给定一系列半平面，求其交集的面积
下面代码p为给定点集，用于得到半平面l
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#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <cmath> using namespace std; const int maxn=1500+10; const double eps=1e-8; int n,pn,dq[maxn],top,bot; struct point{ double x,y; point(){} point(double x,double y):x(x),y(y){} void read() { scanf("%lf%lf",&x,&y); } void print() { printf("(%lf,%lf)\n",x,y); } point operator +(const point &o)const { return point(x+o.x,y+o.y); } point operator -(const point &o)const { return point(x-o.x,y-o.y); } point operator *(double k) const { return point(x*k,y*k); } double operator *(const point &o)const { return x*o.x+y*o.y; } double operator ^(const point &o)const { return x*o.y-y*o.x; } } p[maxn]; struct line{ point a,b; double angle; line(){} line(point oa,point ob) { a=oa; b=ob; angle=atan2(ob.y-oa.y,ob.x-oa.x); } line & operator =(line l) { a.x=l.a.x; a.y=l.a.y; b.x=l.b.x; b.y=l.b.y; angle=l.angle; return *this; } } l[maxn]; int dblcmp(double k) { if (fabs(k)<eps) return 0; return k>0?1:-1; } double multi(point p0,point p1,point p2) { return (p1-p0)^(p2-p0); } bool cmp(const line &l1,const line &l2) { int d=dblcmp(l1.angle-l2.angle); if (!d) { return dblcmp(multi(l1.a,l2.a,l2.b))<0; } return d<0; } void getIntersect(line l1,line l2,point &p) { double A1=l1.b.y-l1.a.y; double B1=l1.a.x-l1.b.x; double C1=(l1.b.x-l1.a.x)*l1.a.y-(l1.b.y-l1.a.y)*l1.a.x; double A2=l2.b.y-l2.a.y; double B2=l2.a.x-l2.b.x; double C2=(l2.b.x-l2.a.x)*l2.a.y-(l2.b.y-l2.a.y)*l2.a.x; p.x=(C2*B1-C1*B2)/(A1*B2-A2*B1); p.y=(C1*A2-C2*A1)/(A1*B2-A2*B1); } bool judge(line l0,line l1,line l2) { point p; getIntersect(l1,l2,p); return dblcmp(multi(p,l0.a,l0.b))>0; } void HalfPlaneIntersect() { int i,j; sort(l,l+n,cmp); for (i=0,j=0;i<n;i++) { if (dblcmp(l[i].angle-l[j].angle)>0) { l[++j]=l[i]; } } n=j+1; dq[0]=0; dq[1]=1; top=1; bot=0; for (int i=2;i<n;i++) { while(top>bot&&judge(l[i],l[dq[top]],l[dq[top-1]])) top--; while(top>bot&&judge(l[i],l[dq[bot]],l[dq[bot+1]])) bot++; dq[++top]=i; } while(top>bot&&judge(l[dq[bot]],l[dq[top]],l[dq[top-1]])) top--; while(top>bot&&judge(l[dq[top]],l[dq[bot]],l[dq[bot+1]])) bot++; dq[++top]=dq[bot]; for (pn=0,i=bot;i<top;i++,pn++) { getIntersect(l[dq[i+1]],l[dq[i]],p[pn]); } } double getArea() { if (pn<3) return 0; double area=0; for (int i=1;i<pn-1;i++) { //p[i].print(); area+=multi(p[0],p[i],p[i+1]); } if (area<0) area=-area; return area/2; } int main() { int t,i; scanf("%d",&t); while(t--) { scanf("%d",&n); for (i=0;i<n;i++) { p[i].read(); } for (i=0;i<n-1;i++) { l[i]=line(p[i],p[i+1]); } l[i]=line(p[i],p[0]); HalfPlaneIntersect(); printf("%.2lf\n",getArea()); } return 0; } |
