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What is the magic underneath the covers that makes T-Splines such a unique and compelling new technology? How does T-Splines overcome limitations that are inherent to existing NURBS and subdivision based modeling approaches? Four key components of the patented T-Splines technology make it all possible:


A non-uniform rational b-spline Surface or NURBS surface is defined by a set of control points which lie, topologically, in a rectangular grid. This means that, in practice, a large percentage of NURBS control points are superfluous in that they contain no significant geometric information, but merely are needed to satisfy the topological constraint.

In the frog model below, 55% of the NURBS control points are superfluous. In contrast, a T-Spline’s control grid is allowed to have partial rows of control points. A partial row of control points terminates in a T-Point, hence the name T-Splines. In the T-Splines frog, the red control points are T-Points.

Frog Frog
NURBS frog (11625 control points) Courtesy Zygote Media T-Splines frog (5035 control points)

Minimizing control points makes it easier to create models, control surface smoothness, decrease file size, and speed up editing time.

Local detail

As a direct result of the ability to create partial rows of control points within a single surface, the user can now create a surface with varying level of detail only where required.

Refinement, the process of adding new control points to a control mesh without changing the surface, is an important basic operation used by designers. A limitation of NURBS is that refinement requires the insertion of an entire row of control points, increasing the density of the mesh across the entire surface. T-Points enable T-Splines to be locally refineable. As shown below, a single control point can be added to a T-Splines control grid.

Above: T-Splines cup, after local refinement, after moving points

Support for local detail in a single surface makes it easier to model complex shapes and create smooth watertight models.

Non-rectangular surfaces with star points

With T-Splines, non-rectangular surfaces can be constructed using star points, also called poles or extraordinary points. This overcomes another fundamental NURBS limitation: In NURBS surface modeling, constructing a complex shape with varying detail, curvature or smoothness requires many individual rectangular patches. Maintaining continuity and smoothness across these patch surfaces is a significant challenge.

Above: Creating the watering can model above (left) required many NURBS patches. This same model in T-Splines (right) is a single watertight surface. Courtesy David Quinn and Juan Santocono

Star points also enable modeling techniques such as extrusion, face deletion, and merging of surfaces that greatly increase design freedom for the user. Star points are used today in subdivision surface modeling, which is popular in animation, but T-Splines introduces them to industrial design in a NURBS-compatible format for the first time.

100% compatibility to NURBS

All T-Splines surfaces are 100% compatible with NURBS and create gap-free, smooth and manufacturable surfaces. T-Splines surfaces can be converted to untrimmed NURBS surfaces, and vice-versa, without any loss or change to the surface shape.

T-Splines provides a far more efficient conversion of designs to NURBS than converting directly from subdivision or polygonal modelers. T-Splines bridges gaps between popular polygonal modeling capabilities and traditional NURBS modeling.

Above: Duck toy model converted from polygons to T-Splines to NURBS

T-Splines easily integrates into existing design processes and workflows, with seamless transfer of designs to engineering and manufacturing.

The T-Spline technology addresses some important limitations that are inherent in conventional NURBS surfaces. T-Splines are based on solid mathematical principles. An important practical consideration is that T-Splines are forward and backward compatible with NURBS.
--Dr. Rich Riesenfeld, Founder of B-splines in CAD