quaternions

I want to find the "distance" between two quaternions. By "distance" I mean a single float or int, not another quaternion (that would be the difference, i.e. inverse(q1)*q2 ). I guess you could call what I want "angular magnitude". I need to apply more torque to a physics object the further it's rotated from its original angle. I don't understand the maths involved in quaternions, so a code-based example would be most helpful. I've looked at several other questions but I don't believe any answer my question, or at least not in a way I understand it. Find the difference quaternion qd = inverse

I'm using quaternions in my game, and I'm wondering how, when I have two orientation quaternions, I can get the rotation quaternion needed to go from the first one, q1, to the second one, q2. I'm self taught, so there may be obvious solutions missing from my vocabulary. In equations, what I'm doing when I rotate from the first one to the other is as follows: q2 = r * q1 However, now r is the unknown. Do the rules of algebra count here too? If that's the case, I'd end up dividing a quaternion by another, something I can't find a good explanation for on the internet. I'm using a program called

i have a coordinate system where the Y axis is UP. I need to convert it to a coordinate system where Z is UP. I have the rotations stored in quaternions, so my question is : if i have a quaternion X,Y,Z can i switch the Y with the Z and get the result that Z is actually UP? Just swpping two axes in a quaternions? No this doesn't work because this flips the chirality. However if you flip the chirality and negate the quaternion's real part then you're back in the original chirality. In general form you can write this as Q'(Q, i'j'k') = ε i'j'k' Q w _w + Q i _i + Q j _j + Q k _k where is the

I'm trying to implement a functionality that can convert an Euler angle into an Quaternion and back "YXZ"-convention using Eigen. Later this should be used to let the user give you Euler angles and rotate around as Quaternion and convert Back for the user. In fact i am realy bad at math but tried my best. I have no Idea if this matrices are correct or anything. The code Works, but my results are way to off, i suppose. Any idea where i take the wrong turn? This is what my Quat.cpp looks like: #include "Quat.h" #include <Eigen/Geometry> #include <Eigen/Dense> #include <cmath> #include <iostream>

I have a model rotated by a quaternion. I can only set the rotation, I can't add or subtract from anything. I need to get the value of an axis, and than add an angle to it (maybe a degree or radian?) and than re-add the modified quaternion. How can I do this? (answer on each axis). You can multiply two quaternions together to produce a third quaternion that is the result of the two rotations. Note that quaternion multiplication is not commutative, meaning order matters (if you do this in your head a few times, you can see why). You can produce a quaternion that represents a rotation by a given

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 Olhovsky 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