HDU 4404 Worms（三角剖分求圆和多边形的面积交）
题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4404
题意：给出一个圆被抛出时的初速度、与x正半轴的夹角、重力加速度，另外给出一个多边形，多边形是固定不变的。给出时间t。求在t时刻圆与多边形的相交面积。
思路：模板。
#include <iostream>
#include <cstdio>
#include <cmath>
#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define PI acos(-1.0)
#define EPS 1e-10
using namespace std;
inline int DB(double x)
{
if(x<-EPS) return -1;
if(x>EPS) return 1;
return 0;
}
struct point
{
double x,y;
point(){}
point(double _x,double _y):x(_x),y(_y){}
point operator-(point a)
{
return point(x-a.x,y-a.y);
}
point operator+(point a)
{
return point(x+a.x,y+a.y);
}
double operator*(point a)
{
return x*a.y-y*a.x;
}
point oppose()
{
return point(-x,-y);
}
double length()
{
return sqrt(x*x+y*y);
}
point adjust(double L)
{
L/=length();
return point(x*L,y*L);
}
point vertical()
{
return point(-y,x);
}
double operator^(point a)
{
return x*a.x+y*a.y;
}
};
struct segment
{
point a,b;
segment(){}
segment(point _a,point _b):a(_a),b(_b){}
point intersect(segment s)
{
double s1=(s.a-a)*(s.b-a);
double s2=(s.b-b)*(s.a-b);
double t=s1+s2;
s1/=t;s2/=t;
return point(a.x*s2+b.x*s1,a.y*s2+b.y*s1);
}
point vertical(point p)
{
point t=(b-a).vertical();
return intersect(segment(p,p+t));
}
int isonsegment(point p)
{
return DB(min(a.x,b.x)-p.x)<=0&&
DB(max(a.x,b.x)-p.x)>=0&&
DB(min(a.y,b.y)-p.y)<=0&&
DB(max(a.y,b.y)-p.y)>=0;
}
};
struct circle
{
point p;
double R;
};
circle C;
point p[105];
int n;
double cross_area(point a,point b,circle C)
{
point p=C.p;
double R=C.R;
int sgn=DB((b-p)*(a-p));
double La=(a-p).length(),Lb=(b-p).length();
int ra=DB(La-R),rb=DB(Lb-R);
double ang=acos(((b-p)^(a-p))/(La*Lb));
segment t(a,b);
point s;
point h,u,temp;
double ans,L,d,ang1;
if(!DB(La)||!DB(Lb)||!sgn) ans=0;
else if(ra<=0&&rb<=0) ans=fabs((b-p)*(a-p))/2;
else if(ra>=0&&rb>=0)
{
h=t.vertical(p);
L=(h-p).length();
if(!t.isonsegment(h)||DB(L-R)>=0) ans=R*R*(ang/2);
else
{
ans=R*R*(ang/2);
ang1=acos(L/R);
ans-=R*R*ang1;
ans+=R*sin(ang1)*L;
}
}
else
{
h=t.vertical(p);
L=(h-p).length();
s=b-a;
d=sqrt(R*R-L*L);
s=s.adjust(d);
if(t.isonsegment(h+s)) u=h+s;
else u=h+s.oppose();
if(ra==1) temp=a,a=b,b=temp;
ans=fabs((a-p)*(u-p))/2;
ang1=acos(((u-p)^(b-p))/((u-p).length()*(b-p).length()));
ans+=R*R*(ang1/2);
}
return ans*sgn;
}
double cal_cross(circle C,point p[],int n)
{
double ans=0;
int i;
p[n]=p[0];
for(i=0;i<n;i++) ans+=cross_area(p[i],p[i+1],C);
return fabs(ans);
}
double x,y,v,det,t,g,R;
int input()
{
scanf("%lf%lf%lf%lf%lf%lf%lf",&x,&y,&v,&det,&t,&g,&R);
return x||y||v||det||t||g||R;
}
int main()
{
while(input())
{
scanf("%d",&n);
int i;
for(i=0;i<n;i++) scanf("%lf%lf",&p[i].x,&p[i].y);
det=det/180*PI;
C.R=R;
C.p.x=x+v*cos(det)*t;
C.p.y=y+v*sin(det)*t-0.5*g*t*t;
double area=cal_cross(C,p,n);
printf("%.2lf\n",area);
}
return 0;
}