模板 圆形

圆形

struct circle{
	//圆心
	Point p;
	//半径
	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;
	}
	//三角形的外接圆
	//需要Point的+ /  rotate()，以及Line的crosspoint()
	//利用两条边的中垂线得到圆心
	circle(Point a,Point b,Point c){
		Line u=Line((a+b)/2,((a+b)/2)+((b-a).rotleft()));
		Line v=Line((b+c)/2,((b+c)/2)+((c-b).rotleft()));
		p=u.crosspoint(v);
		r=p.distance(a);
	}
	//三角形的内切圆
	//参数bool t没有作用，只是为了和上面外接圆函数区别
	circle(Point a,Point b,Point c,bool t){
		Line u,v;
		double m=atan2(b.y-a.y,b.x-a.x),n=atan2(c.y-a.y,c.x-a.x);
		u.s=a;
		u.e=u.s+Point(cos((n+m)/2),sin((n+m)/2));
		v.s=b;
		m=atan2(a.y-b.y,a.x-b.x),n=atan2(c.y-b.y,c.x-b.x);
		v.e=v.s+Point(cos((n+m)/2),sin((n+m)/2));
		p=u.crosspoint(v);
		r=Line(a,b).dispointtoseg(p);
	}
	//输入
	void input(){
		p.input();
		scanf("%lf",&r);
	}
	//输出
	void output(){
		printf("%.2lf %.2lf %.2lf\n",p.x,p.y,r);
	}
	bool operator == (circle v){
		return (p==v.p) && sgn(r-v.r)==0;
	}
	bool operator < (circle v)const{
		return ((p<v.p) || ((p==v.p) && sgn(r-v.r)<0));
	}
	//面积
	double area(){
		return pi*r*r;
	}
	//周长
	double circumference(){
		return 2*pi*r;
	}
	//点和圆的关系
	//0 圆外
	//1 圆上
	//2 圆内
	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;
	}
	//线段和圆的关系
	//比较的是圆心到线段的距离和半径的关系
	int relationseg(Line v){
		double dst=v.dispointtoseg(p);
		if(sgn(dst-r)<0) return 2;
		else if(sgn(dst-r)==0) return 1;
		return 0;
	}
	//直线和圆的关系
	//比较的是圆心到直线的距离和半径的关系
	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;
	}
	//两圆的关系
	//5 相离
	//4 外切
	//3 相交
	//2 内切
	//1 内含
	//需要Point的distance()
	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;
	}
	//求两个圆的交点，返回0表示没有交点，返回1是一个交点，2是两个交点
	//需要relationcircle()
	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;
	}
	//求直线和圆的交点，返回交点个数
	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;
	}
	//得到过a,b两点，半径为r1的两个圆
	int gercircle(Point a,Point b,double r1,circle &c1,circle &c2){
		circle x(a,r1),y(b,r1);
		int t=x.pointcrosscircle(y,c1.p,c2.p);
		if(!t) return 0;
		c1.r=c2.r=r;
		return t;
	}
	//得到与直线u相切，过点q，半径为r1的圆
	int getcircle(Line u,Point q,double r1,circle &c1,circle &c2){
		double dis=u.dispointtoline(q);
		if(sgn(dis-r1*2)>0) return 0;
		if(sgn(dis)==0){
			c1.p=q+((u.e-u.s).rotleft().trunc(r1));
			c2.p=q+((u.e-u.s).rotright().trunc(r1));
			c1.r=c2.r=r1;
			return 2;
		}
		Line u1=Line((u.s+(u.e-u.s).rotleft().trunc(r1)),(u.e+(u.e-u.s).rotleft().trunc(r1)));
		Line u2=Line((u.s+(u.e-u.s).rotright().trunc(r1)),(u.e+(u.e-u.s).rotright().trunc(r1)));
		circle cc=circle(q,r1);
		Point p1,p2;
		if(!cc.pointcrossline(u1,p1,p2))cc.pointcrossline(u2,p1,p2);
		c1=circle(p1,r1);
		if(p1==p2){
			c2=c1;
			return 1;
		}
		c2=circle(p2,r1);
		return 2;
	}
	//同时与直线u,v相切，半径为r1的圆
	int getcircle(Line u,Line v,double r1,circle &c1,circle &c2,circle &c3,circle &c4){
		//两直线平行
		if(u.parallel(v)) return 0;
		Line u1=Line(u.s+(u.e-u.s).rotleft().trunc(r1),u.e+(u.e-u.s).rotleft().trunc(r1));
		Line u2=Line(u.s+(u.e-u.s).rotright().trunc(r1),u.e+(u.e-u.s).rotright().trunc(r1));
		Line v1=Line(v.s+(v.e-v.s).rotleft().trunc(r1),v.e+(v.e-v.s).rotleft().trunc(r1));
		Line v2=Line(v.s+(v.e-v.s).rotright().trunc(r1),v.e+(v.e-v.s).rotright().trunc(r1));
		c1.r=c2.r=c3.r=c4.r=r1;
		c1.p=u1.crosspoint(v1);
		c2.p=u1.crosspoint(v2);
		c3.p=u2.crosspoint(v1);
		c4.p=u2.crosspoint(v2);
		return 4;
	}
	//同时与不相交的圆cx,cy相切，半径为r1的圆
	int getcircle(circle cx,circle cy,double r1,circle &c1,circle &c2){
		circle x(cx.p,r1+cx.r),y(cy.p,r1+cy.r);
		int t=x.pointcrosscircle(y,c1.p,c2.p);
		if(!t) return 0;
		c1.r=c2.r=r1;
		return t;
	}
	//过一点作圆的切线(先判断点和圆的关系)
	int tangentline(Point q,Line &u,Line &v){
		int x=relation(q);
		if(x==2) return 0;
		if(x==1){
			u=Line(q,q + (q-p).rotleft());
			v=u;
			return 1;
		}
		double d=p.distance(q);
		double l=r*r/d;
		double h=sqrt(r*r-l*l);
		u=Line(q,p+((q-p).trunc(l)+(q-p).rotleft().trunc(h)));
		v=Line(q,p+((q-p).trunc(l)+(q-p).rotright().trunc(h)));
		return 2;
	}
	//求两圆相交的面积
	double areacircle(circle v){
		int rel=relationcircle(v);
		if(rel>=4) return 0.0;
		if(rel<=2) return min(area(),v.area());
		double d=p.distance(v.p);
		double hf=(r+v.r+d)/2.0;
		double ss=2*sqrt(hf*(hf-r)*(hf-v.r)*(hf-d));
		double a1=acos((r*r+d*d-v.r*v.r)/(2.0*r*d));
		a1=a1*r*r;
		double a2=acos((v.r*v.r+d*d-r*r)/(2.0*v.r*d));
		a2=a2*v.r*v.r;
		return a1+a2-ss;
	}
	//求圆和三角形pab的相交面积
	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;
	}
};