how do plugins call makeUrlHttps() ?

How can I with an API transform a url string into its https version?

My inquiry is to have a function/method in WordPress HTTPS that can take a string param (uri) and return its https version based on the WordPress HTTPS settings.

For example, config WordPress HTTPS such that:
SSL Host = mysharedhost.different.com
URL Filters= /doit/

I would like to be able to:
$myurl = makeUrlHttps(‘http://mysite.com/doit/’);

and have $myurl now equal:
https://mysharedhost.different.com/doit/

Using 3.3.6 I tried the following. When I passed the uri string into the function, it returned that exact same string unchanged.
$httpsmagic = new WordPressHTTPS();
$outstring = $httpsmagic->makeUrlHttps(‘http://mysite.com/doit/’);

https://ww.wp.xz.cn/plugins/wordpress-https/