In
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
, a T-spline is a
mathematical model for defining
freeform surfaces. A T-spline surface is a type of
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
defined by a network of
control points where a row of control points is allowed to terminate without traversing the entire surface. The control net at a terminated row resembles the letter "T".
Modeling surfaces with T-splines can reduce the number of control points in comparison to
NURBS
Non-uniform rational basis spline (NURBS) is a mathematical model using B-spline, basis splines (B-splines) that is commonly used in computer graphics for representing curves and Surface (mathematics), surfaces. It offers great flexibility and pr ...
surfaces and make pieces easier to merge, but increases the book-keeping effort to keep track of the irregular connectivity. T-splines can be converted into NURBS surfaces, by knot insertion, and NURBS can be represented as T-splines without T's or by removing knots. T-splines can therefore, in theory, do everything that NURBS can do. In practice, an enormous amount of programming was required to make NURBS work as well as they do, and creating the equivalent T-spline functionality would require similar effort. To smoothly join at points where more than three surface pieces meet, T-splines have been combined with
geometrically continuous constructions of degree 3 by 3 (bi-cubic) and, more recently, of degree 4 by 4 (bi-quartic).
Subdivision surfaces, NURBS surfaces, and
polygon mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedral object. The faces usually consist of triangles ( triangle mesh), quadrilaterals (quads), or other simple convex p ...
es are alternative technologies. Subdivision surfaces, as well as T-spline and NURBS surfaces with the addition of geometrically continuous constructions, can represent
everywhere-smooth surfaces of any connectivity and topology, such as holes, branches, and handles. However, none of T-splines, subdivision surfaces, or NURBS surfaces can always accurately represent the (exact, algebraic)
intersection of two surfaces within the same surface representation. Polygon meshes can represent exact intersections but lack the shape quality required in
industrial design. Subdivision surfaces are widely adopted in the animation industry.
Pixar
Pixar Animation Studios (commonly known as Pixar () and stylized as P I X A R) is an American computer animation studio known for its critically and commercially successful computer animated feature films. It is based in Emeryville, Californ ...
's variant of the subdivision surfaces has the advantage of edge weights. T-splines do not yet have edge weights.
T-splines were initially defined in 2003. In 2007 the
U.S. patent office
The United States Patent and Trademark Office (USPTO) is an agency in the U.S. Department of Commerce that serves as the national patent office and trademark registration authority for the United States. The USPTO's headquarters are in Alexa ...
granted patent number 7,274,364 for technologies related to T-Splines. T-Splines, Inc. was founded in 2004 to commercialize the technologies and acquired by
Autodesk, Inc.
Autodesk, Inc. is an American multinational software corporation that makes software products and services for the architecture, engineering, construction, manufacturing, media, education, and entertainment industries. Autodesk is headquartered ...
in 2011.
External links
Technical articles about T-splinesTransitioning from NURBS to T-splines (67-minute video)NURBS and CAD: 30 Years TogetherAn open source T-spline kernel
References
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Computer-aided design
Splines (mathematics)