题意：如题
思路：离散。将所有交点求出来，相当于将多变形的边切成了很多条元边，对每条元边，有两种情况
- 在圆内，答案加上此边长
- 在圆外，答案加上此边相对于圆心的"有向转弧"
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#include "local.h"
#endif
#define X first
#define Y second
#define pb(x) push_back(x)
#define mp(x, y) make_pair(x, y)
#define all(a) (a).begin(), (a).end()
#define mset(a, x) memset(a, x, sizeof(a))
#define mcpy(a, b) memcpy(a, b, sizeof(a))
typedef long long ll;
template<typename T>bool umax(T&a, const T&b){return b<=a?false:(a=b,true);}
template<typename T>bool umin(T&a, const T&b){return b>=a?false:(a=b,true);} namespace ConstSet {
const double PI = acos(-1.0);
const double e = 2.718281828459045;
} const double eps = 1e-8;
struct Real {
double x;
double get() { return x; }
int read() { return scanf("%lf", &x); }
Real(const double &x) { this->x = x; }
Real() {}
Real abs() { return x > ? x : -x; } Real operator + (const Real &that) const { return Real(x + that.x);}
Real operator - (const Real &that) const { return Real(x - that.x);}
Real operator * (const Real &that) const { return Real(x * that.x);}
Real operator / (const Real &that) const { return Real(x / that.x);}
Real operator - () const { return Real(-x); } Real operator += (const Real &that) { return Real(x += that.x); }
Real operator -= (const Real &that) { return Real(x -= that.x); }
Real operator *= (const Real &that) { return Real(x *= that.x); }
Real operator /= (const Real &that) { return Real(x /= that.x); } bool operator < (const Real &that) const { return x - that.x <= -eps; }
bool operator > (const Real &that) const { return x - that.x >= eps; }
bool operator == (const Real &that) const { return x - that.x > -eps && x - that.x < eps; }
bool operator <= (const Real &that) const { return x - that.x < eps; }
bool operator >= (const Real &that) const { return x - that.x > -eps; } friend ostream& operator << (ostream &out, const Real &val) {
out << val.x;
return out;
}
friend istream& operator >> (istream &in, Real &val) {
in >> val.x;
return in;
}
}; struct Point {
Real x, y;
int read() { return scanf("%lf%lf", &x.x, &y.x); }
Point(const Real &x, const Real &y) { this->x = x; this->y = y; }
Point() {}
Point operator + (const Point &that) const { return Point(this->x + that.x, this->y + that.y); }
Point operator - (const Point &that) const { return Point(this->x - that.x, this->y - that.y); }
Real operator * (const Point &that) const { return x * that.x + y * that.y; }
Point operator * (const Real &that) const { return Point(x * that, y * that); }
Point operator / (const Real &that) { return Point(x / that, y / that); }
Point operator += (const Point &that) { return Point(this->x += that.x, this->y += that.y); }
Point operator -= (const Point &that) { return Point(this->x -= that.x, this->y -= that.y); }
Point operator *= (const Real &that) { return Point(x *= that, y *= that); }
Point operator /= (const Real &that) { return Point(x /= that, y /= that); } bool operator == (const Point &that) const { return x == that.x && y == that.y; } Real cross(const Point &that) const { return x * that.y - y * that.x; }
Real abs() { return sqrt((x * x + y * y).get()); }
};
typedef Point Vector; struct Segment {
Point a, b;
Segment(const Point &a, const Point &b) { this->a = a; this->b = b; }
Segment() {}
bool intersect(const Segment &that) const {
Point c = that.a, d = that.b;
Vector ab = b - a, cd = d - c, ac = c - a, ad = d - a, ca = a - c, cb = b - c;
return ab.cross(ac) * ab.cross(ad) < && cd.cross(ca) * cd.cross(cb) < ;
}
Point getSegmentIntersection(const Segment &that) const {
Vector u = a - that.a, v = b - a, w = that.b - that.a;
Real t = w.cross(u) / v.cross(w);
return a + v * t;
}
Real Distance(Point P) {
Point A = a, B = b;
if (A == B) return (P - A).abs();
Vector v1 = B - A, v2 = P - A, v3 = P - B;
if (v1 * v2 < ) return v2.abs();
if (v1 * v3 > ) return v3.abs();
return v1.cross(v2).abs() / v1.abs();
}
bool containPoint(const Point &p) const {
Vector ap = p - a, bp = p - b;
return ap * bp < ;
}
}; struct Line {
Point p;
Vector v;
Line(Point p, Vector v): p(p), v(v) {}
Line() {}
Point point(Real a) {
return p + v * a;
}
};
struct Circle {
Point c;
Real r;
Circle(Point c, Real r): c(c), r(r) {}
Circle() {}
void read() {
c.read();
scanf("%lf", &r.x);
}
Point point(Real a) {
return Point(c.x + r * cos(a.get()), c.y + r * sin(a.get()));
}
int getLineIntersection(Line L, vector<Point> &sol) {
Circle C = *this;
Real a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
Real e = a * a + c * c, f = (a * b + c * d) * , g = b * b + d * d - C.r * C.r;
Real delta = f * f - e * g * ;
Real t1, t2;
if (delta < ) return ;
if (delta == ) {
t1 = t2 = -f / (e * ); sol.push_back(L.point(t1));
return ;
}
t1 = (-f - sqrt(delta.get())) / (e * ); sol.push_back(L.point(t1));
t2 = (-f + sqrt(delta.get())) / (e * ); sol.push_back(L.point(t2));
return ;
}
Real turningAngle(Point a, Point b) {
Vector ca = a - c, cb = b - c;
if (ca.abs() == || cb.abs() == ) return ;//一个点和圆心重合，计算转角是没意义的
Real angle = acos((ca * cb / ca.abs() / cb.abs()).get());
return ca.cross(cb) >= ? angle : -angle;
}
}; const int maxn = 1e3 + ; Point p[maxn]; int main() {
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif // ONLINE_JUDGE
int n;
while (cin >> n, n) {
for (int i = ; i < n; i ++) {
p[i].read();
}
Circle c;
c.read();
vector<Point> vs;
for (int i = ; i < n; i ++) {
vs.pb(p[i]);
vector<Point> v;
Point a = p[i], b = p[(i + ) % n];
c.getLineIntersection(Line(a, b - a), v);
for (int i = ; i < v.size(); i ++) {
if (Segment(a, b).containPoint(v[i])) vs.pb(v[i]);
}
}
Real ans = ;
for (int i = ; i < vs.size(); i ++) {
int j = (i + ) % vs.size();
Point mid = (vs[i] + vs[j]) * 0.5;
Real length = (mid - c.c).abs();
if (length < c.r) ans += (vs[j] - vs[i]).abs();
else ans += c.r * -c.turningAngle(vs[i], vs[j]);
}
cout << (ll)(ans.get() + 0.5) << endl;
}
return ;
}