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I have been carrying out 2D and 3D operations, including graphics, for many years and have never used quaternions so I don't have a feel for them. I know that they can be used for certain operations that are difficult in Euler angles and also that they can be used to find the rotation required to best fit one set of coordinates (X1, X2...XN, X=(xyz)) onto another (X1', X2'... XN').
Are there places where quaternions are essential? And are there places where they make solutions more elegant or more efficient?
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Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis.
The motivation for using quaternions is the data stability, considering that the rotation using Euler angles can present more errors and the occurrence of Gimbal Lock [12, 13].
Quaternions are absolutely more accurate. There is a problem called Gimbal lock which was found in Euler angles. It happens when two axis align together. On the other hand quaternions are more flexible and solved this problem as it is more axis oriented.
Quaternions are an alternate way to describe orientation or rotations in 3D space using an ordered set of four numbers. They have the ability to uniquely describe any three-dimensional rotation about an arbitrary axis and do not suffer from gimbal lock.
They have a smaller memory footprint than rotation matrices and they are more efficient than both matrix and angle/axis representations.
Also:
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