.html removal from URL using .htaccess rewrite rules - apache

Question

I have a static website - a bunch of static html pages. I am trying to remove .html part from the URL of my webpages. I have used an .htaccess file with the following code to do that:
RewriteEngine on
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME}\.html -f
RewriteRule ^(.*)$ $1.html
However, I am getting a 404 error. For example:
The requested URL /home/username/public_html/contact.html was not found on this server.
Ideally, it should redirect to /~username/contact.html.
Addition information
When I used "Options -MultiViews" line above the code it is giving the following error:
500 Internal Server Error: The server encountered an internal error or misconfiguration and was unable to complete your request.
Apache/2.2.15 (Red Hat) server is used here.
Why I am facing this problem? Is root is automatically getting changed from public_html/ folder?
EDIT:
Directory Structure:
Username
.gnome2 (there are empty folders inside it)
.mozilla (there are empty folders inside it)
public_html (I have put css, fonts, js, etc folders and .htaccess, contact.html, index.html, etc files here.)
.bash_logout
.bash_profile
.bashrc
Username folder is under universitynameuniverse folder (whose other folders I cannot see).

Answer 1

Try this code in your .htaccess:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^([^\.]+)$ $1.html [NC,L]
That’s it! You can now link pages inside the HTML document without needing to add the extension of the page.

Answer 2

Try this:
Options +FollowSymLinks
<IfModule mod_rewrite.c>
RewriteEngine on
RewriteBase /
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule !.*\.html$ %{REQUEST_FILENAME}.html [QSA,L]
</IfModule>
## Results
# ~user/contact => ~user/contact.html (only if file exists)
It only works if the ~user/ directory actually exists on the filesystem.
If you need an external redirect instead, append an R flag to the RewriteRule directive.
The problem with your rewrite rule is that it's appending a .html suffix to the whole %{REQUEST_URI} variable which will probably result in a 404.
Update
Re-reading your question I noted that you want to map the ~user part to somewhere out of the apache webroot. In this case, try this:
Options +FollowSymLinks
<IfModule mod_rewrite.c>
RewriteEngine on
RewriteBase /
RewriteCond %{REQUEST_URI} ^/~(.+)/(.+)$
RewriteCond /home/%1/public_html/%2.html -f
RewriteRule . /home/%1/public_html/%2.html [QSA,L]
</IfModule>
## Results
# ~user/contact => /home/user/public_html/contact.html (only if file exists)