Rewrite address bar without redirecting - apache

Question

I have a host in my university's http server under the domain: university.com/~username
Now, I also have a domain on: mydomain.net with GoDaddy
I want to know if it is possible to have a subdomain:
university.mydomain.net that basically redirects to
university.com/~username.
Now, the trick here is that if I want to access
university.com/~username/subdir via university.mydomain.net/subdir
the address bar in the browser shows: university.mydomain.net/subdir no
matter if I access it via university.com/~username or university.mydomain.net
The problem with using permanent redirect with masking in GoDaddy, then if
I am in the dir university.mydomain.net/subdir and go to the subsubdir
university.mydomain.net/subdir/subsubdir then the browser still shows university.mydomain.net/subdir
And about CNAMEs or other kind of register in GoDaddy, I really have no idea
what to do (this is my first domain) and I don't even know if I have the rights
in my university server to make a difference.
I tried with a RewriteRule in a .htaccess file, but this always tries to
redirect (no matter what flag I use) to university.mydomain.com/subdir
while the only thing I want to do is that the address bar shows the direction
without following it.
I really don't even know if this is possible somehow. Sorry if it's an stupid
question, I'm very new with domains and those stuffs.

Answer 1

Under the CNAME you need to add you subdomain entry (in the Godaddy DNS management console)
university.mydomain.net points to #
and in your host the # might be pointing to the IP address where your university server is running.
Then in your apache vhost config, you would need to have rewrite rule like
<VirtualHost *:80>
RewriteEngine on
RewriteCond %{HTTP_HOST} ^university.mydomain.net(:80)?$
RewriteRule ^/(.*) http://university.com/~username/$1 [P,QSA,L]
RewriteCond %{HTTP_HOST} ^university.com(:80)?$
RewriteRule ^/~username/(.*) http://university.mydomain.net/$1 [R=301,L]
</VirtualHost>