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#include "geometry3D/ld/base_ld.hpp"
#pragma once
#include "../../template/template.hpp"
#include "../base_arbitary.hpp"
namespace lib {
using vec = Vec<ld>;
const ld eps = 1e-7;
void ldout(int len = 20) { cout << fixed << setprecision(len); }
int sgn(ld a) { return (a < -eps) ? -1 : (a > eps) ? 1 : 0; }
ld dot(const vec &a, const vec &b){
return a.x*b.x + a.y*b.y + a.z*b.z;
}
vec cross(const vec &a, const vec &b){
return Vec(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);
}
ld norm(const vec &a){
return a.x*a.x+a.y*a.y+a.z*a.z;
}
ld abs(const vec &a){
return sqrtl(norm(a));
}
} // namespace lib
#line 2 "geometry3D/ld/base_ld.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 2 "geometry3D/base_arbitary.hpp"
#line 4 "geometry3D/base_arbitary.hpp"
namespace lib {
template<typename T>
struct Vec {
T x, y, z;
Vec (T _x = 0, T _y = 0, T _z = 0) : x(_x), y(_y), z(_z) {}
Vec& operator*=(const T& a){
x *= a;
y *= a;
z *= a;
return *this;
}
Vec& operator/=(const T& a){
x /= a;
y /= a;
z /= a;
return *this;
}
Vec& operator+=(const Vec& rhs) {
x += rhs.x;
y += rhs.y;
z += rhs.z;
return *this;
}
Vec& operator-=(const Vec& rhs) {
x -= rhs.x;
y -= rhs.y;
z -= rhs.z;
return *this;
}
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 std::ostream &operator<<(std::ostream &os,const Vec&r) {
return os << "(" << r.x << "," << r.y << "," << r.z << ")";
}
};
};
#line 5 "geometry3D/ld/base_ld.hpp"
namespace lib {
using vec = Vec<ld>;
const ld eps = 1e-7;
void ldout(int len = 20) { cout << fixed << setprecision(len); }
int sgn(ld a) { return (a < -eps) ? -1 : (a > eps) ? 1 : 0; }
ld dot(const vec &a, const vec &b){
return a.x*b.x + a.y*b.y + a.z*b.z;
}
vec cross(const vec &a, const vec &b){
return Vec(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);
}
ld norm(const vec &a){
return a.x*a.x+a.y*a.y+a.z*a.z;
}
ld abs(const vec &a){
return sqrtl(norm(a));
}
} // namespace lib