11–20 of 184 posts
Dual quaternions are even better for dealing with dynamic 3D space http://www.chinedufn.com/dual-quaternion-shader-explained/
I kind of expect someone better versed in Geometric Algebra to come along and explain how it somehow also supersedes that.
Also I believe that technically they call under Clifford algebra.
Dual quaternions are even better for dealing with dynamic 3D space http://www.chinedufn.com/dual-quaternion-shader-explained/
This 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.
Also I believe that technically they call under Clifford algebra.
Is this the same Marc Ten Bosch as from Miegakure [1]? Considering the content, probably the same person. [1] http://miegakure.com/
Also, I've seen several articles trying to convince me that alternative transformation representations like these are better, but I haven't seen much code. Has anyone written a library using these concepts that could replace a traditional vector math library like https://glm.g-truc.net/ for games?
This article will take more than than I have to digest right now, but it's definitely saved. I have never really understood quaternions. All I knew is that I could use that instead of euler angles, avoid gimbal lock, and would blindly use them.
It's also great for interpolation
This article will take more than than I have to digest right now, but it's definitely saved. I have never really understood quaternions. All I knew is that I could use that instead of euler angles, avoid gimbal lock, and would blindly use them.
Earlier quoted context omitted.
I kind of expect someone better versed in Geometric Algebra to come along and explain how it somehow also supersedes that.
GA 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.
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!
This article will take more than than I have to digest right now, but it's definitely saved. I have never really understood quaternions. All I knew is that I could use that instead of euler angles, avoid gimbal lock, and would blindly use them.
I think it's called gimbal lock?