Quaternion Class with Comprehensive Quaternion Operations

Quaternions are complex number extensions consisting of one real part and three imaginary parts. The MATLAB quaternion class enables fundamental quaternion operations including addition, subtraction, multiplication, and division through built-in operator overloading. Key functions like quatmultiply handle quaternion multiplication while normalize and conj manage normalization and conjugation operations. Quaternions excel in describing rotational states in physical systems, offering superior readability and mathematical elegance compared to Euler angles. The class implements rotation transformations using quaternion-vector multiplication, typically achieved through the quatrotate function or direct quaternion multiplication with position vectors. In practical applications, quaternions find extensive use in robotics for orientation representation, computer vision for image rotation, and relativity physics for Lorentz transformations. Understanding quaternions and their MATLAB implementation proves particularly valuable when working with 3D transformations, where the quaternion class provides methods like slerp for spherical linear interpolation and euler2quat for conversion from Euler angles. The MATLAB implementation typically involves creating quaternion objects using the quaternion constructor with four components (a + bi + cj + dk), followed by mathematical operations using standard arithmetic operators or specialized quaternion functions for advanced applications.