Truncated T-splines: Fundamentals and methods

In this paper, we present Truncated T-splines as a new type of T-splines suitable for both geometric design and analysis, supporting highly localized refinement. Truncated T-spline basis functions are piece-wise polynomials that are linearly independent and form a partition of unity. Refinement of truncated T-splines produces nested spline spaces. Furthermore, we study truncated T-splines and local refinement on the general domain (2-manifold) with extraordinary points in the T-mesh. G1 continuity is attained around extraordinary points by properly capping quartic Bézier patches, where a constrained optimization problem is solved. In the end, we study benchmark problems using truncated T-splines in the context of isogeometric analysis. We also apply truncated T-splines to complex geometries to show the smooth surfaces and simulation results under local refinement.