On further review of my calculus book and Wiki it appears a Quaternion is a set of 4 numbers (much like a triple or cartesian coordinates) that has another scaler (real number) added to it. or

Code:

Quaternion = W + Xi + Yj + Zk; (don't understand why wiki said that)

Seems by discription this is an ordered quad and not a formula to derive one number. (correct me if I'm wrong)

It would make more sense to me as.

Code:

Quaternion = {w, xi, yj, zk};

W being the 4th point in space. I, J, and K were throwing me off I couldn't find anything about it. Then chapter 11 (Vectors, Points, and Planes) got into a section on Unit Vectors.

Unit Vector - A vector whose length is equal to 1.

Code:

Length = sqrt((x*x) + (y*y) + (z*z))

It defined i, j, and k in the book as defualt unit vectors i.e. vectors that equal 1 in length on their respective plane.

Code:

X unit vector i = (1, 0, 0)
Y unit vector j = (0, 1, 0)
Z unit vector k = (0, 0, 1)

Am I correct in assuming that these are refering to the same thing? Then my guess would be that i, j, and k are unit vectors drawn to represent the angle of rotation of an object, but I don't get how to find 180 degrees of rotation on any given axis with i, j, and k, since they are represented as a length of 1 and therefore can only be denoted.

i || -i ,

j || -j,

k || -k

Web links I've used thus far.

OpenGL:Tutorials:Using Quaternions to represent rotation - GPWiki

Quaternion - Wikipedia, the free encyclopedia

I know the first one has the functions drawn explicitly, but I don't understand the basic math so I'm not going to copy and paste it.