JavaScript: aspect ratio maintaining bg image resize

gistfile1

bgSize: function(){
			var $background	= $('#background'),
				$bgimage		= $background.find('.bgimage'),
				$loading		= $background.find('.loading');

			var loadPage = function() {
				$loading.show();//show loading status image

					$.when(showBGImage()).done(function(){
						//hide the loading status image
						$loading.hide();

					});
				},
				showBGImage = function() {
						//adjusts the dimensions of the image to fit the screen
						adjustImageSize($bgimage);
						$bgimage.fadeIn(1000);
				},
				initWindowEvent = function() {
					//on window resize set the width for the menu
					$(window).bind('resize', function(e) {
						adjustImageSize($bgimage);
					});
				},
					//makes  image "fullscreen" and centered
				adjustImageSize = function($img) {

					var w_w	= $(window).width(),
						w_h	= $(window).height(),
						r_w	= w_h / w_w,
						i_w	= $img.width(),
						i_h	= $img.height(),
						r_i	= i_h / i_w,
						new_w,new_h,
						new_left,new_top;
						
					if(r_w > r_i){
						new_h	= w_h;
						new_w	= w_h / r_i;
					}
					else{
						new_h	= w_w * r_i;
						new_w	= w_w;
					}
						
					$img.css({
						width	: new_w + 'px',
						height	: new_h + 'px',
						left	: (w_w - new_w) / 2 + 'px',
						top		: (w_h - new_h) / 2 + 'px'
					});
				};
			loadPage();
			initWindowEvent();
		}