Question: I'd like to render a very simple 3D scene in a java applet. I could do all the math myself and render that to a bitmap, but as I'm sure I'm not the first person in history to have to draw a few cubes to the screen, I was wondering how this is usually done.

Every place I've read has said either Java3D or LWJGL, but as I understand it these rely on platform-dependent code and need to be installed separately from Java, making them both unsuitable for graphics.

So how is this usually done?

Answer: 
In a plug-in 2 JRE (1.6.0\_10+), you can use JWS extensions for embedded applets. This is important because JWS makes it much easier to ensure the correct binaries are on the run-time class path. AFAIU JOGL and Java 3D both offer JWS extensions for their APIs.

Should you choose to go that way, please make the applet has the draggable parameter added, so the end user might choose if they want a (mostly useless) browser window wrapped around a 3D animation.
Could you use JOGL?

<http://download.java.net/media/jogl/demos/www/applettest-jnlp.html>