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The development of ''Non-Uniform Rational B-Spline'' (NURBS)originated with seminal work at [[Boeing]] and [[SDRC]] (Structural Dynamics Research Corporation) in the 1980s and '90s, a company that led in mechanical computer-aided engineering in those years.<ref>[http://isicad.net/articles.php?article_num=14940 "NURBS and CAD: 30 Years Together"], Ushakov, Dmitry, isicad, December 30, 2011.</ref> Boeing's involvement in NURBS dates back to 1979, when they began developing their own comprehensive CAD/CAM system, TIGER, to support the diverse needs of their aircraft and aerospace engineering groups. Three basic decisions were critical to establishing an environment conducive to developing NURBS. The first was Boeing's need to develop its own in-house geometry capability. Specifically, Boeing had complex surface geometry needs, especially for wing design, that could not be found in any commercially available [[CAD/CAM]] system. As a result, the TIGER Geometry Development Group was established in 1979 and has received strong support for many years. The second decision critical to NURBS development was the removing the constraint of upward geometrical compatibility with the two systems used at Boeing at that time. One of these systems had evolved due to the iterative process inherent to wing design, while the other was best suited for adding to the constraints imposed by manufacturing, such as cylindrical and planar regions. The third crucial decision was simple but essential: adding the "R" to "NURBS." Circles were to be represented precisely, with no cubic approximations allowed.

By late 1979, there were 5five or 6six well-educated mathematicians (PhD'sPhDs from Stanford, Harvard, Washington, and Minnesota). and someSome had many years of software experience, but none of them had any industrial, much less CAD, geometry experience. Those were the days of the oversupply of math PhDs. The task was to choose the representations for the 11 required curve forms, which included everything from lines and circles to Bézier and B-spline curves.

By early 1980, the staff were busy choosing curve representations and developing the geometry algorithms for TIGER. One of the major tasks was curve/curve intersection. It wasbecame noticed very quicklyevident that one could solveif the general intersection problem if one could solve itsolved for the Bézier/Bézier case, sincethen everythingit could be representedsolved infor Bézierany formcase. atThis is because everything from the lowest level. could be represented in Bézier form. It was soon realized that the geometry development task would be substantially simplified if a way could be found to represent all of the curves using a single form.

With this motivation, the staff started down the road toward what became NURBS. The design of a wing demands free-form, C2 continuous, cubic splines to satisfy the needs of aerodynamic analysis, yet the circle and cylinders of manufacturing require at least rational Bézier curves. The properties of Bézier curves and uniform B-splines were well known, but the staff had to gain an understanding of non-uniform B-splines and rational Bézier curves and try to integrate the two. It was necessary to convert circles and other conics to rational Bézier curves for the curve/curve intersection. At the time, none of the staff realized the importance of the work, and it was considered "too trivial" and "nothing new". The transition from uniform to non-uniform B-splines was rather straight forward, since the mathematical foundation had been available in the literature for many years. It just had not yet become a part of standard CAD/CAM applied mathematics.