计算几何-点与多边形的位置判断-zoj1081Points Within

This article is made by Jason-Cow.
Welcome to reprint.
But please post the writer's address.

http://www.cnblogs.com/JasonCow/

叉积判方向

点积判角度

角度和=0°在外面

否则在里面

AC Code 这么短的计算几何，君难道不想收入囊中吗？

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdlib>
 #include <cstdio>
 #include <vector>
 #include <cmath>
 #include <queue>
 #include <map>
 #include <set>
 using namespace std;
 #define sqr(x) ((x)*(x))
 #define RG register
 #define op operator
 #define IL inline
 #define db double
 #define bl bool
 const db pi=acos(-1.0),eps=1e-;
 struct D{db x,y;D(db x=0.0,db y=0.0):x(x),y(y){}};
 typedef D V;
 V operator+(V A,V B){return V(A.x+B.x,A.y+B.y);}
 V operator-(V A,V B){return V(A.x-B.x,A.y-B.y);}
 V operator*(V A,db N){return V(A.x*N,A.y*N);}
 V operator/(V A,db N){return V(A.x/N,A.y/N);}
 V Rotate(V A,db a){return V(A.x*cos(a)-A.y*sin(a),A.x*sin(a)+A.y*cos(a));}
 int dcmp(db x){if(fabs(x)<eps)return ;else return x>?:-;}
 bl OnSegment(D A,D B,D P){return dcmp((P.x-A.x)*(P.x-B.x))<=&&dcmp((P.y-A.y)*(P.y-B.y))<=;}
 db Len(D A){return sqrt(A.x*A.x+A.y*A.y);}
 db Cross(V A,V B){return A.x*B.y-A.y*B.x;}
 db Dot(V A,V B){return A.x*B.x+A.y*B.y;}
 db VectorAngle(V a,V b){return acos(Dot(a,b)/(Len(a)*Len(b)));}

 bl InPolygon(D P,D*R,int n){
   db ans=0.0;
   R[]=R[n];
   for(int i=;i<n;i++){
     D A=R[i],B=R[i+];
     int cross=dcmp(Cross(A-P,B-P));
     if(cross==){if(OnSegment(A,B,P))return true;}
     else{
       db angle=VectorAngle(A-P,B-P);
       ans+=(cross>?angle:-angle);
     }
   }
   return dcmp(ans)!=;
 }
 const int maxn=(int)1e5+;
 D A[maxn];

 int main(){
   int n,m,cnt=;
   db a,b;
   while(scanf("%d",&n)&&n){
     if(cnt!=)puts("");
     printf("Problem %d:\n",++cnt);
     scanf("%d",&m);
     for(int i=;i<=n;i++)scanf("%lf%lf",&A[i].x,&A[i].y);
     for(int i=;i<=m;i++){
       scanf("%lf%lf",&a,&b);
       printf("%s\n",InPolygon(D(a,b),A,n)?"Within":"Outside");
     }
   }
   return ;
 }