Renderer::Renderer(int x, int y, int w, int h, const char *label)
: Fl_Gl_Window(x, y, w, h, label)
, ground_tex(0)
, ground_tex2(0)
, client_(0)
{
  eye[0] = 0;
  eye[1] = -100;
  eye[2] = 100;
  center[0] = 0;
  center[1] = 0;
  center[2] = 0;
  double left[3] = { -1, 0, 0 };
  double cam_dir[3];
  substract_vector(cam_dir, center, eye);
  cross_product(up, cam_dir, left);
}
void gram_schmidt( StateType &x , LyapType &lyap , size_t n )
{
    if( !num_of_lyap ) return;
    if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )
        throw std::domain_error( "renormalization() : size of state does not match the number of lyapunov exponents." );

    typedef typename StateType::value_type value_type;
    typedef typename StateType::iterator iterator;

    value_type norm[num_of_lyap];
    value_type tmp[num_of_lyap];
    iterator first = x.begin() + n;
    iterator beg1 = first , end1 = first + n ;

    std::fill( norm , norm+num_of_lyap , 0.0 );

    // normalize first vector
    norm[0] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
    normalize( beg1 , end1 , norm[0] );

    beg1 += n;
    end1 += n;

    for( size_t j=1 ; j<num_of_lyap ; ++j , beg1+=n , end1+=n )
    {
        for( size_t k=0 ; k<j ; ++k )
        {
            tmp[k] = std::inner_product( beg1 , end1 , first + k*n , 0.0 );
            //  clog << j << " " << k << " " << tmp[k] << "\n";
        }



        for( size_t k=0 ; k<j ; ++k )
            substract_vector( beg1 , end1 , first + k*n , tmp[k] );

        // normalize j-th vector
        norm[j] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
        // clog << j << " " << norm[j] << "\n";
        normalize( beg1 , end1 , norm[j] );
    }

    for( size_t j=0 ; j<num_of_lyap ; j++ )
        lyap[j] += log( norm[j] );
}