Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Computational Study of the 3D Affine Transformation Part I. 3-point Problem

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Robert H. Lewis
Organization: Fordham University
Department: Department of Mathematics
Piroska Zaletnyik
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
Revision date


In case of considerable nonlinearity i.e. in geodesy, photogrammetry, robotics, it is difficult to find proper initial values to solve the parameter estimation problem of 3D affine transformation with 9 parameters via linearization and/or iteration. In this paper, we developed a symbolic - numeric method to achieve the solution without initial guess. Our method employs explicit analytical expressions developed by computer algebra technique via Dixon resultant for solving 3 -point problem. Numerical illustration is presented with real world geodetical data representing Hungarian Datum.

*Applied Mathematics
*Social Science > Geography and Cartography

9-parameter 3D transformation, solution of polynomial system, symbolic solution, Dixon resultant, early discovery factors, Groebner basis, homotopy, Jenkins-Traub algorithm, global minimization, genetic algorithm
Downloads Download Wolfram CDF Player

3Daffine_FullPart_1modified08.nb (2 MB) - Mathematica Notebook [for Mathematica 6.0]