Processing and IntelliJ Idea:
https://github.com/mkj-is/processing-intellij
Read the documentation: http://processing.org/reference/javadoc/core/processing/core/PApplet.html
More specifically, the following is important:
"As of Processing 3.0, we have removed Applet as the base class for PApplet. This means that we can
remove lots of legacy code, however one downside is that it's no longer possible (without extra code) to
embed a PApplet into another Java application.
As of Processing 3.0, we have discontinued support for versions of Java prior to 1.8. We don't have enough
people to support it, and for a project of our (tiny) size, we should be focusing on the future, rather than
working around legacy Java code."
Another source of information:
https://www.klingt.net/posts/processing-2-in-intellij-idea-14/