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The article explained a major advantage of quaternions over matrices. Quaternions interpolate well and matrices don’t. This property is very important for anima
by dahart 2y ago
The article explained a major advantage of quaternions over matrices. Quaternions interpolate well and matrices don’t. This property is very important for animation and other things in computer graphics, like computing frames along a 3d spline curve.
- blt 2y agoIf you are referring to slerp, the matrix version is trivial using the log and exp maps. slerp(A, B, t) = exp(t log(B A^T)) A Something more complex like splines, I am not familiar with the algorithms used for quaternions. I would bet they use Lie algebraic operations, but do they actually use anything specific to quaternions? Not disagreeing that quaternions have some computational advantages over matrices, but most of the points people repeat as "advantages of quaternions" are really "advantages of proper Lie group/algebra operations over Euler angles" that are independent of matrix vs. quaternion representation.
- Certhas 2y agoVery well put.
- Certhas 2y agoThe article also explains that the natural way to look at this property is in terms of matrix exponentials/logarithm. The space of rotation matrices is not a linear space. It's obvious that interpolation is meaningless there. The space of skew symmetric matrices is linear, so you can interpolate the generators of rotations naturally. Without this perspective, how do you even begin to understand what this interpolation does or what it actually means?