Twelve-Parameter Symmetric Affine 3D Coordinate Transformation Based on Dual Quaternions

Abstract

The aim of a coordinate transformation is to determine the coordinates of a point in a second coordinate system, given their known values in the first system. The subject of coordinate transformations has applications in a wide range of areas. There are different types of coordinate transformation methods: orthogonal, similarity, affine, projective, and polynomial transformations. In this study, we considered a symmetric 12-parameter 3D affine transformation based on the dual quaternion. The performances of different transformation models were compared. We also sought to determine which transformation model to use. A transformation implementation including gimbal lock has been added as an Appendix to clearly demonstrate the advantages of quaternions over Euler angles.