AOJ0115.cpp

// AOJ 0115
#include <iostream>
#include <cmath>

using namespace std;

typedef double Real;
const Real EPS = 1e-5;

struct plane{
  Real a, b, c, d;
  plane() {}
  plane(Real a, Real b, Real c, Real d) : a(a), b(b), c(c), d(d) {}
};

struct vect {
  Real x, y, z;
  vect(Real x = 0, Real y = 0, Real z = 0) : x(x), y(y), z(z) {}
  void add(vect& a){
    x += a.x;
    y += a.y;
    z += a.z;
  }
  void sub(vect& a){
    x -= a.x;
    y -= a.y;
    z -= a.z;
  }
  void mul(Real a){
    x *= a;
    y *= a;
    z *= a;
  }
  void div(Real a){
    x /= a;
    y /= a;
    z /= a;
  }
  Real dot(vect& a){
    return (x * a.x + y * a.y + z * a.z);
  }
  Real dot(plane a){
    return (x * a.a + y * a.b + z * a.c);
  }
  Real length(){
    return sqrt(x * x + y * y + z * z);
  }
  Real dist(vect& a){
    vect c = *this;
    c.sub(a);
    return c.length();
  }
  Real& access(int a){
    a %= 3;
    if (a == 0) return x;
    if (a == 1) return y;
    if (a == 2) return z;
    return x;
  }
  vect cross(vect& a){
    vect ret;
    vect u = *this, v = a;
    ret.x = u.y * v.z - u.z * v.y;
    ret.y = u.z * v.x - u.x * v.z;
    ret.z = u.x * v.y - u.y * v.x;
    return ret;
  }
  bool eq(vect& a){
    return x == a.x && y == a.y && z == a.z;
  }
};
ostream &operator<<(ostream &os, const vect &a) { os << "(" << a.x << ", " << a.y << ", " << a.z << ")"; return os; }

struct tri{
  vect p0, p1, p2;
  tri(vect a, vect b, vect c) : p0(a), p1(b), p2(c) {}
  vect normal(){
    Real a = ((p1.y - p0.y) * (p2.z - p0.z)) - ((p2.y - p0.y) * (p1.z - p0.z));
    Real b = ((p1.z - p0.z) * (p2.x - p0.x)) - ((p2.z - p0.z) * (p1.x - p0.x));
    Real c = ((p1.x - p0.x) * (p2.y - p0.y)) - ((p2.x - p0.x) * (p1.y - p0.y));
    vect ret(a, b, c);
    // cout << "ret : " << ret << ", length = " << ret.length() << endl;
    ret.div(ret.length());
    return ret;
  }
  Real area(){
    Real a, b, c, s;
    a = p0.dist(p1), b = p1.dist(p2), c = p2.dist(p0);
    s = (a + b + c) / 2;
    return sqrt(s * (s - a) * (s - b) * (s - c));
  }
};

bool intersect(vect n, vect A, vect B, vect v1, vect *ret)
{
  vect AP = v1; AP.sub(A);
  vect BP = v1; BP.sub(B);
  Real dot_APN = AP.dot(n), dot_BPN = BP.dot(n);

  if (abs(dot_APN) < EPS && abs(dot_BPN) < EPS){
    // cout << "double zero" << endl;
    return false;
  }
  else if ((dot_APN - EPS <= 0.0 && 0.0 <= dot_BPN + EPS) || (dot_BPN - EPS <= 0.0 && 0.0 <= dot_APN + EPS)){
    // RINPANA
  }
  else {
    // cout << "same side" << endl;
    return false;
  }

  vect AB = B; AB.sub(A);
  Real h = abs(dot_APN) / (abs(dot_APN) + abs(dot_BPN));
  // cout << "AP : " << AP << " BP : " << BP << endl;
  // cout << "dot_APN = " << dot_APN << ", dot_BPN = " << dot_BPN << endl;
  // cout << "AB : " << AB << endl;

  ret->x = A.x + (AB.x * h);
  ret->y = A.y + (AB.y * h);
  ret->z = A.z + (AB.z * h);

  return true;
}

int main()
{
  Real x, y, z;

  while (cin >> x){
    if (cin.eof()) break;
    cin >> y >> z;      vect uaz_(x, y, z);
    cin >> x >> y >> z;    vect enemy_(x, y, z);
    cin >> x >> y >> z;    vect v1_(x, y, z);
    cin >> x >> y >> z;    vect v2_(x, y, z);
    cin >> x >> y >> z;    vect v3_(x, y, z);

    tri barrier(v1_, v2_, v3_);

    vect n = barrier.normal();
    vect uaz = uaz_, v1 = v1_;
    vect v = uaz_;

    v.sub(enemy_);
    uaz.sub(v1);

    // cout << n << endl;

    bool ok = true;
    if (abs(v.dot(n)) < EPS){
      // cout << "zero" << endl;
    }
    else {
      // Real t = (uaz.dot(n)) / (v.dot(n));
      // // cout << "DEBUG ***" << t << " " << dst << endl;
      // if (t < 0){
      //   // cout << "back" << endl;
      //   ok = false;
      // }
      // else if (dst < t + EPS){
      //   // cout << "over" << endl;
      //   ok = false;
      // }

      vect inter;
      if (!intersect(n, uaz_, enemy_, v1_, &inter)){
        // NIKOMAKI
        // cout << "empty" << endl;
      }
      else {
        // cout << "intersect point : " << inter << endl;
        // Q, v1, v2
        Real a, b, c, s;
        a = inter.dist(v1_), b = v1_.dist(v2_), c = v2_.dist(inter);
        s = (a + b + c) / 2;
        Real T1 = sqrt(s * (s - a) * (s - b) * (s - c));
        // Q, v2, v3
        a = inter.dist(v2_), b = v2_.dist(v3_), c = v3_.dist(inter);
        s = (a + b + c) / 2;
        Real T2 = sqrt(s * (s - a) * (s - b) * (s - c));
        // Q, v3, v1
        a = inter.dist(v3_), b = v3_.dist(v1_), c = v1_.dist(inter);
        s = (a + b + c) / 2;
        Real T3 = sqrt(s * (s - a) * (s - b) * (s - c));
        // cout << T1 << " " << T2 << " " << T3 << " " << barrier.area() << endl;
        if ((T1 + T2 + T3) < barrier.area() + EPS){
          // inside
          ok = false;
        }
      }
    }
    if (ok){
      cout << "HIT" << endl;
    }
    else {
      cout << "MISS" << endl;
    }
  }

  return 0;
}

// RINPANA

I see you are a person of culture as well

// NIKOMAKI

Nice