| Rapidly convergent algorithms for fitting circles, parabolas, and clothoids to measured points are developed and tested. A solution of the line fitting problem is also presented for a complete treatment of the curves encountered in civil engineering route design. The second order, reduced Hessian method, broadly applicable to the class of scalable, C{dollar}sp2{dollar} parametrizations, is orthogonal distance regression with four-parameter similarity transformations. The local parameters, or state variables, are implicitly eliminated, and second order solutions are rigorously computed in the model parameter space (rank {dollar}le{dollar} 4). The algorithms are further distinguished from earlier works by the inclusion of approximation procedures that yield very good starting values. Additionally, a strong connection between the Helmert transformation and the total least squares problem is established, and a fixed point method is suggested. |
