计算几何模板：

#include<iostream>
#include<algorithm>
#include<queue>
#include<cstdio>
#include<map>
#include<vector>
#include<set>
#include<string>
#include<cmath>
#include<cstring>
#define ll long long
#define pb push_back
#define pm make_pair
#define fi first
#define se second
using namespace std;
const double eps = 1e-8;
int sgn(double x) {
	if(fabs(x) < eps)return 0;
	if(x < 0) return -1;
	return 1;
}
struct Point {
	double x,y;
	int id;
	Point() {}
	Point(double x,double y):x(x),y(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;}
} p[1005];
int pos,n;
struct Line {
	Point s,e;
	Line() {}
	Line(Point s,Point e):s(s),e(e) {}
	pair<Point,int> operator &(const Line &b)const {
		Point res = s;
		if(sgn((s-e)^(b.s-b.e)) == 0) {
			if(sgn((b.s-s)^(b.e-s)) == 0)
				return make_pair(res,0);//两直线重合
			else return make_pair(res,1);//两直线平行
		}
		double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
		res.x += (e.x - s.x)*t;
		res.y += (e.y - s.y)*t;
		return make_pair(res,2);//有交点，并返回交点
	}
};
inline double xmult(Point p0,Point p1,Point p2) { return (p1-p0)^(p2-p0);}//p0p1 X p0p2
bool Seg_inter_line(Line l1,Line l2) { return sgn(xmult(l2.s,l1.s,l1.e))*sgn(xmult(l2.e,l1.s,l1.e)) <= 0;}//判断直线l1和线段l2是否相交
double dist(Point a,Point b) {return sqrt((b - a)*(b - a));}
bool inter(Line l1,Line l2) {//判断线段相交
	return
	    max(l1.s.x,l1.e.x)>=min(l2.s.x,l2.e.x)&&max(l2.s.x,l2.e.x)>=min(l1.s.x,l1.e.x)&&
	    max(l1.s.y,l1.e.y)>=min(l2.s.y,l2.e.y)&&max(l2.s.y,l2.e.y)>=min(l1.s.y,l1.e.y)&&
	    sgn((l2.s-l1.s)^(l1.e-l1.s))*sgn((l2.e-l1.s)^(l1.e-l1.s))<=0&&
		sgn((l1.s-l2.s)^(l2.e-l2.s))*sgn((l1.e-l2.s)^(l2.e-l2.s))<=0;
}
//两线段相交判断
//2 规范相交
//1 非规范相交
//0 不相交
int segcrossseg(Line l1,Line l2) {
	int d1 = sgn((l1.e-l1.s)^(l2.s-l1.s));
	int d2 = sgn((l1.e-l1.s)^(l2.e-l1.s));
	int d3 = sgn((l2.e-l2.s)^(l1.s-l2.s));
	int d4 = sgn((l2.e-l2.s)^(l1.e-l2.s));
	if( (d1^d2)==-2 && (d3^d4)==-2 )return 2;
	return (d1==0 && sgn((l2.s-l1.s)*(l2.s-l1.e))<=0) ||(d2==0 && sgn((l2.e-l1.s)*(l2.e-l1.e))<=0) ||
	       (d3==0 && sgn((l1.s-l2.s)*(l1.s-l2.e))<=0) ||(d4==0 && sgn((l1.e-l2.s)*(l1.e-l2.e))<=0);
}
//直线和线段相交判断
//-*this line -v seg
//2 规范相交
//1 非规范相交
//0 不相交
int linecrossseg(Line l1,Line l2) {//l1直线，l2线段 
	int d1 = sgn((l1.e-l1.s)^(l2.s-l1.s));
	int d2 = sgn((l1.e-l1.s)^(l2.e-l1.s));
	if((d1^d2)==-2) return 2;
	return (d1==0||d2==0);
}

注意：

使用反三角函数时，要注意定义域的范围，比如，经过计算 x = 1.000001

double x = 1.000001;
double acx = acos(x);
//可能会返回runtime error

//此时我们可以加一句判断
double x = 1.000001;
if(fabs(x - 1.0) < eps || fabs(x + 1.0) < eps)
	x = round(x);
double acx = acos(x);