极角排序与凸包

转于 http://www.cnblogs.com/devtang/archive/2012/02/01/2334977.html

介绍几种极角排序：

1.利用叉积的正负来作cmp.(即是按逆时针排序).此题就是用这种方法

1 bool cmp(const point &a, const point &b)//逆时针排序 
2 {
3     point origin;
4     origin.x = origin.y = 0;
5     return cross(origin,b,origin,a) < 0;
6 }

2.利用complex的内建函数。

 1 #include
 2 #define x real()
 3 #define y imag()
 4 #include
 5 using namespace std;
 6 
 7 bool cmp(const Point& p1, const Point& p2)
 8 {
 9     return arg(p1) < arg(p2);
10 }

3.利用arctan计算极角大小。（范围『-180，180』）

1 bool cmp(const Point& p1, const Point& p2)
2 {
3     return atan2(p1.y, p1.x) < atan2(p2.y, p2.x);
4 }

4.利用象限加上极角，叉积。

 1 bool cmp(const point &a, const point &b)//先按象限排序，再按极角排序，再按远近排序 
 2 {
 3     if (a.y == 0 && b.y == 0 && a.x*b.x <= 0)return a.x>b.x;
 4     if (a.y == 0 && a.x >= 0 && b.y != 0)return true;
 5     if (b.y == 0 && b.x >= 0 && a.y != 0)return false;
 6     if (b.y*a.y <= 0)return a.y>b.y;
 7     point one;
 8     one.y = one.x = 0;
 9     return cross(one,a,one,b) > 0 || (cross(one,a,one,b) == 0 && a.x < b.x);   
 
10 }

POJ 2007：

 #include
 #include
 #include
 #include
 #define max(a,b) (a)>(b)?(a):(b)
 #define min(a,b) (a)<(b)?(a):(b)
 #define EPS 1e-8
 using namespace std;
 struct point {
     double x,y;    
 };
 point convex[50];
 
 double cross(const point &p1, const point &p2, const point &q1, const point &q2)
 {
     return (q2.y - q1.y)*(p2.x - p1.x) - (q2.x - q1.x)*(p2.y - p1.y);    
 }
 
 bool cmp(const point &a, const point &b)
 {
     point origin;
     origin.x = origin.y = 0;
     return cross(origin,b,origin,a) < 0;
 }
 
 
 int main()
 {
     int cnt = 0;
     while (scanf("%lf%lf",&convex[cnt].x,&convex[cnt].y) != EOF) {
         ++cnt;
     }
     sort(convex+1,convex+cnt,cmp);
     for (int i(0); i

附凸包模板

#include 
#include 
#include 
#define _DEBUG 1
typedef struct
{
	double x;
	double y;
}POINT;

POINT result[102];							//保存凸包上的点
POINT a[102];								
int n,top;

double Distance(POINT p1,POINT p2)			//两点间的距离
{
	return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}
double Multiply(POINT p1,POINT p2,POINT p3) //叉积
{	
   return ((p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x)); 
}
int Compare(const void *p1,const void *p2)
{
	POINT *p3,*p4;
	double m;
    p3=(POINT *)p1; 
    p4=(POINT *)p2; 
	m=Multiply(a[0],*p3,*p4) ;
	if(m<0) return 1;
	else if(m==0&&(Distance(a[0],*p3)2)
			top--;
       result[top+1].x=a[i].x;
       result[top+1].y=a[i].y;
       top++;
   }
}

int main()
{
#if _DEBUG==1
	freopen("ConvexHull.in","r",stdin);
#endif

   int i,p;
   double px,py,len,temp;
   while(scanf("%d",&n)!=EOF)
   {
       for(i=0;i