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How do most file formats or 3d programs do skeletons?

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I have my own idea on how skeletons work in models, but I need to know how most 3d formats or 3d model programs represent them, becuase I need to implement them. My idea would be that each bone has several vertexes associated at a relative position to it. Then the bones are positioned, and you have skeleton movement. What is the 3d standard of how this is represeented? I could implement my own skeleton system, and a peronal 3d editor, but that would be a waste of time.

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Each bone has a matrix (or quaternion) associated with it, and each vertex has one (or more) bones accosiated with it (with various weights that should all add up to 1). So, v0 may be affect by b0 with a weight of 0.25 and b1 with a weight of 0.75. So, you just transform each vertex by the matrices that affect it, and add those vertices together with the proper weights.


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