icpc_library

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:warning: geometry3D/accurate/line.hpp

Depends on

Code

#pragma once

#include "base_accurate.hpp"
#include "../../utility/rational.hpp"

namespace lib {

template<typename T>
struct Line {
    Vec<T> a, b;
};

int intersection(const Line<rational> &p, const Line<rational> &q){
    // cross_point = alpha * p.a + (1-alpha) * p.b = beta * q.b + (1-beta) * q.a
    // alpha * vp + beta * vq = vr
    using vec = Vec<rational>;
    vec vp = p.a - p.b, vq = q.a - q.b, vr = q.a - p.b;
    vec cpq = cross(vp,vq), cpr = cross(vp,vr), crq = cross(vr,vq);
    // yz projection
    if (cpq.x != 0){
        rational alpha = crq.x / cpq.x, beta = cpr.x / cpq.x;
        // cross
        if (alpha * vp.x + beta * vq.x - vr.x == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // zx projection
    if (cpq.y != 0){
        rational alpha = crq.y / cpq.y, beta = cpr.y / cpq.y;
        // cross
        if (alpha * vp.y + beta * vq.y - vr.y == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // xy projection
    if (cpq.z != 0){
        rational alpha = crq.z / cpq.z, beta = cpr.z / cpq.z;
        // cross
        if (alpha * vp.z + beta * vq.z - vr.z == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // cpq == 0  ->  parallel
    // same
    if (cross(p.a - q.a, p.b - q.a) == vec(0,0,0)){
        return 3;
    }
    // not same
    return 2;
}

Vec<rational> cross_point(const Line<rational> &p, const Line<rational> &q){
    assert(intersection(p,q) == 0);
    // cross_point = alpha * p.a + (1-alpha) * p.b = beta * q.b + (1-beta) * q.a
    // alpha * vp + beta * vq = vr
    using vec = Vec<rational>;
    vec vp = p.a - p.b, vq = q.a - q.b, vr = q.a - p.b;
    vec cpq = cross(vp,vq), cpr = cross(vp,vr), crq = cross(vr,vq);
    auto res = [&](rational alpha){
        return alpha * p.a + (1-alpha) * p.b;
    };
    // yz projection
    if (cpq.x != 0){
        rational alpha = crq.x / cpq.x, beta = cpr.x / cpq.x;
        // cross
        if (alpha * vp.x + beta * vq.x - vr.x == 0){
            return res(alpha);
        }
    }
    // zx projection
    if (cpq.y != 0){
        rational alpha = crq.y / cpq.y, beta = cpr.y / cpq.y;
        // cross
        if (alpha * vp.y + beta * vq.y - vr.y == 0){
            return res(alpha);
        }
    }
    // xy projection
    if (cpq.z != 0){
        rational alpha = crq.z / cpq.z, beta = cpr.z / cpq.z;
        // cross
        if (alpha * vp.z + beta * vq.z - vr.z == 0){
            return res(alpha);
        }
    }
    // NOT expected
    return vec();
}


}  // namespace lib
#line 2 "geometry3D/accurate/line.hpp"

#line 2 "geometry3D/accurate/base_accurate.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/accurate/base_accurate.hpp"

namespace lib {

template<typename T>
bool operator==(const Vec<T>& lhs, const Vec<T>& rhs) {
    return lhs.x == rhs.x && lhs.y == rhs.y && lhs.z == rhs.z;
}

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

template<typename T>
Vec<T> cross(const Vec<T> &a, const Vec<T> &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);
}

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

}  // namespace lib
#line 2 "utility/rational.hpp"

#line 4 "utility/rational.hpp"

namespace lib {

struct rational {
    rational() : p(0), q(1) {}
    rational(ll n) : p(n), q(1) {}
    rational(ll n, ll m) {
        assert(m != 0);
        if (m < 0) n = -n, m = -m;
        ll g = gcd(n, m);
        p = n / g;
        q = m / g;
    }
    explicit operator const ld () const { return ld(p) / ld(q); }
    rational& operator+=(const rational& rhs){
        ll g = gcd(q, rhs.q);
        ll np = rhs.q / g * p + q / g * rhs.p;
        ll nq = q / g * rhs.q;
        ll ng = gcd(np, nq);
        p = np / ng, q = nq / ng;
        return *this;
    }
    rational& operator-=(const rational& rhs) {
        (*this) += rational(-rhs.p, rhs.q);
        return *this;
    }
    rational& operator*=(const rational& rhs) {
        ll g1 = gcd(q, rhs.p), g2 = gcd(p, rhs.q);
        ll np = p / g2 * rhs.p / g1;
        ll nq = q / g1 * rhs.q / g2;
        p = np, q = nq;
        return *this;
    }
    rational& operator/=(const rational& rhs) {
        (*this) *= rational(rhs.q, rhs.p);
        return *this;
    }
    rational operator+() const {
        return *this;
    }
    rational operator-() const {
        return rational() - *this;
    }
    friend rational operator+(const rational& lhs, const rational& rhs) {
        return rational(lhs) += rhs;
    }
    friend rational operator-(const rational& lhs, const rational& rhs) {
        return rational(lhs) -= rhs;
    }
    friend rational operator*(const rational& lhs, const rational& rhs) {
        return rational(lhs) *= rhs;
    }
    friend rational operator/(const rational& lhs, const rational& rhs) {
        return rational(lhs) /= rhs;
    }
    friend bool operator==(const rational& lhs, const rational& rhs) {
        return lhs.p == rhs.p && lhs.q == rhs.q;
    }
    friend bool operator!=(const rational& lhs, const rational& rhs) {
        return lhs.p != rhs.p || lhs.q != rhs.q;
    }
    friend bool operator<(const rational lhs, const rational rhs) {
        return less_than(lhs, rhs);
    }
    friend bool operator>(const rational lhs, const rational rhs) {
        return less_than(rhs, lhs);
    }
    friend bool operator<=(const rational lhs, const rational rhs) {
        return lhs == rhs || lhs < rhs;
    }
    friend bool operator>=(const rational lhs, const rational rhs) {
        return lhs == rhs || lhs > rhs;
    }
    friend std::ostream& operator<<(std::ostream& os, const rational& r) {
        return os << r.p << " / " << r.q;
    }
    std::pair<ll,ll> val() const {
        return {p, q};
    }

  private:
    ll p, q;
    static bool less_than(rational lhs, rational rhs) {
        __int128_t lv = __int128_t(lhs.p) * __int128_t(rhs.q);
        __int128_t rv = __int128_t(lhs.q) * __int128_t(rhs.p);
        return lv < rv;
    }
};

}  // namespace lib
#line 5 "geometry3D/accurate/line.hpp"

namespace lib {

template<typename T>
struct Line {
    Vec<T> a, b;
};

int intersection(const Line<rational> &p, const Line<rational> &q){
    // cross_point = alpha * p.a + (1-alpha) * p.b = beta * q.b + (1-beta) * q.a
    // alpha * vp + beta * vq = vr
    using vec = Vec<rational>;
    vec vp = p.a - p.b, vq = q.a - q.b, vr = q.a - p.b;
    vec cpq = cross(vp,vq), cpr = cross(vp,vr), crq = cross(vr,vq);
    // yz projection
    if (cpq.x != 0){
        rational alpha = crq.x / cpq.x, beta = cpr.x / cpq.x;
        // cross
        if (alpha * vp.x + beta * vq.x - vr.x == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // zx projection
    if (cpq.y != 0){
        rational alpha = crq.y / cpq.y, beta = cpr.y / cpq.y;
        // cross
        if (alpha * vp.y + beta * vq.y - vr.y == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // xy projection
    if (cpq.z != 0){
        rational alpha = crq.z / cpq.z, beta = cpr.z / cpq.z;
        // cross
        if (alpha * vp.z + beta * vq.z - vr.z == 0){
            return 0;
        }
        // nejire
        return 1;
    }
    // cpq == 0  ->  parallel
    // same
    if (cross(p.a - q.a, p.b - q.a) == vec(0,0,0)){
        return 3;
    }
    // not same
    return 2;
}

Vec<rational> cross_point(const Line<rational> &p, const Line<rational> &q){
    assert(intersection(p,q) == 0);
    // cross_point = alpha * p.a + (1-alpha) * p.b = beta * q.b + (1-beta) * q.a
    // alpha * vp + beta * vq = vr
    using vec = Vec<rational>;
    vec vp = p.a - p.b, vq = q.a - q.b, vr = q.a - p.b;
    vec cpq = cross(vp,vq), cpr = cross(vp,vr), crq = cross(vr,vq);
    auto res = [&](rational alpha){
        return alpha * p.a + (1-alpha) * p.b;
    };
    // yz projection
    if (cpq.x != 0){
        rational alpha = crq.x / cpq.x, beta = cpr.x / cpq.x;
        // cross
        if (alpha * vp.x + beta * vq.x - vr.x == 0){
            return res(alpha);
        }
    }
    // zx projection
    if (cpq.y != 0){
        rational alpha = crq.y / cpq.y, beta = cpr.y / cpq.y;
        // cross
        if (alpha * vp.y + beta * vq.y - vr.y == 0){
            return res(alpha);
        }
    }
    // xy projection
    if (cpq.z != 0){
        rational alpha = crq.z / cpq.z, beta = cpr.z / cpq.z;
        // cross
        if (alpha * vp.z + beta * vq.z - vr.z == 0){
            return res(alpha);
        }
    }
    // NOT expected
    return vec();
}


}  // namespace lib
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