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What the title says. Many games have some sort of character generation system. I'm not talking about defaults (such as face1, face2, face 3...), but sliders that allow you to create very different character faces (or even bodies). Skyrim and fallout 4 as examples.

How do they work? Is it some kind of procedural magic? I suspect it might be blend shapes used for mesh 'distortion' instead of animation, but I wonder what techniques and technologies are involved in these kind of character generators.
You're right, it's basically blend shapes. There's some preset shapes like nostril small and nostril big and you fade between them.

To set it up it's taking a base mesh and tweaking it to different extremes for each part.

There might be some additional things like an armature in the head and you adjust the scale and placement of bones for lips and nose and eyes as well but primarily it's blend shapes / shape keys.

Know this guy Neroticus ripped all the Fallout 4 shapes and set up a Blender project with them all so you can make Fallout 4 characters without having to play the game, but I don't think he released it unfortunately.
Alright bit of an update on the last bit about Fallout 4 shapes.

There's a chance he meant the blend shapes used for expressions like raised eyebrows and open mouth and also that he can blend between the different NPC heads.

https://neroticus.tumblr.com/post/141330290093 This is the post where he mentions it.

I looked at Fallout 4's mesh ba2 archive and it looks like you've got the base parts like base male, female, child, etc and head, back of head, body, hands, eyes, etc, and then there's a directory of morphs for open mouth and such and a shitload of NPC heads with hair and all attached that were exported from Facegen.

Good to know that Fallout 4 still used Facegen in its development, just apparently not in the programming and only for churning out NPC heads.
Why are shape keys used, instead of bones? Is there a performance reason, or can bones still be used to deform the mesh?
Just because someone can actually model or sculpt the changes with better detail. Shape keys and bones can both be used but typically bones are for more general resizing or moving of areas and shape keys are for reshaping, like moving a nose up or making it big vs roman or nubian nose shapes.
Thanks anon. Also, another little question: ┬┐are blend shapes multiplicative?, taking noses (>>585573) as an example, could I make "nose type" blend shapes and "nose height (for example)" blend shapes and let them work together.

Like, having an slider for roman-nubian and another slider for relative-to-face-nose-height at the same time?
I think it's dependent on the engine but it's standard for them to add up.

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