Rotations - from complex numbers to quaternions

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MS Student



Rotation is one of the fundamental operations of geometry. It provides a way to transform vectors from one location to another while hinged with respect to a pre-defined axis. In this first part of the two part primer we introduce this simple yet often confusing geometric operation in 2D and 3D. We start with the complex number representation of the rotation operation in 2D and its connection to the standard matrix version. Then we discuss the Euler-angle representation of rotation of vector basis, their extrinsic and intrinsic forms. Ultimately we introduce quaternions, which are the natural extension of complex numbers to 3D. In the process, we also look at Gimbol locking, an intrinsic berrier in Euler-angle represetation. Each concept discussed is explained with a worked out example and a supplemental python--code that numerically implements these examples.

Click here to read the article (a pdf version of this primer is available here).