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Starting a file download before you finalize its contents

In my webapp the user has the option to download a file containing some data, which they do by clicking on a button. For small amounts of data the file starts downloading pretty much immediately and that shows in the browser's download area. Which is good.
For large amounts of data it can take the server a substantial amount of time to calculate the data, even before we start downloading. This is not good. I want to indicate that the calculation is in progress. However I don't want to put a "busy" indicator on my UI, because the action does not block the UI - the user should be able to do other things while the file is being prepared.
A good solution from my point of view would be to start the download process before I have finished the calculation. We always know (or can quickly calculate) the first few hundred bytes of the file. Is there a mechanism where I can have the server respond to a download request with those few bytes, thus starting the download and making the file show up in the download area, and provide the rest of the file when I have finished calculating it? I'm aware that it will look like the download is stalled, and that's not a problem.
I can make a pretty good estimate of the file size very quickly. I would prefer not to have to use a third-party package to achieve this, unless it's a very simple one. We are using Angular but happy to code raw JS if needed.

To indicate that the link points to a download on the client, the easiest way is the download attribute on the link. The presence of the attribute tells the browser not to unload the current tab or create a new one; the value of the attribute is the suggested filename.
For the back-end part, after setting the correct response headers, just write the data to the output stream as it becomes available.

You asked for a general solution
1) First, at your HTML/JS you can prevent the UI from being blocked by setting you download target to any other WebPage, the preferred way for doing this is to set the target to an IFRAME:
<!-- your link must target the iframe "downloader-iframe" -->
<a src="../your-file-generator-api/some-args?a=more-args" target="downloader-iframe">Download</a>
<!-- you don't need the file to be shown -->
<iframe id="downloader-iframe" style="display: none"></iframe>
2) Second, at your back-end you'll have to use both Content-Disposition and Content-Length(optional) headers, be careful using the "length" one, if you miss calculate the fileSize it will not be downloaded. If you don't use Content-Length you'll not see the "downloading progress".
3) Third, at you'r back-end you have to make sure that you are writing your bytes directly at your response! that way your Browser and your Web-Server will know that the download is "in progress",
Example for Java:
Using ServletOutputStream to write very large files in a Java servlet without memory issues
Example for C#:
Writing MemoryStream to Response Object
HOW this 3 steps are built will be up to you, frameworks and libraries you are using, for example Dojo & JQuery have great IFRAME manipulation utilities, all thought you can do the coding by yourself, this is a JQuery sample:
Using jQuery and iFrame to Download a File
Also:
Adding a "busy" animation is ok! you just have to make sure that it's not blocking you'r UI, something like this:

How to get file size from another site src?

So, guys, I get src's, from another site, and have the array like ["www.another.com/pic1.png", "www.another2.com/pic2.jpg"].
I tested XMLHttpRequest, and file.size, but CORS does not allow to do it.
How can I get file size, from this array items?

First of all, You must to resolve CORS problem. so you may can use a Node.js server as web crawler server to get data from another website.
Then you can use any tool which is can get detail of file to know the file size of the image.

how to secure img src path when user clicks on view source using javascript?

How to secure the src path of the image when clicks on inspect element so that user should not get to know about the actual src path..please help me with the solution and it should be done with javascript only no other tags should be used.

You can convert image into base 64 data URIs for embedding images.
Use: http://websemantics.co.uk/online_tools/image_to_data_uri_convertor/
Code sample:
.sprite {
background-image:url(data:image/png;base64,iVBORw0KGgoAAAA... etc );
}

This is commonly done server-side, where you have an endpoint that serves the image file to you as bytes...
You can store the images in a private location on the server where IIS/<your favourite web server> doesn't have direct access to it, but only a web app, running on it, with the required privilege is authorized to do so.
Alternatively people also "store" the images in the database itself and load it directly from there.
In either case, the response which has to be sent back has to be a stream of bytes with the correct mime type.
Edit:
Here are a couple of links to get you started if you are into ASP.NET:
http://www.codeproject.com/Articles/34084/Generic-Image-Handler-Using-IHttpHandler
http://aspalliance.com/1322_Displaying_Images_in_ASPNET_Using_HttpHandlers.5 <- this sample actually does it from a database.
Don't let the choice of front-end framework (asp.net, php, django, etc) hinder you. Search for similar techniques in your framework of choice.
Edit:
Another way if you think html5 canvas is shown here: http://www.html5canvastutorials.com/tutorials/html5-canvas-images/
However you run into the same problem. Someone can view the image url if they can see the page source. You'll have to revert to the above approach eventually.

Force image caching with javascript

I am trying to clone an image which is generated randomly.
Although I am using the exact same url a different image is load. (tested in chrome and firefox)
I can't change the image server so I am looking for a pure javascript/jQuery solution.
How do you force the browser to reuse the first image?
Firefox:
Chrome:
Try it yourself (maybe you have to reload it several times to see it)
Code:
http://jsfiddle.net/TRUbK/
$("<img/>").attr('src', img_src)
$("<div/>").css('background', background)
$("#source").clone()
Demo:
http://jsfiddle.net/TRUbK/embedded/result/

You can't change the image server if it isn't yours, but you can trivially write something on your own server to handle it for you.
First write something in your server-side language of choice (PHP, ASP.NET, whatever) that:
Hits http://a.random-image.net/handler.aspx?username=chaosdragon&randomizername=goat&random=292.3402&fromrandomrandomizer=yes and downloads it. You generate a key in one of two way. Either get a hash of the whole thing (MD5 should be fine, it's not a security-related use so worries that it's too weak these days don't apply). Or get the size of the image - the latter could have a few duplicates, but is faster to produce.
If the image isn't already stored, save it in a location using that key as part of its filename, and the content-type as another part (in case there's a mixture of JPEGs and PNGs)
Respond with an XML or JSON response with the URI for the next stage.
In your client side-code, you hit that URI through XmlHttpRequest to obtain the URI to use with your images. If you want a new random one, hit that first URI again, if you want the same image for two or more places, use the same result.
That URI hits something like http://yourserver/storedRandImage?id=XXX where XXX is the key (hash or size as decided above). The handler for that looks up the stored copies of the images, and sends the file down the response stream, with the correct content-type.
This is all really easy technically, but the possible issue is a legal one, since you're storing copies of the images on another server, you may no longer be within the terms of your agreement with the service sending the random images.

You can try saving the base64 representation of the image.
Load the image in an hidden div/canvas, then convert it in base64. (I'm not sure if a canvas can be hidden, nor if it is possible to convery the img using html4 tag)
Now you can store the "stringified" image in a cookie, and use it unlimited times...

The headers being sent from your random image generator script include a Cache-Control: max-age=0 declaration which is in essence telling the browser not to cache the image.
You need to modify your image generator script/server to send proper caching headers if you want the result to be cached.
You also need to make sure that the URL stays the same (I didn't look at that aspect since there were tons of parameter being passed).

There seems to be two workarounds:
If you go with the Canvas method, see if you can get the image to load onto the Canvas itself so that you can manipulate the image data directly instead of making a 2nd http request for the image. You can feed the image data directly onto a 2nd Canvas.
If you're going to build a proxy, you can have the proxy remove the No-Cache directive so that subsequent requests by your browser use the cache (no guarantees here - depends on browser/user settings).

First off, you can "force" anything on the web. If you need to force things, then web development is the wrong medium for you.
What you could try, is to use a canvas element to copy the image. See https://developer.mozilla.org/en-US/docs/Web/Guide/HTML/Canvas_tutorial/Using_images for examples.

Tell it to stop getting a random image, seems to work the way you want when I add this third replace call:
// Get the canvas element.
var background = ($("#test").css('background-image')),
img_src = background.replace(/^.+\('?"?/, '').replace(/'?"?\).*$/, '').replace(/&fromrandomrandomizer=yes/,'')

try:
var myImg = new Image();
myImg.src = img_src;
and then append "myImg" to where you want:
$(document).append(myImg);

I did this with your fiddler scripts and got the same image every time
#test {
background:url(http://a.random-image.net.nyud.net/handler.aspx?username=chaosdragon&randomizername=goat&random=292.3402&fromrandomrandomizer=yes);
width: 150px;
height: 150px;
}
note the .nyud.net after the domain name.

Return image from HTTP Post request in Javascript

I send data from a browser to a servlet using JavaScript, then the server processes the data and returns an image as a response (all using xmlhttprequest). I'm sure everything is working fine because when I call the server directly, I get my image back in the browser.
What I was wondering is how, in JavaScript, do I parse my response so that I can display it as an image in an img tag?
I figure this should be fairly easy, but not sure how to do it.

You could use data URIs and set the base64 encoded binary data as the src for an image tag.
If you have control over the server, it might be cleaner to have the server give you a URL you can refer to and create a new img tag with that src.

Not sure if this would work with your application, but you could use a server-side script to dynamically serve an image, and then just use javascript to change the source of your image.
i.e.
src="image.php?param1=XXXX&param2=XXXX"
Or just have your XMLHttpRequest return a new path to an existing image on the server and then just change the src attribute of your img.