poj 1279 -- Art Gallery （半平面交）

鏈接：http://poj.org/problem?id=1279

Art Gallery

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 5337		Accepted: 2277

Description

The art galleries of the new and very futuristic building of the Center for Balkan Cooperation have the form of polygons (not necessarily convex). When a big exhibition is organized, watching over all of the pictures is a big security concern. Your task is that for a given gallery to write a program which finds the surface of the area of the floor, from which each point on the walls of the gallery is visible. On the figure 1. a map of a gallery is given in some co-ordinate system. The area wanted is shaded on the figure 2. 

Input

The number of tasks T that your program have to solve will be on the first row of the input file. Input data for each task start with an integer N, 5 <= N <= 1500. Each of the next N rows of the input will contain the co-ordinates of a vertex of the polygon ? two integers that fit in 16-bit integer type, separated by a single space. Following the row with the co-ordinates of the last vertex for the task comes the line with the number of vertices for the next test and so on.

Output

For each test you must write on one line the required surface - a number with exactly two digits after the decimal point (the number should be rounded to the second digit after the decimal point).

Sample Input

1
7
0 0
4 4
4 7
9 7
13 -1
8 -6
4 -4

Sample Output

80.00

Source

Southeastern Europe 2002

 

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这道题好坑的，题目根本没题给定的点有序，然后大家就一起照有序的来做了

自己写了个排序的，发现不行，如果默认有序，再去排序，就会得到错误的结

果，主要是极角排序，是根据角度，一点点逆时针移动，会使原多边形改变形

状，进而求出错误的结果。不知道有没有办法去解决这个问题

 

一下是错误排序代码：

 #include <stdio.h>
 #include <math.h>
 #include <string.h>
 #include <stdlib.h>
 #include <iostream>
 #include <algorithm>

 #define eps 1e-8
 #define MAXX 1510

 typedef struct point
 {
     double x;
     double y;
 }point;

 point p[MAXX],s[MAXX];

 using namespace std;
 bool dy(double x,double y)
 {
     return x>y+eps;
 }
 bool xy(double x,double y)
 {
     return x<y-eps;
 }
 bool dyd(double x,double y)
 {
     return x>y-eps;
 }
 bool xyd(double x,double y)
 {
     return x<y+eps;
 }
 bool dd(double x,double y)
 {
     return fabs(x-y)<eps;
 }

 double crossProduct(point a,point b,point c)
 {
     return (c.x-a.x)*(b.y-a.y)-(c.y-a.y)*(b.x-a.x);
 }

 point IntersectPoint(point u1,point u2,point v1,point v2)
 {
     point ans=u1;
     double t = ((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))/
         ((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
     ans.x += (u2.x-u1.x)*t;
     ans.y += (u2.y-u1.y)*t;
     return ans;
 }

 double Area(point p[],int n)
 {
     double ans=0.0;
     for(int i=; i<n-; i++)
     {
         ans += crossProduct(p[],p[i],p[i+]);
     }
     return fabs(ans)/2.0;
 }

 double dist(point a,point b)
 {
     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
 }

 bool cmp(point a,point b)
 {
     double tmp=crossProduct(p[],a,b);
     if(dd(tmp,0.0))
         return dy(dist(p[],a),dist(p[],b));
     return xy(tmp,0.0);
 }

 point Getsort(int n)
 {
     int tmp=;
     for(int i=; i<n; i++)
     {
         if(xy(p[i].x,p[tmp].x) || dd(p[i].x,p[tmp].x)&&xy(p[i].y,p[tmp].y))
         {
             tmp=i;
         }
     }//                           printf("%d^^",tmp);
     swap(p[],p[tmp]);
     sort(p+,p+n,cmp);
 }

 void cut(point p[],point s[],int n,int &len)
 {
     point tp[MAXX];
     p[n]=p[];
     for(int i=; i<=n; i++)
     {
         tp[i]=p[i];
     }
     int cp=n,tc;
     for(int i=; i<n; i++)
     {
         tc=;
         for(int k=; k<cp; k++)
         {
             if(xyd(crossProduct(p[i],p[i+],tp[k]),0.0))
                 s[tc++]=tp[k];
             if(xy(crossProduct(p[i],p[i+],tp[k])*
                   crossProduct(p[i],p[i+],tp[k+]),0.0))
                 s[tc++]=IntersectPoint(p[i],p[i+],tp[k],tp[k+]);
         }
         s[tc]=s[];
         for(int k=; k<=tc; k++)
             tp[k]=s[k];
         cp=tc;
     }
     len=cp;
 }

 int main()
 {
     int t,n,m,i,j;
     scanf("%d",&t);
     while(t--)
     {
         scanf("%d",&n);
         for(i=; i<n; i++)
         {
             scanf("%lf%lf",&p[i].x,&p[i].y);
         }
         //point tmp=IntersectPoint(p[0],p[1],p[2],p[3]);
         //printf("%lf %lf\n",tmp.x,tmp.y);
         Getsort(n);//for(i=0; i<n; i++)printf("%lf**%lf*\n",p[i].x,p[i].y);
         int len;
         cut(p,s,n,len);//for(i=0; i<len; i++)printf("%lf==%lf=\n",s[i].x,s[i].y);
         double area=Area(s,len);
         printf("%.2lf\n",area);
     }
     return ;
 }

利用面积正负来判断顺or逆，这种代码是以逆时针为主，我的面积顺时针为正，

需要改变方向

这是AC代码：

 #include <stdio.h>
 #include <math.h>
 #include <string.h>
 #include <stdlib.h>
 #include <iostream>
 #include <algorithm>

 #define eps 1e-8
 #define MAXX 1510

 typedef struct point
 {
     double x;
     double y;
 }point;

 point p[MAXX],s[MAXX];

 using namespace std;
 bool dy(double x,double y)
 {
     return x>y+eps;
 }
 bool xy(double x,double y)
 {
     return x<y-eps;
 }
 bool dyd(double x,double y)
 {
     return x>y-eps;
 }
 bool xyd(double x,double y)
 {
     return x<y+eps;
 }
 bool dd(double x,double y)
 {
     return fabs(x-y)<eps;
 }

 double crossProduct(point a,point b,point c)
 {
     return (c.x-a.x)*(b.y-a.y)-(c.y-a.y)*(b.x-a.x);
 }

 point IntersectPoint(point u1,point u2,point v1,point v2)
 {
     point ans=u1;
     double t = ((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))/
         ((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
     ans.x += (u2.x-u1.x)*t;
     ans.y += (u2.y-u1.y)*t;
     return ans;
 }

 double Area(point p[],int n)
 {
     double ans=0.0;
     p[n]=p[];
     point tmp;
     tmp.x=,tmp.y=;
     for(int i=; i<n; i++)
     {
         ans += crossProduct(tmp,p[i],p[i+]);
     }
     return ans/2.0;
 }

 void changeWise(point p[],int n)
 {
     for(int i=; i<n/; i++)
         swap(p[i],p[n-i-]);
 }

 double dist(point a,point b)
 {
     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
 }
 /*
 bool cmp(point a,point b)
 {
     double tmp=crossProduct(p[0],a,b);
     if(dd(tmp,0.0))
         return dy(dist(p[0],a),dist(p[0],b));
     return xy(tmp,0.0);
 }

 point Getsort(int n)
 {
     int tmp=0;
     for(int i=1; i<n; i++)
     {
         if(xy(p[i].x,p[tmp].x) || dd(p[i].x,p[tmp].x)&&xy(p[i].y,p[tmp].y))
         {
             tmp=i;
         }
     }//                           printf("%d^^",tmp);
     swap(p[0],p[tmp]);
     sort(p+1,p+n,cmp);
 }
 */
 void cut(point p[],point s[],int n,int &len)
 {
     point tp[MAXX];
     p[n]=p[];
     for(int i=; i<=n; i++)
     {
         tp[i]=p[i];
     }
     int cp=n,tc;
     for(int i=; i<n; i++)
     {
         tc=;
         for(int k=; k<cp; k++)
         {
             if(xyd(crossProduct(p[i],p[i+],tp[k]),0.0))
                 s[tc++]=tp[k];
             if(xy(crossProduct(p[i],p[i+],tp[k])*
                   crossProduct(p[i],p[i+],tp[k+]),0.0))
                 s[tc++]=IntersectPoint(p[i],p[i+],tp[k],tp[k+]);
         }
         s[tc]=s[];
         for(int k=; k<=tc; k++)
             tp[k]=s[k];
         cp=tc;
     }
     len=cp;
 }

 int main()
 {
     int t,n,m,i,j;
     scanf("%d",&t);
     while(t--)
     {
         scanf("%d",&n);
         for(i=; i<n; i++)
         {
             scanf("%lf%lf",&p[i].x,&p[i].y);
         }
         double tmp=Area(p,n);
         if(dy(tmp,0.0))
             changeWise(p,n);
         //point tmp=IntersectPoint(p[0],p[1],p[2],p[3]);
         //printf("%lf %lf\n",tmp.x,tmp.y);
         //Getsort(n);for(i=0; i<n; i++)printf("%lf**%lf*\n",p[i].x,p[i].y);
         int len;
         cut(p,s,n,len);//for(i=0; i<len; i++)printf("%lf==%lf=\n",s[i].x,s[i].y);
         double area=Area(s,len);
         printf("%.2lf\n",fabs(area));
     }
     return ;
 }