You should not be calling that function directly, otherwise it would be documented. That is just for use of sub-classes.
As documented, for implement the OAuth authorization flow, call the Process function between the Initialize and Finalize calls.
For performing API calls, call the CallAPI function.
Take a look at the mysqli_login_with_google.php script to authorize your application with Google and store tokens in MySQL using MySQLi.
phpclasses.org/package/7700-PHP-Aut
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For performing API calls when the user is offline (for instance from the CLI/Shell) look at the example mysqli_offline_access_to_google.php
phpclasses.org/package/7700-PHP-Aut
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This article gives you more details:
phpclasses.org/blog/package/7700/po
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