Quaternionic analysis

Quaternionic analysis is a branch of mathematics that extends complex analysis into four dimensions using quaternions—numbers consisting of one real part and three imaginary parts. It studies functions defined over these quaternions, exploring how they behave smoothly and how they can be transformed, similar to how complex functions are analyzed with calculus. This field has applications in 3D computer graphics, robotics, and physics, providing tools to describe rotations and spatial relationships more effectively than traditional methods. Essentially, it offers a sophisticated way to analyze and manipulate 3D orientations and movements mathematically.