Fairing spline curves and surfaces by minimizing energy

New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify thèbad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorithms are more general than the existing algorithms in that the new algorithms can adjust more than onèbad' data point in each modi®cation step and they include the existing algorithms [Computer-Aided Design 15(5) (1983) 288±293; 28 (1996) 59±66] as special cases. Test results of the new algorithms are included.