Orthogonal distance fitting of parametric curves and surfaces

Fitting of parametric curves and surfaces to a set of given data points is a relevant subject in various fields of science and engineering. In this paper, we review the current orthogonal distance fitting algorithms for parametric models in a well organized and easily understandable manner, and present a new algorithm. Each of these algorithms estimates the model parameters minimizing the square sum of the error distances between the model feature and the given data points. The model parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The new algorithm is applicable to any kind of parametric curve and surface. We give fitting examples for circle, cylinder, and helix in space.