A nonuniform rational B-spline (NURBS) is a mathematical form used in computer graphics to create 3D models of organic curves and surfaces.

NURBS development began in the 50s of the last century by engineers who wanted to obtain a mathematically accurate representation of arbitrary surfaces (such as the hulls of ships, airplanes, spacecraft, and automobiles) with the ability to copy if necessary. Before the advent of NURBS, an engineer drew a model by hand on paper in a single copy — a reference.

NURBS do not consist of a grid of rectangles, unlike polygons, the division of these surfaces into polygons occurs only at the rendering stage and involves the use of an optimal algorithm to maintain smoothness. Therefore, at any approximation, the smoothness of the surface is maintained.

Due to the fact that NURBS surfaces are always smooth and have no sharp corners, they are widely used in organic modeling to create models of animals, people, cars and other objects. Initially, NURBS could only be used in commercial CAD systems for automotive enterprises. Now these surfaces are an integral part of the software packages SATYA, Maya, 3Ds Max, Cinema 4D, Fusion 360, Kompas 3D, Rhinoceros (Rhino), Moment of Inspiration, Alias, SolidWorks and others.

Using the NURBS design method, it is more expedient to perform reverse engineering of objects of complex shape with a large number of surfaces that change their curvature according to mathematical laws. This approach ensures greater accuracy of the result and reduces labor intensity.

RangeVision decided to find out if it is possible to speed up the NURBS design process by importing data from the Spectrum 3D scanner. The engineers used the sole of a sports shoe as an organic surface.

RangeVision faced several challenges. First, to make a highly detailed digitization of the geometry of the shoe sole. Secondly, based on the scanning data, we need to build the most accurate 3D model using the NURBS design method.

Digitization was performed in the RangeVision office under normal daylight conditions. The specialists placed the sneaker on a turntable and adjusted the Spectrum 3D scanner to a second scanning area suitable for digitizing objects from 30 cm to 1 m.

The sneakers were scanned in two positions and 16 scans were obtained (2 groups of 8 scans each). Digitization of the object took 25 minutes, and another 35 minutes were spent on post-processing and obtaining the final 3D model in .stl format in the RangeVision ScanCenter program.

After that, RangeVision specialist Dmitry Telegin began constructing a 3D model of the sneaker sole using NURBS technology.

At the beginning, the .stl file was imported into the Geomagic Studio program, and the coordinate system was also set.

Next, the scan crop line was drawn and the resulting part was deleted.

The boundary edge was smoothed out, and the existing small voids were filled.

During the preparation for NURBS design, the defects of the sole surface that were present on the standard were eliminated and digital noise was removed.

The construction and editing of the grid made it possible to design an organic surface using NURBS technology.

After the parameters for analyzing the accuracy of the constructions were set, he performed quality control of the 3D model and saved the report.

The constructed 3D model can be saved in .igs or .stp format and exported to any other program (depending on the goals set for the designer) for further work. It took a total of 4 hours to reverse engineer this facility using NURBS technology.

The task was completely solved within one working day. For comparison, it would take about 4 business days to build the same surface "from scratch" without using 3D scanning. The data obtained from the Spectrum 3D scanner was highly detailed, which made it possible to reverse engineer the organic surface using NURBS technology 8 times faster.