Convert mouse events into touch events.

mouseToTouch.js

/**
 * Convert mouse events into touch events.
 * From: http://ross.posterous.com/2008/08/19/iphone-touch-events-in-javascript/
*/
function touchHandler(event) {
    var touch = event.changedTouches[0];

    var simulatedEvent = document.createEvent("MouseEvent");
        simulatedEvent.initMouseEvent({
        touchstart: "mousedown",
        touchmove: "mousemove",
        touchend: "mouseup"
    }[event.type], true, true, window, 1,
        touch.screenX, touch.screenY,
        touch.clientX, touch.clientY, false,
        false, false, false, 0, null);

    touch.target.dispatchEvent(simulatedEvent);
    event.preventDefault();
}

function init() {
    document.addEventListener("touchstart", touchHandler, true);
    document.addEventListener("touchmove", touchHandler, true);
    document.addEventListener("touchend", touchHandler, true);
    document.addEventListener("touchcancel", touchHandler, true);
}

initMouseEvent is deprecated
https://developer.mozilla.org/en-US/docs/Web/API/MouseEvent/initMouseEvent

Use this instead, note that both this and the original can cause very weird behaviour with select elements on iOS, ensure you only use it where appropriate and don't blanket every touch event in your app with it:

Not supported in IE

function touchHandler(event) {
	var touch = event.changedTouches[0];
	var simulatedEvent = new MouseEvent({
		touchstart: "mousedown",
		touchmove: "mousemove",
		touchend: "mouseup"
	}[event.type], {
		bubbles: true, cancelable: true, view: window, detail: 1,
		screenX: touch.screenX, screenY: touch.screenY, clientX: touch.clientX, clientY: touch.clientY,
		ctrlKey: false, altKey: false, shiftKey: false, metaKey: false, button: 0, relatedTarget: null
	});
	touch.target.dispatchEvent(simulatedEvent);
}
function init() {
        // I suggest you be far more specific than "document"
	document.addEventListener("touchstart", touchHandler, true);
	document.addEventListener("touchmove", touchHandler, true);
	document.addEventListener("touchend", touchHandler, true);
	document.addEventListener("touchcancel", touchHandler, true);
}

((win, doc) => {
  /**
   * @param e {MouseEvent}
   */
  function mouseHandler(e) {
    e.preventDefault()
    let type = {
      mousedown: "touchstart",
      mousemove: "touchmove",
      mouseup: "touchend"
    }[e.type]

    let touch = new Touch({
      identifier: e.button,
      clientX: e.clientX,
      clientY: e.clientY,
      screenX: e.screenX,
      screenY: e.screenY,
      target: e.target,
      touchType: "direct"
    })
    let te = new TouchEvent(type, {
      bubbles: true,
      cancelable: true,
      touches: [touch],
      changedTouches: [touch],
      targetTouches: [touch],
    })
    e.target.dispatchEvent(te)
  }

  doc.addEventListener("mousedown", mouseHandler, true)
  doc.addEventListener("mousemove", mouseHandler, true)
  doc.addEventListener("mouseup", mouseHandler, true)
})(window, document)