題目地址：pdf版本

比如說求A,我們知道了向量PR ，只需要求出PA/PR的值，就知道向量PA，這樣加上P就可以求出A。

關於比例的計算，用到梅涅勞斯定理  純平面幾何內容。

然後簡化計算時，用到了輪換對稱性，減少程式碼量。

程式碼：

#include<iostream>
#include<cmath>
#include<cstdio>
#include<algorithm>
const double eps=1e-10;
const double PI=acos(-1);

using namespace std;


struct Point{
    double x;
    double y;
    Point(double x=0,double y=0):x(x),y(y){}
    void operator<<(Point &A) {cout<<A.x<<' '<<A.y<<endl;}
};

int dcmp(double x)  {return (x>eps)-(x<-eps); }

typedef  Point  Vector;

Vector  operator +(Vector A,Vector B) { return Vector(A.x+B.x,A.y+B.y);}

Vector  operator -(Vector A,Vector B) { return Vector(A.x-B.x,A.y-B.y); }

Vector  operator *(Vector A,double p) { return Vector(A.x*p,A.y*p);  }

Vector  operator /(Vector A,double p) {return Vector(A.x/p,A.y/p);}

// ps  cout

ostream &operator<<(ostream & out,Point & P) { out<<P.x<<' '<<P.y<<endl; return out;}

bool  operator< (const Point &A,const Point &B) { return A.x<B.x||(A.x==B.x&&A.y<B.y); }

bool  operator== ( const Point &A,const Point &B) { return dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)==0;}


double  Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}

double  Cross(Vector A,Vector B)  {return A.x*B.y-B.x*A.y; }

double  Length(Vector A)  { return sqrt(Dot(A, A));}


double  Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));}

double  Area2(Point A,Point B,Point C ) {return Cross(B-A, C-A);}

Vector Rotate(Vector A,double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}
Vector Normal(Vector A) {double L=Length(A);return Vector(-A.y/L,A.x/L);}

Point GetLineIntersection(Point P,Vector v,Point Q,Vector w)
{
    Vector u=P-Q;
    double t=Cross(w, u)/Cross(v,w);
    return P+v*t;
    
}

double DistanceToLine(Point P,Point A,Point B)
{
    Vector v1=P-A; Vector v2=B-A;
    return fabs(Cross(v1,v2))/Length(v2);
    
}

double DistanceToSegment(Point P,Point A,Point B)
{
    if(A==B)  return Length(P-A);
    
    Vector v1=B-A;
    Vector v2=P-A;
    Vector v3=P-B;
    
    if(dcmp(Dot(v1,v2))==-1)    return  Length(v2);
    else if(Dot(v1,v3)>0)    return Length(v3);
    
    else return DistanceToLine(P, A, B);
    
}

Point GetLineProjection(Point P,Point A,Point B)
{
    Vector v=B-A;
    Vector v1=P-A;
    double t=Dot(v,v1)/Dot(v,v);
    
    return  A+v*t;
}

bool  SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2)
{
    double c1=Cross(b1-a1, a2-a1);
    double c2=Cross(b2-a1, a2-a1);
    double c3=Cross(a1-b1, b2-b1);
    double c4=Cross(a2-b1, b2-b1);
    
    //cout<<c1<<c2<<c3<<c4<<endl;
    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0 ;
    
}

bool  OnSegment(Point P,Point A,Point B)
{
    return dcmp(Cross(P-A, P-B))==0&&dcmp(Dot(P-A,P-B))<0;
}

double PolygonArea(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;
    
}

Point  read_point()
{
    Point P;
    scanf("%lf%lf",&P.x,&P.y);
    return  P;
}

Point getA(Point P,Point Q,Point R,double a,double b,double c)
{
    double r1=a*b/(a*b+1+a);
    double r2=(c*(a+1))/(1+c*(a+1));
    
    double r=(1-r1)/(1-r1-r2);
    Vector PA=(R-P)*r;
    return PA+P;
}


int main()
{
    int T;
    cin>>T;
    Point A,B,C,P,Q,R;
    double m[6];
    double a,b,c;
    while(T--)
    {
        P=read_point();
        Q=read_point();
        R=read_point();
        for(int i=0;i<6;i++)
        {
            cin>>m[i];
        }
        
        a=m[0]/m[1];
        b=m[2]/m[3];
        c=m[4]/m[5];
    
        A=getA(P, Q, R, a, b, c);
        B=getA(Q,R,P,b,c,a);
        C=getA(R,P,Q,c,a,b);
        
        printf("%.8lf %.8lf %.8lf %.8lf %.8lf %.8lf\n",A.x,A.y,B.x,B.y,C.x,C.y);
        
    }
   
}