Choosing Visible Form Elements

I have a javascript function that loops throught all text boxes inside
a form:

var elems = document.formName.elements;
for(i = 0; i < elems.length; i++) {
if(elems[i].type && elems[i].type.toLowerCase()=="text")
do something
}

This way it goes through every single text box in the form.
But in my form structure, some form elements (text boxes included)
are inside invisible divs.

And what I actually want to do, is to check only the text boxes
that are not inside invisible divs.

Is there a way to say in javascript something like:
choose only textbox that is not inside element (div) whose
className='invisible'?

Or maybe I should try a different approach, instead looping through
all form elements?