point intersect(line & l, segment s) {
double da = fabs(l.dist(s.a)), db = fabs(l.dist(s.b));
if (da + db < eps) {
return s.a;
} else {
double t = da / (da + db);
return s.a + (s.b - s.a) * t;
}
}
result lineIntersectsPolygon(line & l, polygon & P, size_t sz, int k) {
int n = (sz + k - 1) / k;
double minDist = numeric_limits<double>::max();
int minPoint = -1;
unordered_set<int> points;
if (n <= 50) {
point prev = P->get(0);
for (size_t i = k; i < sz; i += k) {
point cur = P->get(i);
segment s = {prev, cur};
if (lineIntersectsSegment(l, s)) {
points.insert(i - k);
} else {
double dist = fabs(l.dist(cur));
if (minDist > dist) {
minDist = dist;
minPoint = i;
}
}
prev = cur;
}
} else {
auto ind = lineIntersectsPolygon(l, P, sz, 2 * k);
if (ind.points.size() != 0) {
for (int i : ind.points) {
point p1 = P->get(i - k);
point p2 = P->get(i);
segment s = {p1, p2};
if (lineIntersectsSegment(l, s)) {
points.insert((i - k + sz) % sz);
} else {
points.insert(i);
}
}
} else {
int i = ind.closest;
point p1 = P->get(i - 2 * k);
point p2 = P->get(i - k);
point p3 = P->get(i);
point p4 = P->get(i + k);
point p5 = P->get(i + 2 * k);
point pts[] = {p1, p2, p3, p4, p5};
segment segs[] = {{p1, p2}, {p2, p3}, {p3, p4}, {p4, p5}};
for (int j = 0; j < 4; j++) {
if (lineIntersectsSegment(l, segs[j])) {
points.insert((i + k * (j - 2) + sz) % sz);
}
}
for (int j = 0; j < 5; j++) {
double dist = fabs(l.dist(pts[j]));
if (minDist > dist) {
minDist = dist;
minPoint = (i + k * (j - 2) + sz) % sz;
}
}
}
}
return {points, minPoint};
}
bool lineIntersectsSegment(line & l, segment & s) {
double da = l.dist(s.a), db = l.dist(s.b);
return !((da > eps && db > eps) || (da < -eps && db < -eps));
}