Efficiently get an element's visible area coordinates

Of course, I could be naïve and call elementFromPoint for every discrete point in the viewport, But performance is crucial since I iterate over all of the elements, and will do it quite often.

Please direct me as to how I can achieve this goal.

Disclaimer: I'm pretty noob to web programming concepts, so I might have used wrong technical terms.

Progress:

I came up with an implementation. The algorithm is pretty simple:

This produces a set of areas / rectangles, each pointing to a single element.

The problems with my implementation are:

As much as I can tell, the elementFromPoint call is the one that takes a lot of time and causes my algorithm to be relatively useless...

Can anyone suggest a better approach?

Here is my implementation:

function AreaPortion(l, t, r, b, currentDoc) {
    if (!currentDoc) currentDoc = document;
    this._x = l;
    this._y = t;
    this._r = r;
    this._b = b;
    this._w = r - l;
    this._h = b - t;

    center = this.getCenter();
    this._elem = currentDoc.elementFromPoint(center[0], center[1]);
}

AreaPortion.prototype = {
    getName: function() {
        return "[x:" + this._x + ",y:" + this._y + ",w:" + this._w + ",h:" + this._h + "]";
    },

    getCenter: function() {
        return [this._x + (this._w / 2), this._y + (this._h / 2)];
    }
}

function getViewport() {
    var viewPortWidth;
    var viewPortHeight;

    // IE6 in standards compliant mode (i.e. with a valid doctype as the first line in the document)
    if (
            typeof document.documentElement != 'undefined' &&
            typeof document.documentElement.clientWidth != 'undefined' &&
            document.documentElement.clientWidth != 0) {
        viewPortWidth = document.documentElement.clientWidth,
        viewPortHeight = document.documentElement.clientHeight
    }

    // the more standards compliant browsers (mozilla/netscape/opera/IE7) use window.innerWidth and window.innerHeight
    else if (typeof window.innerWidth != 'undefined') {
        viewPortWidth = window.innerWidth,
        viewPortHeight = window.innerHeight
    }

    // older versions of IE
    else {
        viewPortWidth = document.getElementsByTagName('body')[0].clientWidth,
        viewPortHeight = document.getElementsByTagName('body')[0].clientHeight
    }

    return [viewPortWidth, viewPortHeight];
}

function getLines() {
    var onScreen = [];
    var viewPort = getViewport();
    // TODO: header & footer
    var all = document.getElementsByTagName("*");

    var vert = {};
    var horz = {};

    vert["0"] = 0;
    vert["" + viewPort[1]] = viewPort[1];
    horz["0"] = 0;
    horz["" + viewPort[0]] = viewPort[0];
    for (i = 0 ; i < all.length ; i++) {
        var e = all[i];
        // TODO: Get all client rectangles
        var rect = e.getBoundingClientRect();
        if (rect.width < 1 && rect.height < 1) continue;

        var left = Math.floor(rect.left);
        var top = Math.floor(rect.top);
        var right = Math.floor(rect.right);
        var bottom = Math.floor(rect.bottom);

        if (top > 0 && top < viewPort[1]) {
            vert["" + top] = top;
        }
        if (bottom > 0 && bottom < viewPort[1]) {
            vert["" + bottom] = bottom;
        }
        if (right > 0 && right < viewPort[0]) {
            horz["" + right] = right;
        }
        if (left > 0 && left < viewPort[0]) {
            horz["" + left] = left;
        }
    }

    hCoords = [];
    vCoords = [];
    //TODO: 
    for (var v in vert) {
        vCoords.push(vert[v]);
    }

    for (var h in horz) {
        hCoords.push(horz[h]);
    }

    return [hCoords, vCoords];
}

function getAreaPortions() {
    var portions = {}
    var lines = getLines();

    var hCoords = lines[0];
    var vCoords = lines[1];

    for (i = 1 ; i < hCoords.length ; i++) {
        for (j = 1 ; j < vCoords.length ; j++) {
            var portion = new AreaPortion(hCoords[i - 1], vCoords[j - 1], hCoords[i], vCoords[j]);
            portions[portion.getName()] = portion;
        }
    }

    return portions;
}

Try

var res = [];
$("body *").each(function (i, el) {
    if ((el.getBoundingClientRect().bottom <= window.innerHeight 
        || el.getBoundingClientRect().top <= window.innerHeight)
        && el.getBoundingClientRect().right <= window.innerWidth) {
            res.push([el.tagName.toLowerCase(), el.getBoundingClientRect()]);
    };
});

jsfiddle http://jsfiddle.net/guest271314/ueum30g5/

See Element.getBoundingClientRect()

$.each(new Array(180), function () {
    $("body").append(
    $("<img>"))
});

$.each(new Array(180), function () {
$("body").append(
$("<img>"))
});

var res = [];
$("body *").each(function (i, el) {
if ((el.getBoundingClientRect().bottom <= window.innerHeight || el.getBoundingClientRect().top <= window.innerHeight)
    && el.getBoundingClientRect().right <= window.innerWidth) {
    res.push(
    [el.tagName.toLowerCase(),
    el.getBoundingClientRect()]);
    $(el).css(
        "outline", "0.15em solid red");
    $("body").append(JSON.stringify(res, null, 4));
    console.log(res)
};
});

body {
    width : 1000px;
    height : 1000px;
}
img {
    width : 50px;
    height : 50px;
    background : navy;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>

I don't know if the performance will be sufficient (especially on a mobile device), and the result is not quite a rectangle-set as you requested, but did you consider using a bitmap to store the result?

Note some elements may have 3d css transform (eg. skew, rotate), some elements may have border radius, and some elements may have invisible background - if you want to include these features as well for your "element from pixel" function then a rectangle set can't help you - but the bitmap can accommodate all of the visual features.

The solution to generate the bitmap is rather simple (I imagine... not tested):