CSS3 zooming on mouse cursor

My goal is to create a plugin that enables zooming & panning operations on a page area, just like how Google Maps currently works (meaning: scrolling with the mouse = zooming in/out of the area, click & hold & move & release = panning).

When scrolling, I wish to have a zoom operation centered on the mouse cursor.

For this, I use on-the-fly CSS3 matrix transformations. The only, yet mandatory, constraint is that I cannot use anything else than CSS3 translate & scale transformations, with a transform origin of 0px 0px.

Panning is out of the scope of my question, since I have it working already. When it comes to zooming, I am struggling to figure out where the glitch is in my Javascript code.

The problem must be somewhere in the MouseZoom.prototype.zoom function, in the calculation of the translation on the x axis and y axis.

First, here is my HTML code:

<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width = device-width, initial-scale = 1.0, user-scalable = no" />
    <meta name="apple-mobile-web-app-capable" content="yes">
    <meta name="apple-mobile-web-app-status-bar-style" content="black" />
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
    <script src="jquery.mousewheel.min.js"></script>
    <script src="StackOverflow.js"></script>
    <style type="text/css" media="all">
        #drawing {
            position: absolute;
            top: 0px; 
            left: 0px; 
            right:0; 
            bottom:0;
            z-index: 0;
            background: url(http://catmacros.files.wordpress.com/2009/09/cats_banzai.jpg) no-repeat;
            background-position: 50% 50%;
        }
    </style>
    <title>Test</title>
</head>
<body>
    <div id="drawing"></div>
    <script>
        var renderer = new ZoomPanRenderer("drawing");
    </script>
</body>
</html>

As you can see, I am using Jquery and the jquery mouse wheel plugin from Brandon Aaron, which can be found here: https://github.com/brandonaaron/jquery-mousewheel/

Here is the content of the StackOverflow.js file:

/***************************************************** 
 * Transformations
 ****************************************************/
function Transformations(translateX, translateY, scale){
    this.translateX = translateX;
    this.translateY = translateY;
    this.scale = scale;
}

/* Getters */
Transformations.prototype.getScale = function(){ return this.scale; }
Transformations.prototype.getTranslateX = function(){ return this.translateX; }
Transformations.prototype.getTranslateY = function(){ return this.translateY; }

/***************************************************** 
 * Zoom Pan Renderer
 ****************************************************/
function ZoomPanRenderer(elementId){
    this.zooming = undefined;
    this.elementId = elementId;
    this.current = new Transformations(0, 0, 1);
    this.last = new Transformations(0, 0, 1);
    new ZoomPanEventHandlers(this);
}

/* setters */
ZoomPanRenderer.prototype.setCurrentTransformations = function(t){ this.current = t; }
ZoomPanRenderer.prototype.setZooming = function(z){ this.zooming = z; }

/* getters */
ZoomPanRenderer.prototype.getCurrentTransformations = function(){ return this.current; }
ZoomPanRenderer.prototype.getZooming = function(){ return this.zooming; }
ZoomPanRenderer.prototype.getLastTransformations = function(){ return this.last; }
ZoomPanRenderer.prototype.getElementId = function(){ return this.elementId; }

/* Rendering */
ZoomPanRenderer.prototype.getTransform3d = function(t){
    var transform3d = "matrix3d(";
    transform3d+= t.getScale().toFixed(10) + ",0,0,0,";
    transform3d+= "0," + t.getScale().toFixed(10) + ",0,0,";
    transform3d+= "0,0,1,0,";
    transform3d+= t.getTranslateX().toFixed(10) + "," + t.getTranslateY().toFixed(10)  + ",0,1)";
    return transform3d;
}

ZoomPanRenderer.prototype.getTransform2d = function(t){
    var transform3d = "matrix(";
    transform3d+= t.getScale().toFixed(10) + ",0,0," + t.getScale().toFixed(10) + "," + t.getTranslateX().toFixed(10) + "," + t.getTranslateY().toFixed(10) + ")";
    return transform3d;
}

ZoomPanRenderer.prototype.applyTransformations = function(t){
    var elem = $("#" + this.getElementId());
    elem.css("transform-origin", "0px 0px");
    elem.css("-ms-transform-origin", "0px 0px");
    elem.css("-o-transform-origin", "0px 0px");
    elem.css("-moz-transform-origin", "0px 0px");
    elem.css("-webkit-transform-origin", "0px 0px");
    var transform2d = this.getTransform2d(t);
    elem.css("transform", transform2d);
    elem.css("-ms-transform", transform2d);
    elem.css("-o-transform", transform2d);
    elem.css("-moz-transform", transform2d);
    elem.css("-webkit-transform", this.getTransform3d(t));
}

/***************************************************** 
 * Event handler
 ****************************************************/
function ZoomPanEventHandlers(renderer){
    this.renderer = renderer;
    
    /* Disable scroll overflow - safari */
    document.addEventListener('touchmove', function(e) { e.preventDefault(); }, false);
    
    /* Disable default drag opeartions on the element (FF makes it ready for save)*/
    $("#" + renderer.getElementId()).bind('dragstart', function(e) { e.preventDefault(); });
    
    /* Add mouse wheel handler */
    $("#" + renderer.getElementId()).bind("mousewheel", function(event, delta) {
        if(renderer.getZooming()==undefined){
            var offsetLeft = $("#" + renderer.getElementId()).offset().left;
            var offsetTop = $("#" + renderer.getElementId()).offset().top;
            var zooming = new MouseZoom(renderer.getCurrentTransformations(), event.pageX, event.pageY, offsetLeft, offsetTop, delta);
            renderer.setZooming(zooming);
            
            var newTransformation = zooming.zoom();
            renderer.applyTransformations(newTransformation);
            renderer.setCurrentTransformations(newTransformation);
            renderer.setZooming(undefined);
        }
        return false;
    });
}

/***************************************************** 
 * Mouse zoom
 ****************************************************/
function MouseZoom(t, mouseX, mouseY, offsetLeft, offsetTop, delta){
    this.current = t;
    this.offsetLeft = offsetLeft;
    this.offsetTop = offsetTop;
    this.mouseX = mouseX;
    this.mouseY = mouseY;
    this.delta = delta;
}

MouseZoom.prototype.zoom = function(){
    var previousScale = this.current.getScale();
    var newScale = previousScale + this.delta/5;
    if(newScale<1){
        newScale = 1;
    }
    var ratio = newScale / previousScale;
    
    var imageX = this.mouseX - this.offsetLeft;
    var imageY = this.mouseY - this.offsetTop;
    
    var previousTx = - this.current.getTranslateX() * previousScale;
    var previousTy = - this.current.getTranslateY() * previousScale;
    var previousDx = imageX * previousScale;
    var previousDy = imageY * previousScale;

    var newTx = (previousTx * ratio + previousDx * (ratio - 1)) / newScale;
    var newTy = (previousTy * ratio + previousDy * (ratio - 1)) / newScale;
    
    return new Transformations(-newTx, -newTy, newScale);
}