Extension of jQueryUI Draggable that works with Isotope

jsd.draggableIsotopeAtom.js

/**
 * The purpose of this jQuery UI plugin is to account for the bug in Firefox that doesn't correctly report the positions
 * of elements that are positioned with CSS transforms.  Luckily, isotope keeps track of what the position should be, so
 * we can calculate the correct offset.
 *
 * @author: John Starr Dewar
 */
(function($) {
   // Arguments to .extend are returned object, merge object 1, merge object 2
    $.widget('jsd.draggableIsotopeAtom', $.ui.draggable, {

        _create: function () {
            this.element.data("draggable", this);
            this._super('_create');
        },

        _setOption: function (key, value) {
            this._super('_setOption', key, value);
        },

        _mouseStart : function (event) {
            var o = this.options;

            //Create and append the visible helper
            this.helper = this._createHelper(event);

            //Cache the helper size
            this._cacheHelperProportions();

            //If ddmanager is used for droppables, set the global draggable
            if($.ui.ddmanager)
                $.ui.ddmanager.current = this;

            /*
             * - Position generation -
             * This block generates everything position related - it's the core of draggables.
             */

            //Cache the margins of the original element
            this._cacheMargins();

            //Store the helper's css position
            this.cssPosition = this.helper.css("position");
            this.scrollParent = this.helper.scrollParent();

            // ****** HERE BE THE CUSTOM CODE WE EXTENDED FOR -- everything else is copy-and-pasted from ui.draggable
            var parentOffset = this.element.parent().offset();
            var isotopePosition = this.element.data('isotope-item-position');

            //The element's absolute position on the page minus margins
            this.offset = this.positionAbs = {
                left: parentOffset.left + isotopePosition.x - this.margins.top,
                top: parentOffset.top + isotopePosition.y - this.margins.left
            };
            // ******

            $.extend(this.offset, {
                click: { //Where the click happened, relative to the element
                    left: event.pageX - this.offset.left,
                    top: event.pageY - this.offset.top
                },
                parent: this._getParentOffset(),
                relative: this._getRelativeOffset() //This is a relative to absolute position minus the actual position calculation - only used for relative positioned helper
            });

            //Generate the original position
            this.originalPosition = this.position = this._generatePosition(event);
            this.originalPageX = event.pageX;
            this.originalPageY = event.pageY;

            //Adjust the mouse offset relative to the helper if 'cursorAt' is supplied
            (o.cursorAt && this._adjustOffsetFromHelper(o.cursorAt));

            //Set a containment if given in the options
            if(o.containment)
                this._setContainment();

            //Trigger event + callbacks
            if(this._trigger("start", event) === false) {
                this._clear();
                return false;
            }

            //Recache the helper size
            this._cacheHelperProportions();

            //Prepare the droppable offsets
            if ($.ui.ddmanager && !o.dropBehaviour)
                $.ui.ddmanager.prepareOffsets(this, event);

            this.helper.addClass("ui-draggable-dragging");
            this._mouseDrag(event, true); //Execute the drag once - this causes the helper not to be visible before getting its correct position

            //If the ddmanager is used for droppables, inform the manager that dragging has started (see #5003)
            if ( $.ui.ddmanager ) $.ui.ddmanager.dragStart(this, event);

            return true;
        },

        _destroy : function () {

        }
    });
})(jQuery);

The backstory.

In jQuery 1.10, line 13 should be:
this.element.data("uiDraggable", this); // Fixes TypeError.

Andrew Bart Conrad contributed this advice to my blog:

"...if you get this kind of problem trying to extend any other UI plugin you can figure out what you need to add by initializing that plugin then looking at the data it adds by running something like $('.class-of-your-element').data()."