
        polynomial_context.beginPath();
        polynomial_context.moveTo(x_to_client(polynomial_xs[min_i]), y_to_client(polynomial_ys[min_i]));
        polynomial_context.lineTo(client_x, client_y);
        polynomial_context.strokeStyle="#AA3311";
        polynomial_context.stroke();
        polynomial_context.closePath();
        polynomial_context.setLineDash([]);
    }
}


// synthesis
var synthesis_xs = [-0.5, 1.0, 7.0, 8.5];
var synthesis_ys = [ 2.0, 1.0, 6.0, 5.0];
var synthesis_n = 4;
var synthesi