Splines and Spline Fitting Revisited

This paper presents a detailed summary of the properties and basic facts about spline spaces and their B-spline bases. Examination is made of the many different joint-continuity conditions. Geometric continuity constraints are of special interest, as they appear to satisfy visual needs of the human observers. Least-squares approximation of analytic curves and discrete point sets is also discussed. Special attention is devoted to the problem of selecting the bast fit to a closed curve, considering all the possible shifted parametric descriptions of the curve.