Basically, I want to modify the rendering system to do the following:

• Duplicate the entity's mesh
• Identify and isolate the silhouette of the mesh
• Extrude the silhouette faces in the direction of the light
• Apply an intersection shader (or a fixed-function LWJGL equivalent) to the mesh, so that only parts of the terrain which intersect the shadow mesh are in shadow

I think that by doing this, I'll be able to add shadow volumes to the game. I also plan on modifying the renderer in other ways later on.

I'm unable to find any information on how to do this, however.  If anyone could help me hook into the game's renderer and render entities the way I'm trying to here, that would be very much appreciated!

Quick question - based on what you said, it sounds like you're trying to make the shadow face towards the light. Am I understanding you correctly?

1 hour ago, scientistknight1 said:

Quick question - based on what you said, it sounds like you're trying to make the shadow face towards the light. Am I understanding you correctly?

Yes, the shadow is intended to point in the direction of the light. I could also make it point in a fixed direction if that information isn’t available for whatever reason. But that’s besides the point.

Ok, I was just wondering. Are you trying to implement Shadesmar, by any chance?

Anyways, I suspect that you'll have better luck trying to work with shaders. Here's a few tutorials I found for using Iris/Optifine to do shaders, though I don't know if they're any good since I have never worked with shaders: 

https://github.com/shaderLABS/Shadow-Tutorial
https://github.com/saada2006/MinecraftShaderProgramming
https://shaderlabs.org/wiki/Getting_Started

Hopefully someone else who knows more than I do can help with what you want.

2 hours ago, scientistknight1 said:

Ok, I was just wondering. Are you trying to implement Shadesmar, by any chance?

Anyways, I suspect that you'll have better luck trying to work with shaders. Here's a few tutorials I found for using Iris/Optifine to do shaders, though I don't know if they're any good since I have never worked with shaders: 

https://github.com/shaderLABS/Shadow-Tutorial
https://github.com/saada2006/MinecraftShaderProgramming
https://shaderlabs.org/wiki/Getting_Started

Hopefully someone else who knows more than I do can help with what you want.

I already know shader programming, it’s just not what I want to do. Using Optifine shaders would require me to replace too much of vanilla Minecraft’s rendering. I want my thing to look like vanilla, but with the addition of simple shadows from entities.

Right now, my primary concern would be finding a way to modify the LWJGL rendering code in Java.