touch-mouse.js

// Keep a reference available throughout the code
var touch = null;

// Called when the document has loaded
// You may choose some other place to do this
// Needs to occur only once
function doLoad()
{
  var element = null;

  // Check to see if there is a touch event handler
  touch = ( 'ontouchstart' in document.documentElement ) ? true : false;

  // Get your desired element to handle the interaction event
  // Quick ternary operation based on previous findings
  element = document.querySelector( '#yourElement' );
  element.addEventListener( touch ? 'touchstart' : 'mousedown', doInputStart );
}

// Called when the mouse is down or the touch has started
// Does whatever you want on that event
function doInputStart( evt ) 
{
  var clientX = null;
  var clientY = null;

  // Get the coordinates based on input type
  if( touch )
  {
    // Stop the default handling of the event
    evt.preventDefault();
  
    // Get the touch coordinates
    clientX = evt.touches[0].clientX;
    clientY = evt.touches[0].clientY;
  } else {
    // Not a tablet so grab mouse coordinates
    clientX = evt.clientX;
    clientY = evt.clientY;
  }

  // Do whatever you want at this point
  console.log( 'Input at: ' + clientX + 'x' + clientY );
}