Tsplines

T-splines, sometimes written as Tsplines, are a type of geometric modeling surface representation that generalizes NURBS by enabling local refinement through T-junctions in a T-mesh. Unlike traditional NURBS, which rely on a rectangular lattice and require global knot insertion to add detail, T-splines allow adding control points locally where extra detail is needed. The surface is defined by rational blending functions over a network of quad elements connected by T-junctions, with boundary behavior compatible with NURBS so that T-splines can be integrated into existing CAD workflows.

Key characteristics include local refinement without reshaping the entire surface, the ability to represent complex topology with fewer control points, and support for rational weights to achieve exact representations of common shapes. T-splines can be used to create smooth surfaces, sharp features, and multi-patch configurations, and they can be trimmed or combined in ways similar to NURBS-based models, though with a more flexible internal mesh.

Development and use of T-splines emerged in the CAD community as a solution to the limitations of global refinement in NURBS. They gained attention through academic work and later through commercial plugins and toolchains that implemented T-spline concepts for surface modeling. Interoperability between T-spline models and traditional NURBS or polygonal formats has been a consideration, affecting adoption in some pipelines.

Applications of T-splines span product design, automotive and aerospace surface modeling, architecture, and other areas where complex, locally refined surfaces are advantageous. Advantages include local control and topology flexibility, while challenges involve managing the more complex data structure and ensuring compatibility across different software environments.