class Conv {
    XYZPlane *plane;
    XYZVector *f1, *f2;
    XYZVector *U, *V, *O;
public:
    Conv(XYZPlane *, XYZVector *, XYZVector *);
    Point *from3Dto2D(XYZPoint *) const;
    XYZPoint *from2Dto3D(Point *) const;
};


Conv::Conv(XYZPlane *pl, XYZVector *ff1, XYZVector *ff2) :
    plane(pl), f1(ff1), f2(ff2)
{
    U = XYZVector::sub(ff1,ff2);
    V = XYZVector::v_mul(U,pl->normal());
    O = XYZVector::middle(ff1,ff2);
}

Point *Conv::from3Dto2D(XYZPoint *p) const {
    XYZVector *OP = XYZVector::sub(new XYZVector(p), O);
    double tmpx = XYZVector::s_mul(OP,U) / sqrt(XYZVector::s_mul(U,U));
    double tmpy = XYZVector::s_mul(OP,V) / sqrt(XYZVector::s_mul(V,V));
    return new Point(tmpx,tmpy);
}

XYZPoint *Conv::from2Dto3D(Point *p) const {
    XYZVector *UP = U->one()->mul_c(p->x);
    XYZVector *VP = V->one()->mul_c(p->y);
    XYZVector *res = XYZVector::add(UP,VP);
    return res;
}