A new approach to solid modeling with trivariate T-splines based on mesh optimization

We present a new method to construct a trivariate T-spline representation of complex genus-zero solids for the application of isogeometric analysis. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation.

► We present a new method to construct a trivariate T-spline model of complex solids. ► The volumetric parameterization of solids uses only the solid surface as input data. ► Adaptive tetrahedral meshes are a result of the parameterization process. ► The procedure is fully automatic for genus-zero solids. ► It might be adapted to solids with surfaces of any genus by using the meccano method.