Art Gallery POJ - 1279 （半平面交，内核面积）

Art Gallery

 POJ - 1279 

思路：半平面交求多边形内核

 1 #include<iostream>
 2 #include<fstream>
 3 #include<iomanip>
 4 #include<cstdio>
 5 #include<cstring>
 6 #include<algorithm>
 7 #include<cstdlib>
 8 #include<cmath>
 9 #include<set>
10 #include<map>
11 #include<queue>
12 #include<stack>
13 #include<string>
14 #include<vector>
15 #include<sstream>
16 #include<cassert>
17 #define LL long long
18 #define eps 1e-7
19 #define inf 1<<30
20 using namespace std;
21 struct Point{
22     double x,y;
23 }p[1505],tp[1505],q[1505];
24 //叉积
25 double xmul(Point p0,Point p1,Point p2){
26     return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);
27 }
28 //通过两点，确定直线方程
29 double Get_equation(Point p1,Point p2,double &a,double &b,double &c){
30     a=p2.y-p1.y;
31     b=p1.x-p2.x;
32     c=p2.x*p1.y-p1.x*p2.y;
33 }
34 //求交点
35 Point Intersection(Point p1,Point p2,double a,double b,double c){
36     double u=fabs(a*p1.x+b*p1.y+c);
37     double v=fabs(a*p2.x+b*p2.y+c);
38     Point t;
39     t.x=(p1.x*v+p2.x*u)/(u+v);t.y=(p1.y*v+p2.y*u)/(u+v);
40     return t;
41 }
42 //求面积，正为顺时针，和叉积写法有关
43 double Get_area(Point p[],int n){
44     double area=0;
45     for(int i=2;i<n;i++)
46         area+=xmul(p[1],p[i],p[i+1]);
47     return -area/2.0;
48 }
49 //改变顺序
50 double Change_dir(Point p[],int n){
51     for(int i=1;i<=n/2;i++)
52         swap(p[i],p[n+1-i]);
53 }
54 //加入一条边，切割
55 void Cut(double a,double b,double c,Point p[],int &cnt){
56     int tmp=0;
57     for(int i=1;i<=cnt;i++){
58         //当前点就在右侧
59         if(a*p[i].x+b*p[i].y+c>-eps) tp[++tmp]=p[i];
60         else{
61             //前一个点在右侧，产生交点
62             if(a*p[i-1].x+b*p[i-1].y+c>eps)
63                 tp[++tmp]=Intersection(p[i-1],p[i],a,b,c);
64             //同理
65             if(a*p[i+1].x+b*p[i+1].y+c>eps)
66                 tp[++tmp]=Intersection(p[i],p[i+1],a,b,c);
67         }
68     }
69     for(int i=1;i<=tmp;i++)
70         p[i]=tp[i];
71     p[0]=p[tmp];p[tmp+1]=p[1];
72     cnt=tmp;
73 }
74 void slove(Point p[],int n){
75     //默认顺时针，通过面积判断一下
76     if(Get_area(p,n)<eps) Change_dir(p,n);
77     p[0]=p[n];p[n+1]=p[1];
78     //
79     for(int i=0;i<=n+1;i++) q[i]=p[i];
80     int cnt=n;
81     for(int i=1;i<=n;i++){
82         double a,b,c;
83         Get_equation(q[i],q[i+1],a,b,c);
84         Cut(a,b,c,p,cnt);
85     }
86     printf("%.2f\n",fabs(Get_area(p,cnt)));
87 }
88 int main(){
89     int t,n;
90     scanf("%d",&t);
91     while(t--){
92         scanf("%d",&n);
93         for(int i=1;i<=n;i++)
94             scanf("%lf%lf",&p[i].x,&p[i].y);
95         slove(p,n);
96     }
97     return 0;
98 }

 

 
posted @ 2020-02-08 19:23  branna  阅读(124)  评论(0)  编辑  收藏  举报