SVG coordinates with transform matrix

I have created a working example of what I believe you are describing on my site here:
http://phrogz.net/svg/drag_under_transformation.xhtml

In general, you convert the mouse cursor into the local space of an object by:

Creating a mousemove event handler:

var svg = document.getElementsByTagName('svg')[0];
document.documentElement.addEventListener('mousemove',function(evt){
  ...
},false);

In that event handler, convert the mouse coordinates (in pixels) into the global space of your SVG document:

var pt = svg.createSVGPoint();
pt.x = evt.clientX;
pt.y = evt.clientY;
var globalPoint = pt.matrixTransform(svg.getScreenCTM().inverse());

Convert the global point into the space of the object you are dragging:

var globalToLocal = dragObject.getTransformToElement(svg).inverse();
var inObjectSpace = globalPoint.matrixTransform( globalToLocal );

For Stack Overflow posterity, here’s the full source of my SVG+XHTML demo (in case my site is down):

<!DOCTYPE HTML>
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"><head> 
<meta http-equiv="content-type" content="application/xhtml+xml;charset=utf-8"/>
<title>Dragging Transformed SVG Elements</title>
<style type="text/css" media="screen">
  html, body {
    background:#eee; margin:0;
    user-select:none; -moz-user-select:none; -webkit-user-select:none;
  }
  p { margin:0.5em; text-align:center }
  svg {
    position:absolute; top:5%; left:5%; width:90%; height:90%;
    background:#fff; border:1px solid #ccc
  }
  svg rect { stroke:#333 }
  svg .drag { cursor:move }
  svg .sizer { opacity:0.3; fill:#ff0; stroke:#630;}
  #footer {
    position:absolute; bottom:0.5em; margin-bottom:0;
    width:40em; margin-left:-20em; left:50%; color:#666;
    font-style:italic; font-size:85%
  }
  #dragcatch { position:absolute; left:0; right:0; top:0; bottom:0; z-index:-1}
</style>
</head><body>
<p>Showing how to drag points inside a transformation hierarchy.</p>
<svg viewBox="0 0 200 100" xmlns="http://www.w3.org/2000/svg"
 xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" baseProfile="full">
  <g transform="scale(1.2,0.8)">
    <rect transform="translate(50,20) rotate(30)"
     class="drag resize" x="50" y="30" width="50" height="30" fill="#69c" />
    <rect class="drag resize" x="5" y="5" width="90" height="50" fill="#c66" />
  </g>
</svg>
<p id="footer">
  Copyright © 2011 <a href="https://stackoverflow.com/questions/4850821/mailto:[email protected]">Gavin Kistner</a>. 
  Comments/criticisms welcome.
</p>
<script type="text/javascript"><![CDATA[
  var svg   = document.getElementsByTagName('svg')[0];
  var svgNS = svg.getAttribute('xmlns');
  var pt    = svg.createSVGPoint();

  function createOn(root,name,prop){
    var el = document.createElementNS(svgNS,name);
    for (var a in prop) if (prop.hasOwnProperty(a)) el.setAttribute(a,prop[a]);
    return root.appendChild(el);
  }

  function rectCorner(rect){
    pt.x = rect.x.animVal.value + rect.width.animVal.value;
    pt.y = rect.y.animVal.value + rect.height.animVal.value;
    return pt.matrixTransform(rect.getTransformToElement(svg));
  }

  function pointIn(el,x,y){
    pt.x = x; pt.y = y;
    return pt.matrixTransform(el.getTransformToElement(svg).inverse());
  }

  function cursorPoint(evt){
    pt.x = evt.clientX; pt.y = evt.clientY;
    return pt.matrixTransform(svg.getScreenCTM().inverse());
  }

  // Make all rects resizable before drag, so the drag handles become drag
  for (var a=svg.querySelectorAll('rect.resize'),i=0,len=a.length;i<len;++i){
    (function(rect){
      var dot = createOn(svg,'circle',{'class':'drag sizer',cx:0,cy:0,r:5});
      var moveDotToRect = function(){
        var corner = rectCorner(rect);
        dot.setAttribute('cx',corner.x);
        dot.setAttribute('cy',corner.y);
      }
      moveDotToRect();
      rect.addEventListener('dragged',moveDotToRect,false);
      dot.addEventListener('dragged',function(){
        var rectXY = pointIn(rect,dot.cx.animVal.value,dot.cy.animVal.value);
        var w = Math.max( rectXY.x-rect.x.animVal.value, 1 );
        var h = Math.max( rectXY.y-rect.y.animVal.value, 1 );
        rect.setAttribute('width', w);
        rect.setAttribute('height',h);
      },false);
    })(a[i]);
  }

  for (var a=svg.querySelectorAll('.drag'),i=0,len=a.length;i<len;++i){
    (function(el){
      var onmove; // make inner closure available for unregistration
      el.addEventListener('mousedown',function(e){
        el.parentNode.appendChild(el); // move to top
        var x = el.tagName=='circle' ? 'cx' : 'x';
        var y = el.tagName=='circle' ? 'cy' : 'y';
        var mouseStart   = cursorPoint(e);
        var elementStart = { x:el[x].animVal.value, y:el[y].animVal.value };
        onmove = function(e){
          var current = cursorPoint(e);
          pt.x = current.x - mouseStart.x;
          pt.y = current.y - mouseStart.y;
          var m = el.getTransformToElement(svg).inverse();
          m.e = m.f = 0;
          pt = pt.matrixTransform(m);
          el.setAttribute(x,elementStart.x+pt.x);
          el.setAttribute(y,elementStart.y+pt.y);
          var dragEvent = document.createEvent("Event");
          dragEvent.initEvent("dragged", true, true);
          el.dispatchEvent(dragEvent);
        };
        document.body.addEventListener('mousemove',onmove,false);
      },false);
      document.body.addEventListener('mouseup',function(){
        document.body.removeEventListener('mousemove',onmove,false);
      },false);
    })(a[i]);
  }
]]></script>
<div id="dragcatch"></div>
</body></html>

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