Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space

This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point. After reviewing the basics for representing curves and surfaces in space and fitting in general, the author presents three algorithms for orthogonal distance fitting combining numerical methods and minimizational methods. These algorithms are applied to implicit and parametric curves and surfaces in 2D and 3D space possessing a broad variety of algorithmic features. Finally, an appendix provides practical information for applying the general orthogonal distance fitting algorithms to fit special model features. Obvious application areas of the algorithms presented are robot navigation, including the navigation of autonomous vehicles or the grasping of work pieces, as well as factory digitization in general.