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The Rotations Conversion Library (RCL) is a collection of C++ functions that address common computations and numerical handling of rotations in 3D Euclidean space, including support for rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. Unit tests for each function are provided to ensure that the library performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required algorithms (see https://sourceforge.net/projects/rotationslib/).