Question

Given a quaternion value, I would like to find its nearest neighbour in a set of quaternions. To do this, I clearly need a way to compare the “distance” between two quaternions. What distance representation is needed for such a comparison and how is it computed?

Thanks,

Josh

Answer 1

Is your quaternion just a point in 3D space with an orientation?

Then the distance between two quaternions x1,y1,z1,w1 and x2,y2,x2,w2 is given by:

distance = sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2), assuming that the w component is used for orientation. I.e. this is the same as the distance between two 3D points.

Is your quaternion a point in 4D space?

Then the distance between them is given by:

distance = sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2 + (w1-w2)^2).

Which is just the extension to 4D space. This euclidean distance formula works in any number of dimensions.