UVa 11437 Triangle Fun

我是求出来所有点的坐标用叉积算的面积……

据说可以证明出来S△PQR = S△ABC/7

#include <cstdio>
#include <cmath>

struct Point
{
    double x, y;
    Point( double x = 0, double y = 0 ):x(x), y(y) { }
};

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

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

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

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

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

Point Rotate( Point A, double rad )
{
    return Point( A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad) );
}

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

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

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

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

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

Point read_Point()
{
    double x, y;
    scanf( "%lf%lf", &x, &y );
    return Point( x, y );
}

Point GetD( Point B, Point C )
{
    return ( C - B ) / 3.0 + B;
}

int main()
{
    Point A, B, C, D, E, F;
    Point P, Q, R;
    int T;
    scanf( "%d", &T );
    while ( T-- )
    {
        A = read_Point();
        B = read_Point();
        C = read_Point();
        D = GetD( B, C );
        E = GetD( C, A );
        F = GetD( A, B );
        Point AD = D - A;
        Point BE = E - B;
        Point CF = F - C;
        P = GetLineIntersection( B, BE, A, AD );
        Q = GetLineIntersection( C, CF, B, BE );
        R = GetLineIntersection( A, AD, C, CF );

        printf( "%.0f\n", Cross( Q - P, R - P ) / 2.0 );
    }
    return 0;
}