Spline Volume Fairing

The use of trivariate NURBS in isogeometric analysis has put the quality of parametrization of NURBS volumes on the agenda. Sometimes a NURBS volume needs a better parametrization to meet requirements regarding smoothness, approximation or periodicity. In this paper we generalize various smoothing methods that already exist for bivariate parametric spline surfaces to trivariate parametric spline volumes. We will also address how rational and polynomial spline volumes create different challenges and solutions in the algorithms.