计算几何--凸包总结

/****************************凸包模板*******************************/
const double eps = 1e-8;
int sgn(double x)
{
    if(fabs(x) < eps)return 0;
    if(x < 0)return -1;
    else return 1;
}
struct Point
{
    double x,y;
    Point(){}
    Point(double _x,double _y)
    {
        x = _x;y = _y;
    }
    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;
    }
    void input(){
        scanf("%lf%lf",&x,&y);
    }
};
struct Line { 
    Point s,e; 
    Line(){} 
    Line(Point _s,Point _e) {         
        s = _s; e = _e; 
    }
}; 
//*两点间距离
double dist(Point a,Point b)
{
    return sqrt((a-b)*(a-b));
}   
/*
* 求凸包，Graham算法
* 点的编号0~n-1
* 返回凸包结果Stack[0~top-1]为凸包的编号
*/
const int MAXN = 1010;
Point List[MAXN];
int Stack[MAXN];//用来存放凸包的点
int top;//表示凸包中点的个数
//相对于List[0]的极角排序
bool _cmp(Point p1,Point p2)
{
    double tmp = (p1-List[0])^(p2-List[0]);
    if(sgn(tmp) > 0)
        return true;
    else if(sgn(tmp) == 0 && sgn(dist(p1,List[0]) - dist(p2,List[0])) <= 0)
        return true;
    else 
        return false;
}
void Graham(int n)
{
    Point p0;
    int k = 0;
    p0 = List[0];
    //找最下边的一个点
    for(int i = 1;i < n;i++)
    {
        if( (p0.y > List[i].y) || (p0.y == List[i].y && p0.x > List[i].x) )
        {
            p0 = List[i];
            k = i;
        }
    }
    swap(List[k],List[0]);
    sort(List+1,List+n,_cmp);
    if(n == 1)
    {
        top = 1;
        Stack[0] = 0;
        return;
    }
    if(n == 2)
    {
        top = 2;
        Stack[0] = 0;
        Stack[1] = 1;
        return ;
    }
    Stack[0] = 0;
    Stack[1] = 1;
    top = 2;
    for(int i = 2;i < n;i++)
    {
        while(top > 1 && sgn((List[Stack[top-1]]-List[Stack[top-2]])^(List[i]-List[Stack[top-2]])) <= 0)
            top--;
        Stack[top++] = i;
    }
}
/****************************凸包模板*******************************/