animation - Why is it difficult to use Quaternions for the LBS(Linear Blend Skinning) formula?

Question

Why would be difficult to use quaternions for the LBS(Linear Blend Skinning) formula?:

See picture:

Linear Blend Skinning Formula

• P': Point transformed
• P: Point
• wi: matrix of weights
• wi(P): weight of point P in entry i
• Ti: Transform at i

I couldn't really find an answer, I thought that maybe because a transform matrix can store 4x4 values rather than quaternions which can only represent a rotation in 4 values then we wouldn't have a way to represent both a translation and rotation for any bone using a quaternion but I'm not too sure.

标签： animationopenglmathquaternionscomplex-numbers

Answer 1

你是绝对正确的。四元数只能表示旋转（和缩放）这一事实使它们无法用于此任务。四元数（双四元数）有一些扩展来规避这个限制。然后，线性混合效果很好。

另外，请记住如何用四元数转换一个点——你有两个乘法而不是一个。因此，您通常会先混合四元数，然后再变换点。虽然也可以混合变换后的点，但这没什么意义，因为它的计算量更大，并且与简单的 LBS 有相同的问题。

这个问题是否针对更多的东西仍然是开放的。