| dc.description.abstract | This paper introduces the concept of interpolation consistency. It is claimed that this property is an essential one for splines that are intended for use in Computer Aided Design. Consistency is defined as the property of an interpolation algorithm that, if the given set of points is extended by any point on the interpolated curve, the algorithm applied to the extended set of points will yield exactly the same curve as before. A clear distinction is made between function interpolation, where y is a function of x, and curve interpolation, where x and y are Cartesian coordinates in the geometric plane. The class of consistent curve interpolating planear splines that corresponds to cubic function interpolation is discussed in some detail and includes the Cornu spiral, the lemniscate, and the tension-free mechanical spline. Next the class that corresponds to pentic function interpolation is considered, and an efficient algorithm is presented for the calculation of one such spline, a planar spline where the curvature is a cubic polynomial in the arclength. This algorithm produces curves where the curvature is, loosely speaking, as constant as possible. Some examples illustrating the desirable properties of this spline are given. | en_US |
