计算几何

typedef double db;
const db eps=1e-6;

//点.向量
struct point
{
    db x,y,len2,angle;
    point() {}
    point(db _x,db _y){set(_x,_y);}
    void set(db _x,db _y)
    {
        x=_x,y=_y;
        len2=x*x+y*y;
        angle=atan2(y,x);
    }
    void print(){printf("(%.6f,%.6f)",(double)x,(double)y);}
    void println(){print();puts("");}
    //逆时针旋转
    point rotate(db alpha)
    {
        db _x=x*cos(alpha)-y*sin(alpha);
        db _y=x*sin(alpha)+y*cos(alpha);
        return point(_x,_y);
    }
    //向量夹角
    db get_angle(point &p)
    {
        return acos((*this)*p/length()/p.length());
    }
    db length(){return sqrt(len2);}
    point operator+(const point &p){return point(x+p.x,y+p.y);}
    point operator-(const point &p){return point(x-p.x,y-p.y);}
    point operator*(const db k){return point(k*x,k*y);}
    point operator/(const db k){return point(x/k,y/k);}
    db operator*(const point &p){return x*p.x+y*p.y;}
    db operator^(const point &p){return x*p.y-y*p.x;}
    bool operator==(const point &p){return fabs(x-p.x)eps;}
    //点在直线上
    bool on_line(point p){return fabs(vec^(p-st))max(st.x,ed.x))
            return false;
        if(p.y+epsmax(st.y,ed.y))
            return false;
        return on_line(p);
    }
    //直线平行
    bool parallel(line l){return fabs(vec^l.vec)n=n;
    }
    db area()
    {
        db res=0.0;
        for(int i=1;i<=n;++i)
            res+=v[i]^v[i+1];
        return fabs(res)/2;
    }
};

球体积交 && 球体积并

const ld pi=acos(-1);

ld pow2(ld x){return x*x;}

ld pow3(ld x){return x*x*x;}

ld dis(ld x1,ld y1,ld z1,ld x2,ld y2,ld z2)
{
    return pow2(x1-x2)+pow2(y1-y2)+pow2(z1-z2);
}

ld cos(ld a,ld b,ld c){return (b*b+c*c-a*a)/(2*b*c);}

ld cap(ld r,ld h){return pi*(r*3-h)*h*h/3;}

//2球体积交
ld sphere_intersect(ld x1,ld y1,ld z1,ld r1,ld x2,ld y2,ld z2,ld r2)
{
    ld d=dis(x1,y1,z1,x2,y2,z2);
    //相离
    if(d>=pow2(r1+r2))return 0;
    //包含
    if(d<=pow2(r1-r2))return pow3(min(r1,r2))*4*pi/3;
    //相交
    ld h1=r1-r1*cos(r2,r1,sqrt(d)),h2=r2-r2*cos(r1,r2,sqrt(d));
    return cap(r1,h1)+cap(r2,h2);
}

//2球体积并
ld sphere_union(ld x1,ld y1,ld z1,ld r1,ld x2,ld y2,ld z2,ld r2)
{
    ld d=dis(x1,y1,z1,x2,y2,z2);
    //相离
    if(d>=pow2(r1+r2))return (pow3(r1)+pow3(r2))*4*pi/3;
    //包含
    if(d<=pow2(r1-r2))return pow3(max(r1,r2))*4*pi/3;
    //相交
    ld h1=r1+r1*cos(r2,r1,sqrt(d)),h2=r2+r2*cos(r1,r2,sqrt(d));
    return cap(r1,h1)+cap(r2,h2);
}