(splīn) 1. A spline interpolator of order m satisfies all specified points and their derivatives up to the order (m–1). Thus a quadratic spline has a continuous first derivative and a cubic spline has both first and second derivatives continuous. Splines are used for digital-to-analog conversion that employs curve (or surface) fitting, to assure a desired degree of smoothness. Splines are implicit features of many modeling and inversion programs, used to provide an analytic form to the properties of the model over the entire data domain. 2. A long flexible strip used in drawing a smooth curve. 3. Both the long flexible strip and analytic splines are sometimes used in residualizing, the smooth curve representing the regional and the difference between the smooth curve and the gravity profile representing the residual. By extension, a smooth surface used to represent a regional gravity field.