Comment by p0nce
7 years ago
Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice).
A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon.
It also encodes the rotation it would take to go from one such observer to another.
Does this assume the earth is a sphere? Can you keep the elegance of this coordinate encoding with convenient transformation operations and define somewhere a mapping from the quaternarion encoding of position into a non-homogenous oblate spheroid encoding like WGS84 ...?
> Does this assume the earth is a sphere?
Of course, speaking about Earth is just for the mental image.
> Can you keep the elegance of this coordinate encoding with convenient transformation operations and define somewhere a mapping from the quaternarion encoding of position into a non-homogenous oblate spheroid encoding like WGS84 ...?
I don't understand the question.
So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?
Encoding your whole orientation would require 3 numbers. You are restricted only to the horizon, so one number is enough.
Orientation is only two numbers, since a unit vector does the job? So, three numbers in total?
That's why it doesn't encode free orientation.