typename T> struct Vec {
    T x, y;
    Vec(T _x = T(0), T _y = T(0)) : x(_x), y(_y) {}
    Vec& operator*=(const T& a) {
        x *= a;
        y *= a;
        return *this;
    }
    Vec& operator/=(const T& a) {
        x /= a;
        y /= a;
        return *this;
    }
    Vec& operator+=(const Vec& rhs) {
        x += rhs.x;
        y += rhs.y;
        return *this;
    }
    Vec& operator-=(const Vec& rhs) {
        x -= rhs.x;
        y -= rhs.y;
        return *this;
    }
    friend bool operator==(const Vec& lhs, const Vec& rhs) {
        return lhs.x == rhs.x && lhs.y == rhs.y;
    }
    friend bool operator!=(const Vec& lhs, const Vec& rhs) {
        return lhs.x != rhs.x || lhs.y != rhs.y;
    }
    friend Vec operator+(const Vec& lhs, const Vec& rhs) {
        return Vec(lhs) += rhs;
    }
    friend Vec operator-(const Vec& lhs, const Vec& rhs) {
        return Vec(lhs) -= rhs;
    }
    friend Vec operator*(const Vec& lhs, const T& rhs) {
        return Vec(lhs) *= rhs;
    }
    friend Vec operator*(const T& rhs, const Vec& lhs) {
        return Vec(lhs) *= rhs;
    }
    friend Vec operator/(const Vec& lhs, const T& rhs) {
        return Vec(lhs) /= rhs;
    }
    friend Vec operator/(const T& rhs, const Vec& lhs) {
        return Vec(lhs) /= rhs;
    }
};

template <typename T> T dot(const Vec<T>& a, const Vec<T>& b) {
    return a.x * b.x + a.y * b.y;
}

// cross > 0 : counter clockwise a -> b
template <typename T> T cross(const Vec<T>& a, const Vec<T>& b) {
    return a.x * b.y - a.y * b.x;
}

template <typename T> ld abs(const Vec<T>& a) {
    return sqrtl(a.x * a.x + a.y * a.y);
}

template <typename T> T norm(const Vec<T>& a) {
    return a.x * a.x + a.y * a.y;
}

template <typename T> struct Line { Vec<T> p, q; };

template <typename T> int intersection(const Line<T>& a, const Line<T>& b) {
    if (cross(a.p - a.q, b.p - b.q) == 0) {
        if (cross(a.p - b.p, a.q - b.p) == 0) return 2;
        return 0;
    }
    return 1;
}

// intersection == 1 (cross(a.p-a.q,b.p-b.q) != 0)
template <typename T> Vec<T> cross_point(const Line<T>& a, const Line<T>& b) {
    Vec<T> va = a.p - a.q, vb = b.p - b.q;
    Vec<T> ba = b.p - a.q;
    T alpha = cross(ba, vb) / cross(va, vb);
    return alpha * a.p + (1 - alpha) * a.q;
}

}  // namespace lib

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