What are NURBS and Why are They Important?

The spline tools in all Ashlar-Vellum CAD and 3D modeling software products create NURBS (Non-Uniform Rational B-Splines) which are a superset of Bezier curves. These splines are curves created by a complex mathematical formula.

NURBS themselves are not surfaces but NURBS surfaces are created by interpolating a surface among NURB splines. A solid can also be constructed from a collection of analytic and NURBS surfaces with a closed boundary.

Kolorado Loung Chair. These seemingly simple surfaces, though easy for a hand craftsman to create, would be impossible for production manufacturing if Mark Robson had not designed this chair for Sifas using NURBS surfaces in Argon™.

NURB splines provide two interrelated functions. First, the curvature continuity of a surface remains intact when the curve is changed. Kinks don’t develop as the spline is altered. Second, NURB splines provide localized control of a complex curve. This lets you isolate an area and make changes without affecting the rest of the spline.

These properties are essential for precision design of objects in many industries. For example, in aerodynamic designs air molecules moving over a wing surface must flow smoothly for maximum aerodynamic lift. If the surface does not maintain curvature continuity, the air molecules separate from the wing surface and cause a vacuum. The vacuum produces an eddy as the molecules try to fill it, disrupting of air flow and increasing drag.

The Smoothie Aircraft. This two-place sport sail plane called “The Smoothie” was carefully designed by Daniel Hatfield using Cobalt™’s NURBS surfaces specifically so that air would flow over it well.

The automotive industry needs smooth air flow to improve gas mileage. Complete curvature continuity also improves styling. The appearance of a car is one of the major sales factors. As a buyer, you would be unimpressed if the reflection of the showroom lights on the car rippled and wavered. It is complete curvature continuity that makes a smooth reflection.

On-Track Electric Airport Scooter. Jean-François Jacques of Météore Design created the sleek lines and subtle curves of the award-winning On-Track electric airport scooter using the NURB surfaces in Cobalt.

Localized control of complex curves allow minor modifications to be made without adversely affecting the shape. For example, if a new, bigger engine doesn’t fit under a perfectly designed hood, you would adjust the NURB splines defining the hood surface to raise the center of the hood without changing the basic design or the continuous flow of the surface.

Surfaces created from NURB splines are also valuable for injection mold designs to eliminate the swirl of plastic as it is injected into the mold. Such designs provide better surface finishes and allow thinner cross-sections in the die.

Sand Moving Tool. Celso Santos and Christian Albanese of Rio 21 Design used NURBS surfaces to create these augers as “sand moving tools” for the award winning Spirit sun umbrella. NURBS surface definitions are mathematically efficient in describing these shapes in Cobalt as well as creating tool paths in CAM software with minimum surfaces.

Finally, consumer products also benefit greatly form the use of NURBS which make it possible for the computer to describe and manufacture shapes that our human brains find more pleasing. What was once simple to create with hand craftsmanship was impossible on a computer without NURBS because the transitions of surfaces defined by Euclidean geometry are easily detected both visually and tactilely. With the invention of NURBS technology, product shapes drawn on a computer could not only be easily adjusted, but could now contain continuous curves with efficient mathematical definitions.

Electronic Otoscope. Handheld devices, such as this electronic otoscope by Nelson Au, which allows a doctor to look inside a patient’s ear, feel better when transitions between surfaces are curvature continuous as allowed by NURBS surfaces.