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Programming modifyable meshes

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How do games like skyrim allow the meshes to be modified (in the characters face section for instance)?

One way I was thinking about doing it was to simply have shape keys (as they are called in blender), that I could then apply to the mesh with sliders, but 1. I don't know if such a file format exists or if I'll have to come up with a format myself, 2. I don't know if "shape keys" if the official name for what they are (basically they are hierarchical (or not) vertex modifiers), and 3. I don't know if this is the way to go, or if I'm complicating (or simplifying) things here.

Any insight on the subject would be much appreciated, and thank you in advance.

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I think there are several terms for "shape keys," one of which is "morph targets."

The vertices are gradually approaching a final state from an initial state.

Per-vertex animation.
Shape interpolation.

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Ok thanks, morph targets seems to be the closest to what I was looking for search wise. I still don't know if there is a file type I should be using to store these targets, or if there is no convention regarding that. Should I just export the targets to a file and use it with the mesh it belongs to?

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