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Bone animation and skinning

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Hi everyone,

I'm not exactly a beginner (I do quite a bit of OpenGL coding), but I'd like some advice on skeletal animation systems and how they work.
This is not a post about the artistry involved - I have no questions about how Maya/3DS Max or other packages work.

My question is really, how do I use the following data to calculate the correct position of a vertex?

for each bone I have:
- a bind pose matrix.
- a function to get the local bone transform at a specific time.

for each vertex I have:
- a position (in model space).
- an array of bone ids.
- an array of bone weights (corresponding to bone ids).

How do I go about transforming the vertex using that info?
Could someone please also explain what exactly the bind pose is used for? I've read a few documents about this, but none are very clear.

I've been stuck on this for a few days - so if I could finally understand it, it would be great.

Any help is much appreciated.

Thanks in advance!

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Bind pose is the skeletal pose, that corresponds to untransformed skin. I.e. for normal biped characters it is T-pose. I assume it is the global transformation - if not, you have to calculate the global bind matrix yourself.
The vertex transformation is done the following way:

Let matrix B2S be the rest (bind) global transformation of bone.
Let matrix P2S be the rest (bind) global transformation of the parent of given bone
Let matrix AB2P be the animated local transformation of bone
Let V be untransformed vertex and V' animated vertex


V' = (P2S * AB2P * B2S(-1))

The trick is to precalculate everything you can - B2S(-1) can be calculated once for bone, P2S * AB2P can be calculated once for animation frame

Now, if you have more than one bone transforming given vertex you just have to calculate weighted average of all transformations (i.e. weighted average of transformed vectors).
How to best do that in vertex shader depends on shader model used. If you do not want to use integer attributes and dynamic loops, you will use matrix palettes. Basically each vertex is always influenced by all bones. If in reality given bone does not transform given vertex, it's weight will be 0 for that bone.
Simple matrix palette implementation can kill performance because you have very long list of matrix operations for each vertex, most with weight 0. Depending on model and skeleton complexity it may be beneficial (or necessary) to break model into fragments so that each fragment is influenced by only subset of all bones.

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