void normalize() {
set<segment> T; set<point> U;
for (int i = 0; i < n; i++) make_barrier(i, i);
for (int i = 0; i < m; i++) {
point p = v[b[i].first], q = v[b[i].second];
set<point> S;
S.insert(p); S.insert(q);
for (int j = 0; j < m; j++) {
point r = v[b[j].first], s = v[b[j].second];
if (r == p || r == q || s == p || s == q) continue;
if (cmp((q - p) % (s - r)) == 0) {
if (between(p, r, q)) S.insert(r);
if (between(p, s, q)) S.insert(s);
} else if (seg_intersect(p, q, r, s)) {
S.insert(line_intersect(p, q, r, s));
}
}
foreach (st, all(S)) {
if (st != S.begin()) T.insert(segment(p, *st));
U.insert(p = *st);
}
}
clear();
foreach (it, all(U)) v[n++] = *it;
foreach (it, all(T)) {
int i = lower_bound(v, v+n, it->first) - v;
int j = lower_bound(v, v+n, it->second) - v;
make_barrier(i, j);
}
polygon poly_intersect(polygon &P, polygon &Q){
int m = Q.size(), n = P.size();
int a = 0, b = 0, aa = 0, ba = 0, inflag = 0;
polygon R;
while( (aa < n || ba < m) && aa < 2*n && ba < 2*m){
Point p1 = P[a], p2 = P[(a+1) % n], q1 = Q[b], q2 = Q[(b+1) % m];
Point A = p2 - p1, B = q2 - q1;
int cross = cmp(A ^ B), ha = turn(p2, q2, p1), hb = turn(q2, p2, q1);
if(cross == 0 && turn(p1, q1, p2) == 0 && cmp(A * B) < 0){
if(between(p1, q1, p2)) R.push_back(q1);
if(between(p1, q2, p2)) R.push_back(q2);
if(between(q1, p1, q2)) R.push_back(p1);
if(between(q1, p2, q2)) R.push_back(p2);
if(R.size() < 2) return polygon();
inflag = 1; break;
}else if(cross != 0 && seg_intersect(p1, p2, q1, q2)) {
if(inflag == 0) aa = ba = 0;
R.push_back(intersection(p1, p2, q1, q2));
inflag = (hb > 0) ? 1 : -1;
}
if(cross == 0 && hb < 0 && ha < 0) return R;
bool t = cross == 0 && hb == 0 && ha == 0;
if(t ? (inflag == 1) : (cross >= 0) ? (ha <= 0) : (hb > 0)){
if(inflag == -1) R.push_back(q2);
ba++; b++; b %= m;
}else{
if(inflag == 1) R.push_back(p2);
aa++; a++; a %= n;
}
}
if(inflag == 0){
if (in_polygon(P[0], Q)) return P;
if (in_polygon(Q[0], P)) return Q;
}
R.erase(unique(R.begin(), R.end()), R.end());
if(R.size() > 1 && R.front() == R.back()) R.pop_back();
return R;
}
