计算几何模板（点+线段）2.1

Orz发现之前的版子有小错误都不知道怎么在用2333

8.8更新多边形计算+求直线交点 顺便把之前版子统一了一下 希望这周解决计算几何 然后就不用再看模板了

忘记加重载 / 了。。 更了另一个求交点情况，不会有除0情况出现

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 100;
const double eps = 1e-6;

int sgn(double x) { return x<-eps?-1:x>eps?1:0;}
double sqr(double x) { return x*x;}
double mysqrt(double n) { return sqrt(max(0.0,n));}

struct point
{
    double x,y;
    point(double _x=0,double _y=0)
    {
        x = _x; y = _y;
    }
};
typedef point Vector;

//向量-向量
Vector operator -(const Vector &a, const Vector &b) {return Vector(a.x-b.x, a.y-b.y);}
//向量+向量
Vector operator +(const Vector &a, const Vector &b) {return Vector(a.x+b.x, a.y+b.y);}
//向量*常数
Vector operator *(const double &a, const Vector &b) {return Vector(a*b.x, a*b.y);}
Vector operator *(const Vector &a, const double &b) {return Vector(a.x*b, a.y*b);}
Vector operator /(const Vector &a, const double &b) {return Vector(a.x/b,a.y/b);}
//向量*向量 Dot
double dot(const Vector &a,const Vector &b) {return a.x*b.x+a.y*b.y;}
//向量X向量
double cross(const Vector &a,const Vector &b) {return a.x*b.y-a.y*b.x;}
//向量==向量
bool isequal(const Vector &a,const Vector &b) {return sgn(a.x-b.x)==0&&sgn(a.y-b.y)==0;}

double Length(Vector a) {return sqrt(dot(a,a));}
//AB夹角
double Angle(Vector a,Vector b) {return acos( dot(a,b)/Length(a)/Length(b) );}
//AB、AC组成的平行四边形面积
double Area(point a,point b,point c) {return cross((b-a),(c-a));}
//A逆时针旋转弧度rad后的向量
Vector Rotate(Vector a,double rad) {return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));}
//计算A的单位法线，保证A不为0向量
Vector Normal(Vector a)
{
    double L = Length(a);
    return Vector(-a.y/L,a.x/L);
}

struct line
{
    point s,e;
    line(){}
    line(point _s,point _e)
    {
        s = _s; e = _e;
    }
};

//线段是否相交、端点算相交
bool inter(line l1,line l2)
{
    return
    min(l1.s.x,l1.e.x)<=max(l2.s.x,l2.e.x) &&
    min(l2.s.x,l2.e.x)<=max(l1.s.x,l1.e.x) &&
    min(l1.s.y,l1.e.y)<=max(l2.s.y,l2.e.y) &&
    min(l2.s.y,l2.e.y)<=max(l1.s.y,l1.e.y) &&
    sgn(cross((l2.s-l1.e),(l1.s-l1.e))) * sgn(cross((l2.e-l1.e),(l1.s-l1.e)))<=0 &&
    sgn(cross((l1.s-l2.e),(l2.s-l2.e))) * sgn(cross((l1.e-l2.e),(l2.s-l2.e)))<=0;
}

//线段是否相交、端点不算相交
bool inter2(line l1,line l2)
{
    point a1=l1.s,a2=l1.e;
    point b1=l2.s,b2=l2.e;
    double c1 = cross((a2-a1),(b1-a1)), c2 = cross((a2-a1),(b2-a1));
    double c3 = cross((b2-b1),(a1-b1)), c4 = cross((b2-b1),(a2-b1));
    return sgn(c1)*sgn(c2)<0 && sgn(c3)*sgn(c4)<0;
}
//求n边形的面积、res[0~n-1]顺序存顶点、n为顶点数,res[n]=res[0]
double area(point res[],int n)
{
    double ret = 0;
    res[n] = res[0];
    for(int i=0;i<n;i++)
    {
        ret += cross(res[i],res[i+1]);
    }
    return fabs(ret/2);
}

//求两线交点，要先判断有无交点
point GetLineInterPoint(line l1,line l2)
{
    Vector v = l1.e-l1.s;
    Vector w = l2.e-l2.s;
    Vector u = l1.s-l2.s;
    double t = cross(w,u)/cross(v,w);
    return l1.s+v*t;
}
//求ab与pq交点，功能同上个函数一样
point crosspt(const point &a, const point &b, const point &p, const point &q)
{
    double a1 = cross(b-a,p-a);
    double a2 = cross(b-a,q-a);
    return (p*a2-q*a1)/(a2-a1);
}