模板 点或向量

计算几何基础

const double eps=1e-6;
const double inf=1e20;
const double pi=acos(-1.0);

//符号函数
int sgn(double x){
	if(fabs(x)<eps) return 0;
	if(x>0) return 1;
	return -1;
}

//平方
double squ(double x){
      return x*x;
}

点或向量

struct Point{
	double x,y;
	Point(){}
	Point(double _x,double _y){
		x=_x;
		y=_y;
	}
        void input(){
		scanf("%lf%lf",&x,&y);
	}
	void output(){
		printf("%.2f %.2f\n",x,y);
	}
	bool operator == (Point b)const{
		return sgn(x-b.x)==0 && sgn(y-b.y)==0;
	}
	//按照横坐标为第一优先级，纵坐标为第二优先级排序
	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);
	}
	//叉积
	double operator ^ (const Point &b)const{
		return x*b.y-y*b.x;
	}
	//点积
	double operator * (const Point &b)const{
		return x*b.x+y*b.y;
	}
	//返回长度
	double len(){
		return hypot(x,y);//库函数
	}
	//返回长度的平方
	double len_squ(){
		return x*x+y*y;
	}
	//返回两点的距离
	double distance(Point p){
		return hypot(x-p.x,y-p.y);
	}
	Point operator + (const Point &b)const{
		return Point(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);
	}
	//计算pa和pb的夹角
	double rad(Point a,Point b){
		Point p=*this;
		return fabs(atan2(fabs((a-p)^(b-p)),(a-p)*(b-p)));
	}
	//化为长度为r的向量
	Point trunc(double r){
		double l=len();
		if(!sgn(l)) return *this;
		r/= l;
		return Point(x*r,y*r);
	}
	//逆时针旋转90度
	Point rotleft(){
		return Point(-y,x);
	}
	//顺时针旋转90度
	Point rotright(){
		return Point(y,-x);
	}
	//绕着p点逆时针旋转angle角度
	Point rotate(Point p,double angle){
		Point v=(*this)-p;
		double c=cos(angle),s=sin(angle);
		return Point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c);
	}
};

具有公共起点向量的点积和叉积

//AB X AC
double cross(Point A,Point B,Point C){
	return (B-A)^(C-A);
}
//AB*AC
double dot(Point A,Point B,Point C){
	return (B-A)*(C-A);
}