Weighted T-splines with application in reparameterizing trimmed NURBS surfaces

To facilitate isogeometric analysis, this paper presents a new type of T-spline named the weighted T-spline, which introduces a new weighting idea to T-spline basis functions. Weighted T-spline basis functions satisfy partition of unity and are linearly independent. In addition, we apply the bicubic weighted T-splines to reparameterize trimmed NURBS surface patches. Edge interval extension is performed to reconstruct the trimming curve on the T-spline surface, and the trimming curve can be exactly preserved. Comparisons with standard T-splines show that the weighted T-splines can decrease the required number of control points and T-mesh elements. The surface error introduced by weighted T-spline basis functions is bounded (within 0.5%), and the error introduced by the trimming curve is constrained within its three-ring neighboring elements. Weighted T-spline models are also applied to solve the linear elasticity problems and Poisson’s equation, demonstrating that they can be used in isogeometric analysis.