Kolizje dowolnego trójkąta z prostokątem (zaznaczanie trójkątów)

bool intersectionTwoLines( sf::Vector2f p1, sf::Vector2f p2, sf::Vector2f q1, sf::Vector2f q2 ) {
   
    // first line
    if( p1.x > p2.x ) {
        sf::Vector2f p = p1;
        p1 = p2;
        p2 = p;
    }
   
    // second line
    if( q1.x > q2.x ) {
        sf::Vector2f q = q1;
        q1 = q2;
        q2 = q;
    }
   
    // p1.y = a*p1.x + b;
    // p2.y = a*p2.x + b;
    // b = p1.y - a*p1.x;
    // p2.y = a*p2.x + p1.y - a*p1.x;
    // p2.y = a(p2.x - p1.x) + p1.y;
    // a(p2.x - p1.x)  = p2.y - p1.y;
    // a = (p2.y - p1.y)/(p2.x - p1.x);
    // b = p1.y - a * p1.x;
   
    // first function y = ax + b
    float a1, b1;
    a1 =( p2.y - p1.y ) /( p2.x - p1.x );
    b1 = p1.y - a1 * p1.x;
   
    if( p2.x - p1.x < 0 ) {
        a1 *= - 1.0f;
        b1 *= - 1.0f;
    }
   
    // second function y = ax + b
    float a2, b2;
    a2 =( q2.y - q1.y ) /( q2.x - q1.x );
    b2 = q1.y - a2 * q1.x;
   
    if( q2.x - q1.x < 0 ) {
        a2 *= - 1.0f;
        b2 *= - 1.0f;
    }
   
    if( a1 == a2 )
         return false;
   
    // commont point
    sf::Vector2f center;
    center.x =( b2 - b1 ) /( a1 - a2 );
    center.y = a1 * center.x + b1;
   
    // intersections
    float min_x_line1 = min( p1.x, p2.x );
    float min_x_line2 = min( q1.x, q2.x );
    float min_x = min( min_x_line1, min_x_line2 );
   
    float min_y_line1 = min( p1.y, p2.y );
    float min_y_line2 = min( q1.y, q2.y );
    float min_y = min( min_y_line1, min_y_line2 );
   
    float max_x_line1 = max( p1.x, p2.x );
    float max_x_line2 = max( q1.x, q2.x );
    float max_x = max( max_x_line1, max_x_line2 );
   
    float max_y_line1 = max( p1.y, p2.y );
    float max_y_line2 = max( q1.y, q2.y );
    float max_y = max( max_y_line1, max_y_line2 );
   
    if( center.x <= max_x && center.x >= min_x && center.y <= max_y && center.y >= min_y )
         return true;
   
    return false;
}