常用算法整理之圆

#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);

}