SGU 227 The art to the broad masses!（圆弧求交点）
题目链接：http://acm.sgu.ru/problem.php?contest=0&problem=227
题意：给定一些圆弧。求圆弧的交点。
思路：求出圆心交点。判断交点在不在圆弧内用叉积。
int DB(double x)
{
if(x>1e-10) return 1;
if(x<-1e-10) return -1;
return 0;
}
class point
{
public:
double x,y;
point(){}
point(double _x,double _y)
{
x=_x;
y=_y;
}
void get()
{
RD(x,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 operator*(double t)
{
return point(x*t,y*t);
}
double operator^(point a)
{
return x*a.x+y*a.y;
}
double getLen()
{
return sqrt(x*x+y*y);
}
point operator/(double t)
{
return point(x/t,y/t);
}
double getAng(point a)
{
return atan2(*this*a,*this^a);
}
int operator==(const point &a) const
{
return DB(x-a.x)==0&&DB(y-a.y)==0;
}
int operator<(const point &a) const
{
if(DB(x-a.x)) return x<a.x;
return y<a.y;
}
point adjust(double p)
{
point t=*this;
double x=p/t.getLen();
return point(x*t.x,x*t.y);
}
point zhuanNi(double ang)
{
return point(x*cos(ang)-y*sin(ang),x*sin(ang)+y*cos(ang));
}
point zhuanShun(double ang)
{
return point(x*cos(ang)+y*sin(ang),-x*sin(ang)+y*cos(ang));
}
point vertical()
{
return point(y,-x);
}
void print()
{
if(DB(x)==0) x=0;
if(DB(y)==0) y=0;
printf("%.3lf %.3lf\n",x,y);
}
};
const int N=55;
point p[N][3],O[N];
vector<point> ans;
double R[N];
int n,d[N];
point getCross(point a,point b,point p,point q)
{
double s1=(a-p)*(b-p);
double s2=(b-q)*(a-q);
return (p*s2+q*s1)/(s1+s2);
}
int cmp(point a,point b)
{
if(DB(a.x-b.x)) return a.x<b.x;
return a.y<b.y;
}
point getCenter(point a,point b,point c)
{
point M1=(a+b)/2,dir1=(b-a).vertical();
point M2=(b+c)/2,dir2=(c-b).vertical();
return getCross(M1,M1+dir1,M2,M2+dir2);
}
int isInside(point a,int t)
{
return DB((p[t][0]-p[t][2])*(a-p[t][2]))*d[t];
}
void judge(int x,int y)
{
if(!isInside(p[x][0],y)&&!isInside(p[x][2],y)&&d[x]==d[y])
{
puts("Infinity");
exit(0);
}
if(isInside(p[x][0],y)>0||isInside(p[x][2],y)>0||isInside(p[y][0],x)>0||isInside(p[y][2],x)>0)
{
puts("Infinity");
exit(0);
}
if(!isInside(p[x][0],y)) ans.pb(p[x][0]);
if(!isInside(p[x][2],y)) ans.pb(p[x][2]);
}
void calCross(int x,int y,point &a,point &b)
{
double L=(O[x]-O[y]).getLen();
double ang=(sqr(R[y])+sqr(L)-sqr(R[x]))/(2*R[y]*L);
ang=acos(ang);
point A=O[x]-O[y],B;
B=A.zhuanNi(ang);
B=B.adjust(R[y]);
a=O[y]+B;
B=A.zhuanShun(ang);
B=B.adjust(R[y]);
b=O[y]+B;
}
void deal()
{
int i,j,k,t;
double L;
point a,b;
for(i=1;i<=n;i++) for(j=i+1;j<=n;j++)
{
if(O[i]==O[j]&&!DB(R[i]-R[j]))
{
judge(i,j);
continue;
}
L=(O[i]-O[j]).getLen();
if(DB(L-(R[i]+R[j]))>0||DB(L-fabs(R[i]-R[j]))<0) continue;
calCross(i,j,a,b);
if(isInside(a,i)>=0&&isInside(a,j)>=0) ans.pb(a);
if(isInside(b,i)>=0&&isInside(b,j)>=0) ans.pb(b);
}
}
int main()
{
RD(n);
int i;
FOR1(i,n)
{
p[i][0].get();
p[i][2].get();
p[i][1].get();
O[i]=getCenter(p[i][0],p[i][1],p[i][2]);
d[i]=DB((p[i][0]-p[i][2])*(p[i][1]-p[i][2]));
R[i]=(O[i]-p[i][0]).getLen();
}
deal();
sort(ans.begin(),ans.end(),cmp);
int S=unique(ans.begin(),ans.end())-ans.begin();
PR(S);
for(i=0;i<S;i++) ans[i].print();
return 0;
}