HDU5130 (Signal Interference)[计算几何，圆交多边形]

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题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5130

首先考虑下干扰的关系，设A(x1,y1),B(x2,y2),P(x,y)，可以列出式子：
sqrt((x-x2)^2 + (y-y2)^2) = k * sqrt((x-x1)^2 + (y-y1)^2)
化简后可以得到一个圆的方程，然后就转化为圆交多边形模板题了

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#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const double eps=1e-8;
const double inf=1e20;
const int maxp=509;
const double pi=acos(-1.0);
int sgn(double x) {
    if(fabs(x)<eps) return 0;
    if(x<0) return -1;
    else return 1;
}
inline double sqr(double x) { return x*x; }
struct Point {
    double x,y;
    Point() {}
    Point(double _x,double _y) {
        x=_x;
        y=_y;
    }
    double distance(Point p) {
        return hypot(x-p.x,y-p.y);
    }
    double len() {
        return hypot(x,y);
    }
	double len2() {
		return x*x+y*y;
	}
    Point trunc(double r) {
        double l=len();
        if(!sgn(l)) return *this;
        r/=l;
        return Point(x*r,y*r);
    }
    bool operator ==(Point b) const {
        return sgn(x-b.x)==0 && sgn(y-b.y)==0;
    }
    bool operator <(Point b) const {
        return sgn(x-b.x)==0 ? sgn(y-b.y)<0:x<b.x;
    }
    Point operator -(const Point& b) const {
        return Point(x-b.x,y-b.y);
    }
    Point operator +(const Point& b) const {
        return Point(x+b.x,y+b.y);
    }
    double operator ^(const Point& b) const {
        return x*b.y-y*b.x;
    }
    double operator *(const Point& b) const {
        return x*b.x+y*b.y;
    }
	Point operator *(const double& k) const {
		return Point(x*k,y*k);
	}
	Point operator /(const double& k) const {
		return Point(x/k,y/k);
	}
    Point rotleft() {
        return Point(-y,x);
    }
    Point rotright() {
        return Point(y,-x);
    }
	double rad(Point a,Point b) {
		Point p=*this;
		return fabs(atan2(fabs((a-p)^(b-p)),(a-p)*(b-p)));
	}

};
struct Line {
	Point s,e;
	Line() {}
	Line(Point _s,Point _e) {
		s=_s;
		e=_e;
	}
	bool operator ==(Line v) {
		return (s==v.s)&&(e==v.e);
	}
	double length() {
		return s.distance(e);
	}
	double dispointtoline(Point p) {
		return fabs((p-s)^(e-s)) / length();
	}
	Point lineprog(Point p) {
		return s+(((e-s)*((e-s)*(p-s)))/((e-s).len2()));
	}
};
struct circle {
    Point p;
    double r;
    circle() { }
    circle(Point _p,double _r) {
        p=_p;
        r=_r;
    }
    circle(double x,double y,double _r) {
        p=Point(x,y);
        r=_r;
    }
	int relation(Point b) {
		double dst=b.distance(p);
		if(sgn(dst-r)<0) return 2;
		else if(sgn(dst-r)==0) return 1;
		return 0;
	}
    int relationcircle(circle v) {
        double d=p.distance(v.p);
        if(sgn(d-r-v.r)>0) return 5;
        if(sgn(d-r-v.r)==0) return 4;
        double l=fabs(r-v.r);
        if(sgn(d-r-v.r)<0 && sgn(d-l)>0) return 3;
        if(sgn(d-l)==0) return 2;
        if(sgn(d-l)<0) return 1;
    }
    int pointcrosscircle(circle v,Point& p1,Point& p2) {
        int rel=relationcircle(v);
        if(rel==1 || rel==5) return 0;
        double d=p.distance(v.p);
        double l=(d*d+r*r-v.r*v.r)/(2*d);
        double h=sqrt(r*r-l*l);
        Point tmp=p+(v.p-p).trunc(l);
        p1=tmp+((v.p-p).rotleft().trunc(h));
        p2=tmp+((v.p-p).rotright().trunc(h));
        if(rel==2 || rel==4)
            return 1;
        return 2;
    }
	int relationline(Line v) {
		double dst=v.dispointtoline(p);
		if(sgn(dst-r)<0) return 2;
		else if(sgn(dst-r)==0) return 1;
		return 0;
	}
	int pointcrossline(Line v,Point &p1,Point &p2) {
		if(!(*this).relationline(v)) return 0;
		Point a=v.lineprog(p);
		double d=v.dispointtoline(p);
		d=sqrt(r*r-d*d);
		if(sgn(d)==0) {
			p1=a;
			p2=a;
			return 1;
		}
		p1=a+(v.e-v.s).trunc(d);
		p2=a-(v.e-v.s).trunc(d);
		return 2;
	}
	double areatriangle(Point a,Point b) {
		if(sgn((p-a)^(p-b))==0) return 0.0;
		Point q[5];
		int len=0;
		q[len++]=a;
		Line l(a,b);
		Point p1,p2;
		if(pointcrossline(l,q[1],q[2])==2) {
			if(sgn((a-q[1])*(b-q[1]))<0) q[len++]=q[1];
			if(sgn((a-q[2])*(b-q[2]))<0) q[len++]=q[2];
		}
		q[len++]=b;
		if(len==4 && sgn((q[0]-q[1])*(q[2]-q[1]))>0) swap(q[1],q[2]);
		double res=0;
		for(int i=0;i<len-1;i++) {
			if(relation(q[i])==0 || relation(q[i+1])==0) {
				double arg=p.rad(q[i],q[i+1]);
				res+=r*r*arg/2.0;
			}
			else {
				res+=fabs((q[i]-p)^(q[i+1]-p))/2.0;
			}
		}
		return res;
	}
};
struct polygon {
	int n;
	Point p[maxp];
	Line l[maxp];
	void add(Point q) {
		p[n++]=q;
	}
	double areacircle(circle c) {
		double ans=0;
		for(int i=0;i<n;i++) {
			int j=(i+1)%n;
			if(sgn((p[j]-c.p)^(p[i]-c.p))>=0)
				ans+=c.areatriangle(p[i],p[j]);
			else ans-=c.areatriangle(p[i],p[j]);
		}
		return fabs(ans);
	}
}poly;
int main() {
	int cas=0;
	int n;
	double x,y,r,k;
	double x1,y1,x2,y2;
	while(~scanf("%d%lf",&n,&k)) {
		poly.n=0;
		for(int i=1;i<=n;i++) {
			scanf("%lf%lf",&x,&y);
			poly.add(Point(x,y));
		}
		scanf("%lf%lf",&x1,&y1);
		scanf("%lf%lf",&x2,&y2);
		x=(x2-k*k*x1)/(1-k*k);
		y=(y2-k*k*y1)/(1-k*k);
		r=k*sqrt(sqr(x1-x2)+sqr(y1-y2))/(1-k*k);
		printf("Case %d: %.10f\n",++cas,poly.areacircle(circle(x,y,r)));
	}
}