y_to_client(y2));
    }
    runge_context.strokeStyle="#661100";
    runge_context.stroke();
    runge_context.closePath();

    // dots
    runge_context.beginPath();
    for(var i = 0; i < runge_n; ++i){
        runge_context.moveTo(x_to_client(runge_xs[i])-5.5, y_to_client(runge_ys[i])+5.5);
        runge_context.lineTo(x_to_client(runge_xs[i])+5.5, y_to_client(runge_ys[i])-5.5);
        runge_context.moveTo(x_to_client(runge_xs[i])+5.5, y_to_client(runge_ys[i])+5.5);
        runge_context.lineTo(x_to_cl