PrefaceLeast-squares is a term which implies that the model parameters are determined by minimizing the square sum of some predefined error measures. If a data set is a set of measurement points in 2-D/3-D space, the most natural error measure is the shortest distance between the model feature and the measurement point. This is because the measurement point is a probable observation of the nearest object point to the measurement point. The least-squares model fitting with this error measure is called orthogonal distance fitting (ODF). The square sum of the error distances can be described in two ways: the distance-based cost function and the coordinate-based cost function. The numerical methods minimizing these two cost functions are respectively called the distance-based algorithm and the coordinate-based algorithm.The ODF task has two sub-problems: not only do the model parameters have to be found but also the shortest distance points on a model feature from each given point. In general, the shortest distance point is by nature nonlinear to the model parameters. Thus, the ODF problem is inherently a nonlinear minimization problem solved through iteration. There are two minimization strategies for solving the ODF problems through iteration. The total method simultaneously finds both the model parameters and the shortest distance points, whilst the variable-separation method finds them alternately using a nested iteration scheme. Four combinations of the two numerical methods and the two minimization strategies can be applied. The combination of the distance-based algorithm with the total method results in an underdetermined linear equation system for iteration and is thus impractical for solving ODF problems. As a result, three algorithmic approaches for solving ODF problems are realistic:-Algorithm I: combination of the coordinate-based algorithm with the total method -Algorithm II: combination of the distance-based algorithm with the variableseparation method -Algorithm III: combination of the coordinate-based algorithm with the variableseparation method.This book presents the ODF Algorithms I-III for implicit and parametric curves/ surfaces in 2-D/3-D space possessing the following algorithmic features:-Estimation of the model parameters minimizing the square sum of the shortest distances between a model feature and the given points in 2-D/3-D space -General application to parametric and implicit curves/surfaces VIII Preface -Estimation of the model parameters in terms of form, position, and rotation -General implementation of the distance-based and coordinate-based algorithms -General implementation of the total and variable-separation methods -Solving ODF problems with additional constraints -Provision of parameter-testing possibilities -Robust and fast convergence -Low computing costs and memory space usage -Low implementation costs for a new model feature -Automatic determination of the initial parameter values for iteration.Chapter 1 first reviews the mathematical descriptions of curves and surfaces in s...