两点间距离、点到直线距离、点到线段距离、线段到线段距离

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//两点间距离
double getDistancePP(Point a,Point b)
{
//这个代码是部分代码,有些逻辑没有展现完全,大家往下看!
    Point c(b.x-a.x,b.y-a.y);//返回一个新的点
    return  c.abs();//取模
}

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//点到直线距离(利用外积平行四边形)
double getDistancePL(Point a,Point b,Point c)
{
    Vector ab(b.x-a.x,b.y-a.y);
    Vector ac(c.x-a.x,c.y-a.y);

    return cross(ab,ac)/ab.abs();//cross函数求两个向量的外积模,abs函数求向量模
}

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//点到线段距离
double getDistancePS(Point a,Point b,Point c)
{
    //定义4个向量
    Vector ab(b.x-a.x,b.y-a.y);
    Vector ba(a.x-b.x,a.y-b.y);
    Vector ac(c.x-a.x,c.y-a.y);
    Vector bc(c.x-b.x,c.y-b.y);
    //dot函数用于求内积
    if(dot(ab,ac)<0.0) return getDistancePP(a,c);//到左端点距离
    if(dot(ba,bc)<0.0) return getDistancePP(b,c);//到右端点距离

    return getDistancePL(a,b,c);//点到直线距离
}

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//线段到线段的距离
double getDistanceSS(Point a,Point b,Point c,Point d)
{
    //从4个点到2线段距离中取最小
    return min(min(getDistancePS(c,d,a),getDistancePS(c,d,b)),min(getDistancePS(a,b,c),getDistancePS(a,b,d)));
}

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#include <bits/stdc++.h>

using namespace std;

class Point
{

public:
    double x,y;

    Point(double x=0,double y=0):x(x),y(y) {}

    //向量加法
    Point operator+(Point p)
    {
        return Point(x+p.x,y+p.y);
    }
    //向量减法
    Point operator-(Point p)
    {
        return Point(x-p.x,y+p.y);
    }
    //向量伸缩
    Point operator*(double a)
    {
        return Point(x*a,y*a);
    }
    Point operator/(double a)
    {
        return Point(x/a,y/a);
    }
    //向量大小
    double abs()
    {
        return sqrt(norm());
    }
    //向量范数
    double norm()
    {
        return x*x+y*y;
    }

    bool operator<(const Point &p) const
    {
        return x!=p.x?x<p.x:y<p.y;
    }

    bool operator==(const Point &p)const
    {
        return x-p.x<1e-10&&y-p.y<1e-10;
    }

};

typedef Point Vector;

//向量内积
double dot(Vector a,Vector b)
{
    return a.x*b.x+a.y*b.y;
}

//向量外积
double cross(Vector a,Vector b)
{
    return abs(a.x*b.y-a.y*b.x);
}

//正交
bool isOrthogonal(Vector a,Vector b)
{
    return a.x*b.x+a.y*b.y==0;
}
//平行
bool isParallel(Vector a,Vector b)
{
    return a.x*b.y-a.y*b.x==0;
}

//投影
Point project(Point a,Point b,Point c)
{
    Vector ab(b.x-a.x,b.y-a.y);
    Vector ac(c.x-a.x,c.y-a.y);
    double  r=dot(ab,ac)/ab.norm();//比例
    Vector h(ab*r);
    return Point(a.x+h.x,a.y+h.y);
}

//映象

Point reflect(Point a,Point b,Point c)
{
    //c到ab的投影点
    Point r=project(a,b,c);
    Vector cr(r.x-c.x,r.y-c.y);
    //cr扩大二倍
    Vector cr_2=cr*2;//上面重载过*
    //向量加法
    return Point(c.x+cr_2.x,c.y+cr_2.y);
}

//两点间距离
double getDistancePP(Point a,Point b)
{
    Point c(b.x-a.x,b.y-a.y);
    return  c.abs();
}

//点到直线距离(利用外积平行四边形)
double getDistancePL(Point a,Point b,Point c)
{
    Vector ab(b.x-a.x,b.y-a.y);
    Vector ac(c.x-a.x,c.y-a.y);

    return cross(ab,ac)/ab.abs();
}

//点到线段距离
double getDistancePS(Point a,Point b,Point c)
{
    //定义4个向量
    Vector ab(b.x-a.x,b.y-a.y);
    Vector ba(a.x-b.x,a.y-b.y);
    Vector ac(c.x-a.x,c.y-a.y);
    Vector bc(c.x-b.x,c.y-b.y);

    if(dot(ab,ac)<0.0) return getDistancePP(a,c);
    if(dot(ba,bc)<0.0) return getDistancePP(b,c);

    return getDistancePL(a,b,c);
}


//线段到线段的距离
double getDistanceSS(Point a,Point b,Point c,Point d)
{
    //从4个点到2线段距离中取最小
    return min(min(getDistancePS(c,d,a),getDistancePS(c,d,b)),min(getDistancePS(a,b,c),getDistancePS(a,b,d)));
}
int main()
{
    int x0,y0,x1,y1,x2,y2,x3,y3;
    cin>>x0>>y0>>x1>>y1>>x2>>y2;
    Point a(x0,y0);
    Point b(x1,y1);
    cout<<"a,b两点间距离"<<getDistancePP(a,b)<<endl;
    Point c(x2,y2);
    cout<<"c点到直线ab距离"<<getDistancePL(a,b,c)<<endl;
    
    cout<<"c点到线段ab的距离"<<getDistancePS(a,b,c)<<endl;
    cin>>x3>>y3;
    
    Point d(x3,y3);
    cout<<"线段ab到线段cd的距离"<<getDistanceSS(a,b,c,d)<<endl;

    return 0;
}