Quote:Original post by lesshardtofind
"Do some more reading. And keep Einstein out of this."
I was hoping to get actual mathematic responses, not insults of implied ignorance that mean nothing when they are unquantified.
Sorry, I didn't mean to insult you. But you wrote a whole lot of text based on not much understanding of the situation, so I suggest you read more, get familiar with the computations, write some code, experiment a bit... These things take time. If you just heard about quaternions, it's understandable that you are confused.
I am going to try to explain why some of the things you said didn't make sense to me. But please don't take it as an insult.
Quote:Well it can be assumed that a unit vector is also a radius of a Unit Circle.
I am already not sure of what you mean. The radius of a circle is either a segment or a length, not a vector. And if you mean to imply a circle centered at the origin, and to have the vector represent the segment from the origin to some point at a distance of one, you should really say these things. Even then, there are many possible circles for which that segment is a radius.
Quote:I assumed that taking three unit vectors could derive a unit sphere[...]
That part I just don't understand at all.
Quote:From there it is safe to assume that you can find any given angle in radians and degrees from any given two points within that sphere using the calculus omega function. Angle between any two vectors or points can be derived from.
Both A and B are vectors
(I believe this equation is coplanar though so that you can translate it to a change in X, Y, or Z
)
cos Omega = (A*B)/A.length * B.length
or
Omega(radians) = acos((A*B)/(A.length * B.Length))
This is how angles are defined. I don't know what it has to do with your three circles, though.
Quote:Then knowing that i, j, k represent a "unit" vector of a "unit" sphere then you could establish that unit as a One radian or Pi.
Now you are mixing vectors and angles. I don't understand what you mean. Are you talking about rotations already?
Quote:Knowing that any point in space is created by 3 Planes XY, XZ, YZ you could assume the same would be true with any point on this sphere being represented by 3 diffent unit circles Unit Circle XY, XZ, YZ.
Points are not "created" by planes. There are other things you can say about points and planes that might be what you mean, but as it is, I don't understand it.
Quote:[...whole paragraph where I didn't understand anything...]
What I'm not able to figure out at this moment, why the need for W. And based on Einsteins theory of relativity why even W and not T? And if it was T then it could be assumed that all objects in a current rendering process have the same T so why even use it at all?
It is not the case that any 4-dimensional space represents the space-time continuum of Einstein. This one in particular has nothing to do with it. You cannot interpret the real part of the quaternions as time because that's not what it represents.
I would go back to the way complex multiplication by a unit-length number represents 2D rotation. The real part is the cosine of the angle of rotation. In quaternions the situation is similar, except rotation is achieved by multiplying a quaternion times a vector times the inverse of the quaternion (the conjugation of the vector by the quaternion), so you end up applying the angle twice, so the real part is the cosine of half the angle. This last sentence is not very precise, but perhaps it can help you develop some intuition.
In complex numbers, the real part tells you how much you'll rotate by, and the imaginary part is then determined up to sign by the fact that the length should be 1. The sign just tells you which way you rotate. In 3 dimensions, the real part still tells you how much to rotate, but now you need to specify which axis to rotate around, which is why you need a three-dimensional imaginary part.