T-Spline (mathematics)
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This article does not cite any references or sources. (October 2012) |
T-spline is a method of representing a smooth surface. The T-spline technology is a bridge between NURBS surfaces and subdivision surfaces. A T-spline can be thought of as a NURBS surface for which a row of control points is allowed to terminate, without traversing the entire surface, in a point called the star point. The star points are also called inner T-points, poles, or extraordinary points. T-splines eliminate superfluous control points and are easier to merge than the NURBS surfaces. Modeling organic surfaces with T-splines reduces the number of control points twofold in comparison with the NURBS surfaces. T-splines are forward and backward compatible with NURBS surfaces because they are a superset of NURBS, and they can, in theory, do everything that NURBS can do. In practice, enormous amount of programming was required to make NURBS work as well as they do, and creating the equivalent functionality in T-Splines would require similar effort. T-splines were invented by Thomas W. Sederberg in 2003. In 2007 the U.S. patent office granted him patent number 7,274,364. The acquisition of T-spline technology by Autodesk in 2011 implies that this technology is very important for the CAD industry.
T-splines, subdivision surfaces, NURBS surfaces, and polygon meshes are competing technologies. Subdivision surfaces are gaining widespread adoption in the animation industry. Polygon meshes hold a major advantage over NURBS surfaces in that they can contain any topology, such as holes, branches, and handles. Another flaw of the NURBS surfaces is that it is mathematically impossible for a trimmed NURBS surface to accurately represent the intersection of two NURBS surfaces without introducing gaps in the model. Polygon meshes are in general ignored in industrial design because of their lack of precision. Also, trimming is not yet possible with polygon meshes and subdivision surfaces. T-splines can function as a bridge between the polygon meshes and the NURBS surfaces. Pixar variant of the subdivision surfaces has the advantage of edge weights. T-splines do not yet have edge weights but they are generally superior to the subdivision surfaces and polygon meshes.
