hdu3982

//半平面交+多边形和圆的交的面积
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <iostream>
using namespace std;
const int N = 2050;
const  double eps = 1e-8;
const double pi = acos(-1.0);

int sign(double d){
	return d < -eps ? -1 : (d > eps);
}
struct point{
	double x, y;
	point(double _x=0, double _y=0) : x(_x), y(_y) {}
	bool operator== (point p){
		return fabs(x-p.x) < eps && fabs(y-p.y) < eps;
	}
	void read(){
		scanf("%lf%lf", &x, &y);
	}
	void set(double _x, double _y){
		x = _x;
		y = _y;
	}
}pque[N], po[N];
struct seg{
	point st, ed;
	double ang;
	void calang(){
		ang = atan2(ed.y-st.y, ed.x-st.x);
	}
}sque[N], segs[N];

struct circle{
	point c;
	double r;
};

int n;
double r;
point cen, cherry;

inline double xmul(point st1, point ed1, point st2, point ed2){
	return (ed1.x - st1.x) * (ed2.y - st2.y) - (ed1.y - st1.y) * (ed2.x - st2.x);
}
point intersectPoint(point st1, point ed1, point st2, point ed2){  //求相交直线的交点
	double t = xmul(st2, st1, st2, ed2) / ((ed1.y-st1.y) * (ed2.x-st2.x) - (ed1.x-st1.x) * (ed2.y-st2.y));
	return point(st1.x+(ed1.x-st1.x)*t, st1.y+(ed1.y-st1.y)*t);
}
bool cmpseg(seg a, seg b){
//	return a.ang < b.ang;
	return sign(a.ang - b.ang) < 0;
}
//半平面交,第个扳半平面为segs[i][0]->segs[i][1]的右侧,结果放在ps中
void halfPlaneInter(seg* segs, int sn, point* ps, int& pn){
	int i, j, k, l, r;
	seg ts;
	for(i = 0; i < sn; i++){
		segs[i].calang();
	}
	sort(segs, segs+sn, cmpseg);
	for(k = i = 0; i < sn; i++){
		for(j = i; j < sn && sign(segs[i].ang-segs[j].ang) == 0; j++) ;
		for(ts = segs[i], i++; i < j; i++){
			if(sign(xmul(ts.st, ts.ed, ts.st, segs[i].st)) > 0){
				ts = segs[i];
			}
		}
		segs[k++] = ts;
		i = j-1;
	}
	sn = k;
	if(sn <= 0){
		pn = 0;
		return;
	}
	if(sn <= 2){
		segs[sn] = segs[0];
		for(l = r = 0; r < sn; r++){
			sque[r] = segs[r];
			pque[r] = intersectPoint(segs[r].st, segs[r].ed, segs[r+1].st, segs[r+1].ed);
		}
	}else{
		l = r = 0;
		sque[r++] = segs[0];
		sque[r++] = segs[1];
		pque[0] = intersectPoint(sque[0].st, sque[0].ed, sque[1].st, sque[1].ed);
		for(i = 2; i < sn; i++){
			while(r-l >= 2 && sign(xmul(segs[i].st, segs[i].ed, segs[i].st, pque[r-2])) <= 0) r--;
			sque[r++] = segs[i];
			pque[r-2] = intersectPoint(sque[r-2].st, sque[r-2].ed, sque[r-1].st, sque[r-1].ed);
		}
		//删除多余的 半平面
		while(r-l >= 2){
			bool flag = false;
			if(sign(xmul(sque[r-1].st, sque[r-1].ed, sque[r-1].st, pque[l])) <= 0){
				flag = true;
				l++;
			}
			if(sign(xmul(sque[l].st, sque[l].ed, sque[l].st, pque[r-2])) <= 0){
				flag = true;
				r--;
			}
			if(!flag) break;
		}
		//这里需要注意,最后的结果可能是一个无限平面.
		pque[r-1] = intersectPoint(sque[l].st, sque[l].ed, sque[r-1].st, sque[r-1].ed);
	}
	for(pn = 0, i = l; i < r; i++){
		ps[pn++] = pque[i];
	}
}
double xmul(point st, point ed1, point ed2){
	return (ed1.x-st.x) * (ed2.y-st.y) - (ed1.y-st.y) * (ed2.x-st.x);
}
double dist(point p1, point p2){
	return sqrt(pow(p1.x - p2.x, 2.0) + pow(p1.y - p2.y, 2.0));
}

double dmul(point st, point ed1, point ed2){
	return (ed1.x-st.x) * (ed2.x-st.x) + (ed1.y-st.y) * (ed2.y-st.y);
}

point getRoot(point p, point st, point ed){
	point ans;
    double u=((ed.x-st.x)*(ed.x-st.x)+(ed.y-st.y)*(ed.y-st.y));
    u = ((ed.x-st.x)*(ed.x-p.x)+(ed.y-st.y)*(ed.y-p.y))/u;
    ans.x = u*st.x+(1-u)*ed.x;
    ans.y = u*st.y+(1-u)*ed.y;
    return ans;
}
//二维空间计算点到直线的距离
double disptoline(point p, point st, point ed){
	return fabs(xmul(p, st, ed)) / dist(st, ed);
}
//二维计算点到线段的最短距离
double disptoseg(point p, point st, point ed){
	double d1 = dist(p, st);
	double d2 = dist(p, ed);
	double d3 = dist(st, ed);
	if(fabs(d1+d2-d3) < eps) return 0;
	if(fabs(d1+d3-d2) < eps || fabs(d2+d3-d1) < eps) return min(d1, d2);
	if((d3*d3+d2*d2-d1*d1) < eps || (d3*d3+d1*d1-d2*d2) < eps){
		return min(d1, d2);
	}
	return disptoline(p, st, ed);
}
//求点p1和p2对应的劣弧对应的扇形的面积
double getSectorArea(circle cir, point p1, point p2){
	double ang = acos(dmul(cir.c, p1, p2)/(dist(cir.c, p1)*dist(cir.c, p2)));
	return cir.r*cir.r*fabs(ang)*0.5;
}
//求点p1和p2对应的劣弧对应的弓形的面积
double getBowArea(circle cir, point p1, point p2){
	double ang = acos(dmul(cir.c, p1, p2)/(dist(cir.c, p1)*dist(cir.c, p2)));
	double ans = cir.r*cir.r*fabs(ang)*0.5;
	return ans - cir.r*cir.r*sin(ang)*0.5;
}
//求从st走到ed遇到的第一个圆上的点(st到ed上的点到cir.c的距离得递增,并起,st在圆内,ed在圆外)
point getPoint(circle cir, point st, point ed){
	double l, r, mid, teps = 1e-10;
	point k(ed.x-st.x, ed.y-st.y), tp;
	l = 0.;
	r = 1.;
	while(l <= r){
		mid = (l+r)*0.5;
		tp.x = st.x+mid*k.x;
		tp.y = st.y+mid*k.y;
		if(dist(tp, cir.c) <= cir.r){
			l = mid+teps;
		}else{
			r = mid-teps;
		}
	}
	mid = l-teps;
	tp.x = st.x+mid*k.x;
	tp.y = st.y+mid*k.y;
	return tp;
}
double getArea(circle cir, point p1, point p2){
	double ans = 0;
	int k1, k2;
	k1 = sign(dist(p1, cir.c)-cir.r);
	k2 = sign(dist(p2, cir.c)-cir.r);
	if(k1 <= 0 && k2 <= 0){
		ans = fabs(xmul(cir.c, p1, p2))*0.5;
	}else if(k1 > 0 && k2 > 0){
		ans = getSectorArea(cir, p1, p2);
		if(sign(disptoseg(cir.c, p1, p2) - cir.r) < 0){
			point rp = getRoot(cir.c, p1, p2);
			p1 = getPoint(cir, rp, p1);
			p2 = getPoint(cir, rp, p2);
			ans -= getBowArea(cir, p1, p2);
		}
	}else{
		if(k1 > 0){
			swap(p1, p2);
		}
		point rp = getRoot(cir.c, p1, p2), p3;
		p3 = getPoint(cir, rp, p2);
		ans = getSectorArea(cir, p3, p2);
		ans += fabs(xmul(cir.c, p1, p3))*0.5;
	}
	return ans;
}
//返回圆和多边形交的面积
double area(point* ps, int n, circle cir){
	if(n <= 0) return 0;
	ps[n] = ps[0];
	int i;
	double ans, tmp;
	ans = 0;
	for(i = 1; i <= n; i++){
		if(fabs(ps[i-1].x-ps[i].x) < eps && fabs(ps[i-1].y-ps[i].y) < eps) continue;
		tmp = getArea(cir, ps[i-1], ps[i]);
		if(sign(xmul(cir.c, ps[i-1], ps[i])) > 0){
			ans += tmp;
		}else{
			ans -= tmp;
		}
	}
	return fabs(ans);
}

bool input(){
	scanf("%lf%d", &r, &n);
	int i;
	for(i = 0; i < n; i++){
		segs[i].st.read();
		segs[i].ed.read();
	}
	cherry.read();
	for(i = 0; i < n; i++){
		if(sign(xmul(segs[i].st, segs[i].ed, segs[i].st, cherry)) < 0){
			swap(segs[i].st, segs[i].ed);
		}
	}
	return true;
}
int ca = 0;
void solve(){
	int cnt;
	double len = r*2;
	segs[n].st.set(-len, -len); segs[n++].ed.set(len, -len);
	segs[n].st.set(len, -len); segs[n++].ed.set(len, len);
	segs[n].st.set(len, len); segs[n++].ed.set(-len, len);
	segs[n].st.set(-len, len); segs[n++].ed.set(-len, -len);
	halfPlaneInter(segs, n,  po, cnt);
	circle cir;
	cir.c.set(0, 0);
	cir.r = r;
	double ans = fabs(area(po, cnt, cir));
	ans /= r*r*pi;
	printf("Case %d: %.5lf%%\n", ++ca, ans*100);
}
int main(){
	int t;
	scanf("%d", &t);
	while(t--){
		input();
		solve();
	}
	return 0;
}
 

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