计算几何-点与多边形的位置判断-zoj1081Points Within

Posted 2020-09-09 Jason-Cow

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？

 1 #include <algorithm>
 2 #include <iostream>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <cstdio>
 6 #include <vector>
 7 #include <cmath>
 8 #include <queue>
 9 #include <map>
10 #include <set>
11 using namespace std;
12 #define sqr(x) ((x)*(x))
13 #define RG register
14 #define op operator
15 #define IL inline
16 #define db double
17 #define bl bool
18 const db pi=acos(-1.0),eps=1e-10;
19 struct D{db x,y;D(db x=0.0,db y=0.0):x(x),y(y){}};
20 typedef D V;
21 V operator+(V A,V B){return V(A.x+B.x,A.y+B.y);}
22 V operator-(V A,V B){return V(A.x-B.x,A.y-B.y);}
23 V operator*(V A,db N){return V(A.x*N,A.y*N);}
24 V operator/(V A,db N){return V(A.x/N,A.y/N);}
25 V Rotate(V A,db a){return V(A.x*cos(a)-A.y*sin(a),A.x*sin(a)+A.y*cos(a));}
26 int dcmp(db x){if(fabs(x)<eps)return 0;else return x>0?1:-1;}
27 bl OnSegment(D A,D B,D P){return dcmp((P.x-A.x)*(P.x-B.x))<=0&&dcmp((P.y-A.y)*(P.y-B.y))<=0;}
28 db Len(D A){return sqrt(A.x*A.x+A.y*A.y);}
29 db Cross(V A,V B){return A.x*B.y-A.y*B.x;}
30 db Dot(V A,V B){return A.x*B.x+A.y*B.y;}
31 db VectorAngle(V a,V b){return acos(Dot(a,b)/(Len(a)*Len(b)));}
32 
33 bl InPolygon(D P,D*R,int n){
34   db ans=0.0;
35   R[0]=R[n];
36   for(int i=0;i<n;i++){
37     D A=R[i],B=R[i+1];
38     int cross=dcmp(Cross(A-P,B-P));
39     if(cross==0){if(OnSegment(A,B,P))return true;}
40     else{
41       db angle=VectorAngle(A-P,B-P);
42       ans+=(cross>0?angle:-angle);
43     }
44   }
45   return dcmp(ans)!=0;
46 }
47 const int maxn=(int)1e5+10;
48 D A[maxn];
49 
50 int main(){    
51   int n,m,cnt=0;
52   db a,b;
53   while(scanf("%d",&n)&&n){
54     if(cnt!=0)puts("");
55     printf("Problem %d:\\n",++cnt);
56     scanf("%d",&m);
57     for(int i=1;i<=n;i++)scanf("%lf%lf",&A[i].x,&A[i].y);
58     for(int i=1;i<=m;i++){
59       scanf("%lf%lf",&a,&b);
60       printf("%s\\n",InPolygon(D(a,b),A,n)?"Within":"Outside");
61     }
62   }
63   return 0;
64 }