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For a research project, I need to reimplement Blender's constraints with behaviour as close as possible to their Blender implementation. I am currently struggling to understand how the inverse kinematics (IK) constraint uses the pole target in its computation. I see it has something to do with the x axis of the first bone of the chain, chain[0] (let's say that chain is a list of bones starting from the first one all the way to the effector, which is the one which bears the IK constraint)

I understand the effect of the pole angle (it applies after the IK solve, and simply rotates the first bone of the chain around the (chain[-1].tail - chain[0].head) axis). So for the sake of simplicity we can only discuss the case where that pole angle is 0.

According to this stackexchange, the IK constraint (with a pole angle of 0) supposedly aligns pole_target.head - chain[0].head (projected on the XZ plane of chain[0]) and chain[0]'s x axis. However, when I try to compute those vectors, they turn out not to be aligned.

So my question is : does anyone have any idea which vectors are aligned by the IK constraint?

Thanks!

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