3 ms·
Dual quaternions are even better for dealing with dynamic 3D space http://www.chinedufn.com/dual-quaternion-shader-explained/ http://www.chinedufn.com/dual-qua
by adamnemecek 8y ago
Dual quaternions are even better for dealing with dynamic 3D space
http://www.chinedufn.com/dual-quaternion-shader-explained/ http://www.chinedufn.com/dual-quaternion-shader-explained/
- vanderZwan 8y agoI kind of expect someone better versed in Geometric Algebra to come along and explain how it somehow also supersedes that.
- adamnemecek 8y agoGA is more general, however my claim is that the DQ space is the most useful one. E.g. sedenion have little use right now. Also I believe that technically they call under Clifford algebra.
- eigenspace 8y agoClifford himself called it the geometric algebra, so many prefer to call it that, at least when applied to geometric problems. I think that there is a lot of useful structure in the geometric algebra that gets thrown out when one moves to talking about its subalgebras (ie. quaternions, dual quaternions, vectors, etc.). Its ultimately up to taste but I often find that I prefer to use the full GA instead of its subalgebras. Often some unexpected beauty or useful result drops out!
- eigenspace 8y agoThis can be better expressed in the geometric algebra by just considering a geometric algebra with a degenerate metric (ie. you use basis elements x̂, ŷ, ẑ and ϵ̂ where x̂² = ŷ² = ẑ² = 1 and ϵ̂² = 0). Including factors of ϵ̂ in your rotors now is equivalent to a dual quaternion. This way, one gets the wonderful properties of geometric algebra and the useful properties of dual quaternions together.
- adamnemecek 8y agoGA is more general, however my claim is that the DQ space is the most useful one. E.g. sedenion have little use right now. Also I believe that technically they call under Clifford algebra.