Tspline

Tspline, or T-spline, is a family of surface representations used in computer-aided design and isogeometric analysis. They generalize traditional NURBS by allowing T-junctions in the control grid, enabling local refinement without requiring a global remeshing. This capability makes it easier to add detail to specific regions of a surface while preserving the rest of the model.

A T-spline surface is defined on a T-mesh, a two-dimensional grid that permits T-shaped junctions where grid lines terminate at interior vertices. The associated basis functions have local support, sum to unity, and can be arranged to achieve the desired continuity across grid lines. Local refinement is performed by inserting new knot lines that create additional T-junctions, without altering distant control points, thereby maintaining a coherent modeling workflow.

Key advantages include reduced control point counts for complex geometries, flexible topology, and smoother integration with design and analysis pipelines. T-splines can represent certain shapes more efficiently than tensor-product NURBS and support refinement where it is needed most, which is beneficial in iterative design and in isogeometric analysis where geometry and analysis share a common basis.

Limitations and considerations involve a lack of universal standardization and varying software support, as well as more complex data structures to manage T-meshes. Practical use often requires careful handling of continuity and patch compatibility when stitching multiple surfaces together. Despite challenges, T-splines remain a notable approach for flexible, locally refined surface modeling.