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This comment addresses the accuracy of conclusions regarding 3D coordinate transformations using dual quaternions.

March 26, 2026Earth Planets and Space0 citationsOpen Access

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

Key Points

This comment addresses the accuracy of conclusions regarding 3D coordinate transformations using dual quaternions.
Analysis of Zeng et al.'s comparison between Quaternion Algorithm (QA) and Dual Quaternion Algorithm (DQA) methods.
Critical evaluation of precise and accurate data between the two algorithms.
The comment argues against the conclusion that the DQA method is superior to QA in precision.
Highlights potential inaccuracies in Zeng et al.'s assessment of method effectiveness.

Abstract

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

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Sebahattin Bektaş (Tue,) studied this question.

synapsesocial.com/papers/69c4cd98fdc3bde44891a310 https://doi.org/https://doi.org/10.1186/s40623-025-02242-5

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