Parametric Cubic Spline Research Articles

Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers

The complex feedback between process and form that governs planform migration of meandering rivers is still incompletely understood. Current theoretical models aimed at predicting planform migration relate the rate of meander migration at a particular location to the channel curvature at and upstream of that location. However, these models are still incapable of reproducing complex forms of bend development, such as compound loops. Evaluation of such models requires a representation of planform curvature better than that provided by traditional methods where the curvature is calculated from directional change between the successive digitized points—an approach that provides a discrete representation of curvature dependent on the density of the digitized points used to characterize the channel planform. This article presents and evaluates a methodology that provides a continuous functional representation of the planform geometry and curvature of meandering rivers. The method involves the fitting of splines, specifically parametric cubic splines (PCSs), to discrete digitization data of the channel centerline (CL) and the arc‐length parameterization of the resulting composite curve. The arc‐length parameterized PCS‐interpolated curve is then used to compute analytically the channel CL location and curvature for any value of the streamwise axis. Evaluation of the method involves examination of the effects of digitization interval size and digitization error on the characterization of the planform geometry and curvature using PCS fitting. The derivation of curvature values from continuous planform function for any location and any spatial interval overcomes the reliance either on average bend curvature values or on discrete curvature values based on digitized points.

Modelling the Interface Pressure Applied by Knitted Structures Designed for Medical-textile Applications

A theoretical model is proposed for prediction of the interface-pressure profile applied by plain-knitted elastomeric structures used in compression therapy. Compression therapy may be applied through pressure garments to prevent and reduce venous reflux and peripheral oedema. The interface pressure induced by a compression garment is defined by Laplace's equation, and the geometrical and mechanical behaviour of knitted structures is modelled to predict interface pressure. The geometrical mesostructure is modelled by parametric cubic-spline curves, and the mechanical system is modelled on energy-based principles. The model incorporates all possible mechanisms of deformation, including elongation, bending, compression, and volume changes of the yarns. The theoretical predictions are compared with experimental pressure profiles for four different radii of curvature.