Applications of Lodrigues matrix in 3D coordinate transformation

Abstract

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: 1 the traditional rotation angles θ,φ,ψ, are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; 2 directly and accurately calculating the formula of seven parameters in any value of rotation angles; and 3 a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.