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.