TY - JOUR
T1 - Solution of Nine-Parameter Affine Transformation Based on Quaternions
AU - Özgür Uygur, Süreyya
AU - Akyilmaz, Orhan
AU - Aydin, Cüneyt
N1 - Publisher Copyright:
© 2021 American Society of Civil Engineers.
PY - 2021/8/1
Y1 - 2021/8/1
N2 - A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.
AB - A least-squares solution for (a)symmetric nine-parameter three-dimensional affine coordinate transformation based on quaternions is presented. Retrieval of the nine transformation parameters (three translations, three scale factors, and three Euler rotation angles) and their covariance matrix from the quaternion-based estimates is given in detail. The proposed method can successfully handle all the cases regardless of the magnitude of the parameters and full covariance matrices of the control points. Efficiency and consistency of the solution are discussed within five different case studies consisting of many numerical examples.
UR - http://www.scopus.com/inward/record.url?scp=85107305291&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)SU.1943-5428.0000364
DO - 10.1061/(ASCE)SU.1943-5428.0000364
M3 - Article
AN - SCOPUS:85107305291
SN - 0733-9453
VL - 147
JO - Journal of Surveying Engineering, - ASCE
JF - Journal of Surveying Engineering, - ASCE
IS - 3
ER -