Periodic Smoothing Spline Surface and Its Application to Dynamic Contour Modeling of Wet Material Objects

This paper considers a problem of optimal design of periodic smoothing spline surfaces employing normalized uniform B-splines as the basis functions. The surface can be periodic in either of two variables or in both. The expressions for optimal solutions are concise and are readily solved numerically. These periodic surfaces can be used to construct closed or semiclosed surfaces in the 3-D space. Assuming that the data are obtained by sampling some surface with noises, we present convergent properties of optimal spline surface when the number of data becomes infinity. The results are applied to the problem of modeling contour of wet material objects with deforming motion. The effectiveness is examined by numerical and experimental studies.