For pattern recognition and computer vision, fitting of curves and surfaces to a set of given data points in space is a relevant subject. In this paper, we review the current orthogonal distance fitting algorithms for parametric model features, and, present two new algorithms in a well organized and easily understandable manner. Each of these algorithms estimates the model parameters which minimize the square sum of the shortest 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. We give various examples of fitting curves and surfaces to a point set in space.