const double eps = 1e-8;struct Point{    double x,y;    Point(double tx = 0,double ty = 0) : x(tx),y(ty){}};typedef Point Vtor;//向量的加减乘除Vtor operator + (Vtor A,Vtor B) { return Vtor(A.x + B.x,A.y + B.y); }Vtor operator - (Point A,Point B) { return Vtor(A.x - B.x,A.y - B.y); }Vtor operator * (Vtor A,double p) { return Vtor(A.x*p,A.y*p); }Vtor operator / (Vtor A,double p) { return Vtor(A.x/p,A.y/p); }bool operator < (Point A,Point B) { return A.x < B.x || (A.x == B.x && A.y < B.y);}int dcmp(double x){ if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }bool operator == (Point A,Point B) {return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0; }//向量的点积，长度，夹角double Dot(Vtor A,Vtor B) { return A.x*B.x + A.y*B.y; }double Length(Vtor A) { return sqrt(Dot(A,A)); }double Angle(Vtor A,Vtor B) { return acos(Dot(A,B)/Length(A)/Length(B)); }//叉积，三角形面积double Cross(Vtor A,Vtor B) { return A.x*B.y - A.y*B.x; }double Area2(Point A,Point B,Point C) { return Cross(B - A,C - A); }//向量的旋转,求向量的单位法线（即左转90度，然后长度归一）Vtor Rotate(Vtor A,double rad){ return Vtor(A.x*cos(rad) - A.y*sin(rad),A.x*sin(rad) + A.y*cos(rad)); }Vtor Normal(Vtor A){    double L = Length(A);    return Vtor(-A.y/L, A.x/L);}//直线的交点Point GetLineIntersection(Point P,Vtor v,Point Q,Vtor w){    Vtor u = P - Q;    double t = Cross(w,u)/Cross(v,w);    return P + v*t;}//点到直线的距离double DistanceToLine(Point P,Point A,Point B){    Vtor v1 = B - A;    return fabs(Cross(P - A,v1))/Length(v1);}//点到线段的距离double DistanceToSegment(Point P,Point A,Point B){    if (A == B) return Length(P - A);    Vtor v1 =  B - A , v2 = P - A, v3 = P - B;    if (dcmp(Dot(v1,v2)) < 0) return Length(v2);    else if (dcmp(Dot(v1,v3)) > 0) return Length(v3);    else return fabs(Cross(v1,v2))/Length(v1);}//点到直线的映射Point GetLineProjection(Point P,Point A,Point B){    Vtor v = B - A;    return A + v*Dot(v,P - A)/Dot(v,v);}//判断线段是否规范相交bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){    double c1 = Cross(a2 - a1,b1 - a1), c2 = Cross(a2 - a1,b2 - a1),           c3 = Cross(b2 - b1,a1 - b1), c4 = Cross(b2 - b1,a2 - b1);    return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0;}//判断点是否在一条线段上bool OnSegment(Point P,Point a1,Point a2){    return dcmp(Cross(a1 - P,a2 - P)) == 0 && dcmp(Dot(a1 - P,a2 - P)) < 0;}//多边形面积double PolgonArea(Point *p,int n){    double area = 0;    for (int i = 1; i < n - 1; ++i)    area += Cross(p[i] - p[0],p[i + 1] - p[0]);    return area/2;}

　　

 

和圆有关的计算

struct Line{    Point p;    Vtor v;    Line(Point p,Vtor v) : p(p),v(v){}    Point point(double t) { return p + v*t; }};struct Circle{    Point c;    double r;    Circle(Point tc,double tr) : c(tc),r(tr){}    Point point(double a)    {        return Point(c.x + cos(a)*r + c.y + sin(a)*r);    }};//判断圆与直线是否相交以及求出交点int getLineCircleIntersection(Line L,Circle C,double t1,double t2,vector
     
       &sol){    //注意sol没有清空哦    double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;    double e = a*a + c*c , f = 2*(a*b + c*d),  g = b*b + d*d;    double delta = f*f - 4*e*g;    if (dcmp(delta) < 0) return 0;    else if (dcmp(delta) == 0)    {        t1 = t2 = -f/(2*e);        sol.push_back(L.point(t1));        return 1;    }    t1 = (-f - sqrt(delta))/(2*e); sol.push_back(L.point(t1));    t2 = (-f + sqrt(delta))/(2*e); sol.push_back(L.point(t2));    return 2;}//判断并求出两圆的交点double angle(Vtor v) { return atan2(v.y, v.x); }int getCircleIntersection(Circle C1,Circle C2,vector
      
        &sol){    double d = Length(C2.c - C1.c);    // 圆心重合    if (dcmp(d) == 0)    {        if (dcmp(C1.r - C2.r) == 0) return -1; // 两圆重合        return 0; // 包含    }    // 圆心不重合    if (dcmp(C1.r + C2.r - d) < 0) return 0; // 相离    if (dcmp(fabs(C1.r - C2.r) - d) > 0) return 0; // 包含    double a = angle(C2.c - C1.c);    double da = acos(C1.r*C1.r + d*d - C2.r*C2.r) / (2*C1.r*d);    Point p1 = C1.point(a - da), p2 = C1.point(a + da);    sol.push_back(p1);    if (p1 == p2) return 1;    sol.push_back(p2);    return 2;}//求点到圆的切线int getTangents(Point p,Circle C,Vtor *v){    Vtor u = C.c - p;    double dis = Length(u);    if (dis < C.r)  return 0;    else if (dcmp(dis - C.r) == 0)    {        v[0] = Rotate(u,PI/2);        return 1;    }    else    {        double ang = asin(C.r / dis);        v[0] = Rotate(u, -ang);        v[1] = Rotate(u, ang);        return 2;    }}//求两圆的切线int getCircleTangents(Circle A,Circle B,Point *a,Point *b){    int cnt = 0;    if (A.r < B.r) { swap(A,B); swap(a, b) ; }    //圆心距的平方    double d2 = (A.c.x - B.c.x)*(A.c.x - B.c.x) + (A.c.y - B.c.y)*(A.c.y - B.c.y);    double rdiff = A.r - B.r;    double rsum = A.r + B.r;    double base = angle(B.c - A.c);    //重合有无限多条    if (d2 == 0 && dcmp(A.r - B.r) == 0) return -1;    //内切    if (dcmp(d2 - rdiff*rdiff) == 0)    {        a[cnt] = A.point(base);        b[cnt] = B.point(base); cnt++;        return 1;    }    //有外公切线    double ang = acos((A.r - B.r) / sqrt(d2));    a[cnt] = A.point(base + ang); b[cnt] = B.point(base + ang); cnt++;    a[cnt] = A.point(base - ang); b[cnt] = B.point(base - ang); cnt++;    //一条内切线    if (dcmp(d2 - rsum*rsum) == 0)    {        a[cnt] = A.point(base); b[cnt] = B.point(PI + base); cnt++;    }//两条内切线    else if (dcmp(d2 - rsum*rsum) > 0)    {        double ang = acos((A.r + B.r) / sqrt(d2));        a[cnt] = A.point(base + ang); b[cnt] = B.point(base + ang); cnt++;        a[cnt] = A.point(base - ang); b[cnt] = B.point(base - ang); cnt++;    }    return cnt;}