Comment on: “dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation” by Zeng et al. (2024)

Abstract A recent paper by (Zeng et al., Earth Planets Sp 76:20, 2024) Dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation. Earth Planets Space 76, 20. https://doi.org/10.1186/s40623-024-01967-z on 3D symmetric coordinate transformations based on dual quaternions. One particular point in the paper caught my attention. The authors compared the Quaternion Algorithm (QA) and Dual Quaternion Algorithm (DQA) methods and concluded that the DQA method is more precise. However, I strongly disagree with this judgement. The purpose of this comment is not to denigrate Zeng's work, but rather to correct what I perceive to be an erroneous conclusion. Graphical Abstract