It is possible to GENERIC method to point a webpage to a different page when the page doesn't have extension specified without physically redirecting the consumer towards the actual URL?

e.g. 
http://www.mydomain.com/  points to http://www.mydomain.com/public
http://www.mydomain.com/auth  points to http://www.mydomain.com/public/auth 
http://www.mydomain.com/auth/process points to http://www.mydomain.com/public/auth/process 
http://www.mydomain.com/auth/process/done points to http://www.mydomain.com/public/auth/process/done 

Maybe this is exactly what you'll need:

RewriteCond %{REQUEST_URI} !^/(public)(.*)$ [NC]
RewriteRule ^(.*)$ /public/$1 [L]

Edit:

Add this RewriteCond to check on to have an extension:

RewriteCond %{REQUEST_URI} !(\.[a-zA-Z0-9]{1,5}|/)$

yes , it can be done by rewrite rules but you need to know something about URL or some conditions about this to avoid rewritting other Web addresses.

for instance rewrite rule for the given URL is:

RewriteRule ^auth/(.*)$  public/auth/$1 [L]
RewriteRule  ^$   public [L]