Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C2-continuity everywhere except the local region around irregular nodes. Finally, a Bézier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.