ACM计算几何--关于圆的问题

#include <math.h>  
#define eps 1e-8  
struct point{double x,y;};  
  
  
double xmult(point p1,point p2,point p0){  
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);  
}  
  
  
double distance(point p1,point p2){  
    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));  
}  
  
  
double disptoline(point p,point l1,point l2){  
    return fabs(xmult(p,l1,l2))/distance(l1,l2);  
}  
  
  
point intersection(point u1,point u2,point v1,point v2){  
    point ret=u1;  
    double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))  
            /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));  
    ret.x+=(u2.x-u1.x)*t;  
    ret.y+=(u2.y-u1.y)*t;  
    return ret;  
}  
  
  
//判直线和圆相交,包括相切  
int intersect_line_circle(point c,double r,point l1,point l2){  
    return disptoline(c,l1,l2)<r+eps;  
}  
  
  
//判线段和圆相交,包括端点和相切  
int intersect_seg_circle(point c,double r,point l1,point l2){  
    double t1=distance(c,l1)-r,t2=distance(c,l2)-r;  
    point t=c;  
    if (t1<eps||t2<eps)  
        return t1>-eps||t2>-eps;  
    t.x+=l1.y-l2.y;  
    t.y+=l2.x-l1.x;  
    return xmult(l1,c,t)*xmult(l2,c,t)<eps&&disptoline(c,l1,l2)-r<eps;  
}  
  
  
//判圆和圆相交,包括相切  
int intersect_circle_circle(point c1,double r1,point c2,double r2){  
    return distance(c1,c2)<r1+r2+eps&&distance(c1,c2)>fabs(r1-r2)-eps;  
}  
  
  
//计算圆上到点p最近点,如p与圆心重合,返回p本身  
point dot_to_circle(point c,double r,point p){  
    point u,v;  
    if (distance(p,c)<eps)  
        return p;  
    u.x=c.x+r*fabs(c.x-p.x)/distance(c,p);  
    u.y=c.y+r*fabs(c.y-p.y)/distance(c,p)*((c.x-p.x)*(c.y-p.y)<0?-1:1);  
    v.x=c.x-r*fabs(c.x-p.x)/distance(c,p);  
    v.y=c.y-r*fabs(c.y-p.y)/distance(c,p)*((c.x-p.x)*(c.y-p.y)<0?-1:1);  
    return distance(u,p)<distance(v,p)?u:v;  
}  
  
  
//计算直线与圆的交点,保证直线与圆有交点  
//计算线段与圆的交点可用这个函数后判点是否在线段上  
void intersection_line_circle(point c,double r,point l1,point l2,point& p1,point& p2){  
    point p=c;  
    double t;  
    p.x+=l1.y-l2.y;  
    p.y+=l2.x-l1.x;  
    p=intersection(p,c,l1,l2);  
    t=sqrt(r*r-distance(p,c)*distance(p,c))/distance(l1,l2);  
    p1.x=p.x+(l2.x-l1.x)*t;  
    p1.y=p.y+(l2.y-l1.y)*t;  
    p2.x=p.x-(l2.x-l1.x)*t;  
    p2.y=p.y-(l2.y-l1.y)*t;  
}  
  
  
//计算圆与圆的交点,保证圆与圆有交点,圆心不重合  
void intersection_circle_circle(point c1,double r1,point c2,double r2,point& p1,point& p2){  
    point u,v;  
    double t;  
    t=(1+(r1*r1-r2*r2)/distance(c1,c2)/distance(c1,c2))/2;  
    u.x=c1.x+(c2.x-c1.x)*t;  
    u.y=c1.y+(c2.y-c1.y)*t;  
    v.x=u.x+c1.y-c2.y;  
    v.y=u.y-c1.x+c2.x;  
    intersection_line_circle(c1,r1,u,v,p1,p2);  
}  
  
  
//将向量p逆时针旋转angle角度  
Point Rotate(Point p,double angle) {  
    Point res;  
    res.x=p.x*cos(angle)-p.y*sin(angle);  
    res.y=p.x*sin(angle)+p.y*cos(angle);  
    return res;  
}  
//求圆外一点对圆(o,r)的两个切点result1和result2  
void TangentPoint_PC(Point poi,Point o,double r,Point &result1,Point &result2) {  
    double line=sqrt((poi.x-o.x)*(poi.x-o.x)+(poi.y-o.y)*(poi.y-o.y));  
    double angle=acos(r/line);  
    Point unitvector,lin;  
    lin.x=poi.x-o.x;  
    lin.y=poi.y-o.y;  
    unitvector.x=lin.x/sqrt(lin.x*lin.x+lin.y*lin.y)*r;  
    unitvector.y=lin.y/sqrt(lin.x*lin.x+lin.y*lin.y)*r;  
    result1=Rotate(unitvector,-angle);  
    result2=Rotate(unitvector,angle);  
    result1.x+=o.x;  
    result1.y+=o.y;  
    result2.x+=o.x;  
    result2.y+=o.y;  
    return;  
}