void convex_hull(polygon in, polygon& hull){
hull.clear();
if(in.size() < 3){ hull = in; return; }
int pos = 0;
for(int i = 1; i < in.size(); i++) if(in[i] < in[pos]) pos = i;
swap(in[0], in[pos]);
refer = in[0];
sort(in.begin() + 1, in.end(), cmp_angle);
in.resize(unique(in.begin(), in.end()) - in.begin());
hull.push_back(in[0]); hull.push_back(in[1]);
in.push_back(in[0]); //isto evita pontos colineares no final do poligono
for(int i = 2; i < in.size(); ){
if(hull.size() > 2 && side_sign(hull[hull.size() - 2], hull[hull.size() - 1], in[i]) <= 0){
hull.pop_back();
}
else hull.push_back(in[i++]);
}
//tira a duplicata
hull.pop_back();
}
//testa se o ponto esta dentro de um poligono (nao necessariamente convexo)
bool inside_poly(pt p, polygon poly){
poly.push_back(poly[0]);
for(int i = 0; i < poly.size()-1; i++)
if(point_and_seg(poly[i], poly[i+1], p)) return true; //na borda
for(int i = 0; i < poly.size()-1; i++) poly[i] = poly[i] - p;
p = pt(0, 0);
double theta, y;
while(true){
theta = (double)rand()/10000.0;
bool inter = false;
//evita que um ponto fique no eixo x
for(int i = 0; i < poly.size()-1; i++){
poly[i] = rotate(poly[i], theta);
if( !cmp(poly[i].x) ) inter = true;
}
if( !inter ){
poly[poly.size()-1] = poly[0];
//testa as possiveis intersecoes
for(int i = 0; i < poly.size()-1; i++){
if( cmp( poly[i].x * poly[i+1].x ) < 0 ){
y = poly[i+1].y - poly[i+1].x * (poly[i].y - poly[i+1].y) / (poly[i].x - poly[i+1].x);
if( cmp(y) > 0 ) inter = !inter; //se interecao valida
}
}
return inter; //testa a paridade da semi-reta vertical partindo de p
}
}
return true;
}
// Returns a list of points on the convex hull in counter-clockwise order.
// NOTE: the last point in the returned list is the same as the first one.
void convex_hull_2(polygon P, polygon& hull) {
hull.clear();
// Sort points lexicographically
sort(P.begin(), P.end());
P.resize(unique(P.begin(), P.end()) - P.begin());
// Build lower hull
for (int i = 0; i < P.size(); i ++) {
while (hull.size() >= 2 && side_sign(hull[hull.size() - 2], hull[hull.size() - 1], P[i]) <= 0)
hull.pop_back();
hull.push_back(P[i]);
};
// Build upper hull
for (int i = P.size()-2, t = hull.size() + 1; i >= 0; i --) {
while (hull.size() >= t && side_sign(hull[hull.size()-2], hull[hull.size()-1], P[i]) <= 0)
hull.pop_back();
hull.push_back(P[i]);
};
}
void rotatingCalipers(polygon pg)
{
pg.push_back(pg.front());
for (int i = 0, j = 1, n = pg.size() - 1; i < n; i++)
{
while (cross(pg[i + 1] - pg[i], pg[j + 1] - pg[j]) > 0)
j = (j + 1) % n;
double dist1 = pg[i].distTo(pg[j - 1]);
double dist2 = pg[i].distTo(pg[j]);
double dist3 = pg[i].distTo(pg[j + 1]);
int r1 = j + 1, r2 = j + 2;
cout << (j - 1) << '=' << dist1 << ' ' << j << '=' << dist2 << ' ' << (j + 1) << '=' << dist3 << '\n';
if (r1 >= n) r1 = 1;
if (r2 >= n) r2 = 1;
if (dist2 > dist3) cout << r1 << '\n';
else if (dist3 > dist2) cout << r2 << '\n';
else cout << min(r1, r2) << '\n';
}
}