Surface Blending Using T-splines in Semi-NURBS Form

Surface blending is a permanent topic in computer aided geometric design. This modeling operation that generates smooth connection between given surfaces has been studied by many researchers. However, as the interests grow of integrated modeling system based on isogeometric analysis (IGA), some requirements that have not been fully discussed by conventional approaches become crucial, such as the exact spline representation of the blending surface, and the seamless merging of the modeling results. To address these problems, a surface blending method based on T-splines in semi-NURBS form is proposed in this paper. The flexibility and unstructured nature of T-splines provide a powerful foundation to achieve blending construction between incompatible NURBS or T-spline surfaces without disturbing them or inserting any redundant control points. Through a reasonable arrangement of the topological T-mesh, C² continuity constraints between T-splines are transformed into explicit formulae to construct the blending surface. Additionally, the generated model is one single watertight T-spline surface that can be easily used for isogeometric analysis. Several experimental examples validate the effectiveness and flexibility of the proposed blending method.