计算几何小车头（施工中）

struct geometric{
    double x,y;
    geometric(double X=0,double Y=0):x(X),y(Y) {}
    friend geometric operator + (const geometric a,const geometric b){return geometric(a.x+b.x,a.y+b.y);} 
    friend geometric operator - (const geometric a,const geometric b){return geometric(a.x-b.x,a.y-b.y);} 
    friend geometric operator * (const geometric a,double p){return geometric(a.x*p,a.y*p);}
    friend geometric operator / (const geometric a,double p){return geometric(a.x/p,a.y/p);}// 向量的四则运算
    double dis(geometric a,geometric b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));} // 向量模长
    double dot(geometric a1,geometric a2,geometric b1,geometric b2){return (a2.x-a1.x)*(b2.x-b1.x)+(a2.y-a1.y)*(b2.y-b1.y);}// 点积
    double cross(geometric a1,geometric a2,geometric b1,geometric b2){return (a2.x-a1.x)*(b2.y-b1.y)-(a2.y-a1.y)*(b2.x-b1.x);} // 叉积
    double corner(geometric a1,geometric a2,geometric b1,geometric b2){return dot(a1,a1,b1,b2)/(dis(a1,a2)*dis(b1,b2));}// 向量夹角
    double area(geometric a1,geometric a2,geometric b1,geometric b2){return fabs(cross(a1,a2,b1,b2));}// 两向量围成的四边形面积
    double angle(geometric a){return atan2(a.y,a.x);}// 极角
	geometric rotate_clockwise(geometric a,double theta){return geometric(a.x*cos(theta)-a.y*sin(theta),a.x*sin(theta)+a.y*cos(theta));} // 向量顺时针旋转
    geometric rotate_counterclockwise(geometric a,double theta){return geometric(a.x*cos(theta)+a.y*sin(theta),-a.x*sin(theta)+a.y*cos(theta));} // 向量逆时针旋转
}opt;

struct line{
    geometric A,B;double An;
    line(geometric a,geometric b):A(a),B(b) {An=opt.angle(B);}
    line(){}
	bool operator < (const line &a)const{return An<a.An;}
    geometric sdot(line a,line b){
        geometric c=a.A-b.A;
        double k=opt.cross(origin,b.B,origin,c)/opt.cross(origin,a.B,origin,b.B);
        return a.A+a.B*k;
    }
};
// 二维计算几何

struct geometric{
    double x,y,z;
    geometric(double X=0,double Y=0,double Z=0):x(X),y(Y),z(Z) {}
    friend geometric operator + (const geometric a,const geometric b){return geometric(a.x+b.x,a.y+b.y,a.z+b.z);} 
    friend geometric operator - (const geometric a,const geometric b){return geometric(a.x-b.x,a.y-b.y,a.z-b.z);} 
    friend geometric operator * (const geometric a,double p){return geometric(a.x*p,a.y*p,a.z*p);}
    friend geometric operator / (const geometric a,double p){return geometric(a.x/p,a.y/p,a.z/p);}// 向量的四则运算
    double dis(geometric a,geometric b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)+(a.z-b.z)*(a.z-b.z));} // 向量模长
    double dot(geometric a1,geometric a2,geometric b1,geometric b2){return (a2.x-a1.x)*(b2.x-b1.x)+(a2.y-a1.y)*(b2.y-b1.y)+(a2.z-a1.z)*(b2.z-b1.z);}// 点积
    geometric cross(geometric a1,geometric a2,geometric b1,geometric b2){geometric a,b;return geometric(a.y*b.z-b.y*a.z,b.x*a.z-a.x*b.z,a.x*b.y-b.x*a.y);} // 叉积
}opt;

struct plane{
    geometric a,b,c;
    plane(geometric A=origin,geometric B=origin,geometric C=origin):a(A),b(B),c(C) {}
    double area(){return fabs(opt.dis(origin,opt.cross(a,b,a,c)))/2.0;}
};
// 平面

// 三维计算几何