Quaternions are a way of specifying a rotation through a axis and the cosine of half the angle. They main advantage is I can pick any two quaternions and smoothly interpolate between them. Rotors are another way to perform rotations.
After a couple awesome moments of understanding, I understood it for imaginary numbers, but I'm still having trouble extending the thoughts to quaternions. How can someone intuitively think about quaternions and how they allow for rotations in 3D space?
How many questions about understanding quaternions have you read on the site? This is something that people are constantly asking about, so there is plenty of material. If you're mainly trying to 'rubber-duck' until you understand it, I would recommend mathematics chat, not posts.
If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis. The order of rotation ma...
I think the geometric algebra interpretation of complex numbers and quaternions is the best, since it reveals more directly the fact that the "imaginary numbers" can be seen as encodings of rotations/reflections. Here is a pretty straightforward explanation.
The demo generates 10 random unit quaternions and then interpolates between them indefinitely. It shows 12 WebGL canvas instances, 2 per algorithm. The top canvas displays the quaternions in 4d space and the current interpolated quaternion, the bottom canvas displays a cube that is being rotated by the current quaternion.
Simply Using Quaternions all the time for rotations is a HUGE huge mistake. Assuming the Yaw Pitch Roll convention note that this Euler angle (60, 45, 45) achieves an orientation that can ALSO be realized by (-120, 135, -135).
When dealing with quaternions, there are two variations in conventions which should be stated when describing the quaternions. The first one is if the scalar element is first or last, the second is if the coordinate system is right handed or left handed. To convert between scalar last and scalar first quaternions simply move the scalar <qx,qy,qz,qw> -> <qw,qx,qy,qz> To convert between right ...
I am using quaternions to represent orientation as a rotational offset from a global coordinate frame. Is it correct in thinking that quaternion distance gives a metric that defines the closeness ...
Why are the only (associative) division algebras over the real numbers the real numbers, the complex numbers, and the quaternions? Here a division algebra is an associative algebra where every nonzero number is invertible (like a field, but without assuming commutativity of multiplication).
