How to get the MouseEvent coordinates for an element that has CSS3 Transform?

I want to detect where a MouseEvent has
occurred, in coordinates relative to the clicked element. Why? Because I want to add an absolutely positioned child element
at the clicked location.

I know how to detect it when no CSS3 transformations exist (see description below). However, when I add a CSS3 Transform, then my algorithm breaks, and I don‘t know how to fix it.

I‘m not using any JavaScript library, and I want to understand how things work in plain JavaScript. So, please, don‘t answer with "just use jQuery".

By the way, I want a solution that works for all MouseEvents, not just "click". Not that it matters, because I believe all mouse events share the same properties, thus the same solution should work for all of them.

Background information

According to DOM
Level 2 specification, a MouseEvent has
few properties related to getting the event coordinates:

• screenX and screenY return
  the screen coordinates (the origin is the top-left corner of user‘s monitor)
• clientX and clientY return
  the coordinates relative the document viewport.

Thus, in order to find the position of the MouseEvent relative
to the clicked element content, I must do this math:

ev.clientX - this.getBoundingClientRect().left - this.clientLeft + this.scrollLeft

• ev.clientX is
  the coordinate relative to the document viewport
• this.getBoundingClientRect().left is
  the position of the element relative to the document viewport
• this.clientLeft is
  the amount of border (and scrollbar) between the element boundary and the inner coordinates
• this.scrollLeft is
  the amount of scrolling inside the element

getBoundingClientRect(), clientLeft and scrollLeft are
specified at CSSOM
View Module.

Experiment without CSS Transform (it works)

Confusing? Try the following piece
of JavaScript and HTML. Upon clicking, a red dot should appear exactly where the click has happened. This version is "quite simple" and works as expected.

function click_handler(ev) {
    var rect = this.getBoundingClientRect();
    var left = ev.clientX - rect.left - this.clientLeft + this.scrollLeft;
    var top = ev.clientY - rect.top - this.clientTop + this.scrollTop;

    var dot = document.createElement(‘div‘);
    dot.setAttribute(‘style‘, ‘position:absolute; width: 2px; height: 2px; top: ‘+top+‘px; left: ‘+left+‘px; background: red;‘);
    this.appendChild(dot);
}

document.getElementById("experiment").addEventListener(‘click‘, click_handler, false);

<div id="experiment" style="border: 5px inset #AAA; background: #CCC; height: 400px; position: relative; overflow: auto;">
    <div style="width: 900px; height: 2px;"></div>
    <div style="height: 900px; width: 2px;"></div>
</div>

Experiment adding a CSS Transform (it fails)

Now, try adding a CSS transform:

#experiment {
    transform: scale(0.5);
    -moz-transform: scale(0.5);
    -o-transform: scale(0.5);
    -webkit-transform: scale(0.5);
    /* Note that this is a very simple transformation. */
    /* Remember to also think about more complex ones, as described below. */
}

The algorithm doesn‘t know about the transformations, and thus calculates a wrong position. What‘s more, the results are different between Firefox 3.6 and Chrome 12. Opera 11.50 behaves just like Chrome.

In this example, the only transformation was scaling, so I could multiply the scaling factor to calculate the correct coordinate. However, if we think about arbitrary transformations (scale, rotate, skew, translate, matrix), and even nested transformations
(a transformed element inside another transformed element), then we really need a better way to calculate the coordinates.