Short quaternions guide

[-HP-]

Addition and multiplication please
Maybe... exponential powers too ^^

[Fizyk]

jayg20769: I didn't see what you wrote, because you edited your post, but I believe Magos Mechanicus already answered your question in a separate thread

Dav1d: heh, thanks

-HP-: I'm not sure what you mean, but you already can add and multiply quaternions. There are exp() and log() functions and a ^ operator too

[Magos Mechanicus]

You just mean go through them? Just remember your parentheses and how ijk multiply with each other, really. But don't say Fizyk didn't warn you, because it's not readable at all.
(A + Bi + Cj + Dk) + (E + Fi + Gj + Hk) = A + E + (B+F)i + (C+G)j + (D+H)k

(A + Bi + Cj + Dk) * (E + Fi + Gj + Hk)
= AE + AFi + AGj + AHk + BEi + BFii + BGij + BHik + CEj + CFji + CGjj + CHjk + DEk + DFki + DGkj + DHkk
= AE + AFi + AGj + AHk + BEi - BF + BGk - BHj + CEj - CFk - CG + CHi + DEk + DFj - DGi - DH
= AE -BF - CG - DH + (AF + BE + CH - DG)i +(AG - BH + CE + DF)j + (AH + BG - CF + DE)k

For (A + Bi + Cj + Dk)^X use the multiplication method.
X=2: AA - BB - CC - DD + (AB + BA + CD - DC)i + (AC -BD + CA + DB)j + (AD + BC - CB + DA)k
= AA - BB - CC - DD + 2ABi + 2ACj + 2ADk

[Whodunnit]

hmmm , i might try quaternions, they look cool and some random problems with rotation matrices were causing me problems.

edit: http://en.wikipedia.org/wiki/Rodrigu...tation_formula this is apparently equivalent, which is what i was already using, i must have an error somewhere i need to work out . :P

[-HP-]

You just mean go through them? Just remember your parentheses and how ijk multiply with each other, really. But don't say Fizyk didn't warn you, because it's not readable at all.
(A + Bi + Cj + Dk) + (E + Fi + Gj + Hk) = A + E + (B+F)i + (C+G)j + (D+H)k

(A + Bi + Cj + Dk) * (E + Fi + Gj + Hk)
= AE + AFi + AGj + AHk + BEi + BFii + BGij + BHik + CEj + CFji + CGjj + CHjk + DEk + DFki + DGkj + DHkk
= AE + AFi + AGj + AHk + BEi - BF + BGk - BHj + CEj - CFk - CG + CHi + DEk + DFj - DGi - DH
= AE -BF - CG - DH + (AF + BE + CH - DG)i +(AG - BH + CE + DF)j + (AH + BG - CF + DE)k

For (A + Bi + Cj + Dk)^X use the multiplication method.
X=2: AA - BB - CC - DD + (AB + BA + CD - DC)i + (AC -BD + CA + DB)j + (AD + BC - CB + DA)k
= AA - BB - CC - DD + 2ABi + 2ACj + 2ADk

That's what I was after ^_^
It actually makes a little sense if you look into it

[shuntaiyo]

ummm jw what class will i learn this in in school?

ill be dreading it

[Fizyk]

Depends on where you live. Here, in Poland, it's not in the school program at all, you learn it when you go to the university, and that's only when you do something related to maths. Some teachers teach it (complex numbers, quaternions are rarely taught) as an interesting thing to know, though.

[Matte]

Depends on where you live. Here, in Poland, it's not in the school program at all, you learn it when you go to the university, and that's only when you do something related to maths. Some teachers teach it (complex numbers, quaternions are rarely taught) as an interesting thing to know, though.

I've never really understood quaternions, but I'll 'book' some time in my tight schedule to read through your guide and some other guides, so I'll know it once and for all

Do you have any good links to where I might read about quaternions?

[Drunkie]

I think my brain just exploded.

[shuntaiyo]

As a very stupid human yup I am I cannot understand this guide (I'm announcing this as a representative of the lessers of WM).
There probably isn't a better way to make this guide but if you could make it simpler it would be deeply appreciated.
(I put a decent effort into trying to understand it)

also