## What are NURBS curves in 3D modeling?

Despite the odd name, NURBS curves and surfaces are a hugely important feature in parametric 3D modeling. NURBS curves are **mathematical representations of curved shapes in three dimensions**.

Using NURBS modeling, engineers and designers can create **rounded shapes with gradual slopes and organic forms**. NURBS modeling uses complex mathematical equations to create realistic circles, arcs, and 2D surfaces that are used to draw flexible, accurate, and highly lifelike 3D models.

The rather strange acronym NURBS stands for **Non-Uniform Rational B-Splines **Modeling. The Non-Uniform part denotes that NURBS can be used to create freeform shapes. That is, you can manipulate the geometry to form whatever you want, instead of relying on set parametric shapes.

The word ‘rational’ is used to denote how NURBS evaluates and prioritizes the perceived weight or effect of each control point on the curve itself in a non-homogeneous manner. A simple B-spline cannot be used to create parabolic shapes as it must follow a uniform distribution between control points.

That B denotes the word ‘basis’. Splines are used in 3D design software to create vector works and polylines. A spline is a curve that travels along a continuous path mapped out by anchor points and control points.

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## What are splines and why are they important in NURBS modeling?

The concept of splines in 3D modeling can be hard to grasp. Originally, splines were flexible wooden strips that were used to provide an outline that designers could trace when designing curves for airplanes and boats.

**Splines work using control points** in NURBS modeling. The control points in NURBS modeling act to **define a curve by a process called ‘interpolation’**. NURBS modeling sets the control points and performs mathematical equations to average out the distance between each point.

Instead of using thousands of tiny dot points to draw a curve, the computer takes a few control points, assesses the position and rotation of each handle, and creates a continuous smooth curve. Moving any of the control points will create a new curve. Splines are an essential component in freeform modeling. Curves created with splines are highly complex. They are not as likely to warp or distort applied textures.

## The historical background of NURBS modeling

The first recorded use of B-splines is credited to Russian mathematician **Nicolai Ivanovich Lobachesky** all the way back in the 1800s. The birth of modern spline theory happened in 1946 when a Romanian- American mathematician called **Isaac Jacob Schoenberg** released a paper on data approximation.

B-splines were further refined throughout the 1970s by mathematicians **M.G. Cox** and **C. de Boor**. Cox and Boor independently invented algorithms that extended the famous de Casteljau algorithm, which was used by famed designer** Pierre Bézier** to develop the iconic curves of the Citroën DS. Further research by **W. J. Gordon** and **R. Riesenfeld **proved that Bézier curves were subsets of B-splines and outlined the powerful possibilities of B-splines for design.

The breakthrough came in 1979, when **Ken Versprille** of Syracuse University, New York, published a Ph.D. thesis on Rational B-Splines–NURBS=Non-Uniform Rational B-Splines. Versprille’s revolutionary design theories were soon developed into workable code by the tech company **Computervision**. Soon after, NURBS were taken up by the aerospace giant Boeing and used in their CAD program **TIGER**. NURBS are now an integral design tool and can be found in every CAD modeling program.

## What industries use NURBS modeling for design?

NURBS modeling is used for a **wide variety of applications**. Many universities teach NURBS geometry as part of computer science or mathematics degrees. NURBS modeling is used for any instance where a designer or engineer is required to create an accurate and lifelike digital representation of a real or theoretical physical object.

The ability of NURBS to create smooth, realistic contours that can be made even more lifelike by adding textures means that it is commonly used in **product development**, for the aerospace and automotive industries, in **architecture**, manufacturing, and in **mechanical engineering**. NURBS are also widely used in CGI imagery and 3D animations.

## How NURBS modeling relates to other modeling techniques

NURBS modeling, polygonal modeling, subdivision modeling, and parametric 3D modeling are all common methods of creating CAD models and designs. While there are certainly similarities, there are some significant differences between these techniques.

### Polygonal modeling and NURBS modeling

NURBS modeling uses control points that are connected by splines to create curves. Polygonal modeling works by **meshing thousands of flat triangular planes to create a shape**. You cannot easily create a perfectly smooth curve using polygonal modeling as the computer always calculates polygons as a straight line between two control points.

To create a curve using polygonal modeling, a designer must use smoothing groups and huge numbers of polygons grouped together. This then appears as a smooth curvature when viewed on a screen. However, polygonal modeling is not suitable for manufacturing as CNC tools require a perfectly smooth curve in order to create quality products. Only NURBS modeling can achieve this.

### Subdivision modeling and NURBS modeling

Subdivision modeling creates a 3D mesh that can be manipulated in any manner the user wishes via a **push-and-pull method**. Also known as SubD, subdivision modeling is better suited to organic shapes that **do not have to be particularly precise**. As such, SubD modeling is more often used for 3D rendering animations for movies and video games.

### Parametric modeling and NURBS modeling

Parametric modeling is based on NURBS modeling techniques. A parametric model will **automatically update whenever a dimension is changed**. There is no need for the designer to keep redrawing the model, unlike the freeform method of SubDmodeling.

## NURBS modeling techniques

The basics of NURBS modeling techniques with CAD software include functions such as:

- Curve Creation
- Surface Creation
- Surface Editing

### Curve Creation

Control points are set within a digital 3D space, a curve degree is set and the program creates a NURBS curve based on these parameters.

### Surface Creation

A NURBS surface is created by compiling a mesh of weighted control points.

### Surface Editing

Each control point on a NURBS surface has a ‘weight’ attached to it, meaning that it can be manipulated to ‘pull’ the surface towards it.

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## Advantages of NURBS modeling

The biggest advantage of using NURBS is that they allow designers to create an absolutely **smooth curve**. The mathematical algorithms that are used to create NURBS curves mean that the surfaces are completely smooth regardless of how closely the shape is examined.

NURBS modeling allows for much **greater precision** and control compared to other techniques. This is why it is so often used for product design and for the design of automotive chassis and airplane fuselages.

The **lower polygon counts** involved in creating NURBS curves and surfaces require less computing power, so they are more lightweight and can be used to create 3D models in less time than other methods.

## The limitations and challenges of NURBS modeling

Although there are many benefits to NURBS modeling, the technology does have drawbacks and limitations. NURBS are much **more suited to hard surface models** such as commercial products or vehicles that have rounded surfaces. Many designers and engineers experience **difficulties with creating sharp edges and corners** using NURBS.

NURBS software often has a **steeper learning curve** than SubDor polygonal modeling software. For this reason, users require a higher level of expertise to work with NURBS. Often, a designer or engineer must have a **solid understanding of the complex mathematical principles behind NURBS** in order to achieve their desired results.

## Nurbs modeling - Conclusion & Perspective

NURBS modeling uses complex mathematical equations to depict curvatures and sloping inclines. NURBS modeling is a **highly useful CAD tool used to create highly realistic 3D rendered models** of objects that have rounded shapes. It is mostly used for automotive and aeronautical design but is also widely used for CGI effects in film and in 3D animations.

The development of NURBS represented a dramatic breakthrough in CAD technology. NURBS allowed designers to create highly detailed complex shapes that had perfect curvatures. It is **ideal for product development purposes**. NURBS modeling is also essential for CNC processes since polygonal molding does not result in perfectly curved lines and therefore cannot be used by CNC machining tools.

If you are interested in any type of CAD design work, then you need to familiarize yourself with NURBS modeling techniques. While NURBS modeling is not suitable for every type of CAD application, the wide breadth of uses that it does have makes it a crucial knowledge point for any designer or engineer.

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## Frequently asked Questions

The vast majority of stand-alone and online CAD modeling software use NURBS, so in most cases, compatibility is not an issue.

It is more challenging to learn NURBS modeling than other techniques, such as SubD modeling.

Many NURBS CAD programs require powerful computer systems, however, users can access NURBS software via browser-based 3D modeling or web CAD software that uses cloud computing technology.

Yes, common applications include NURBS modeling for product design, NURBS modeling for engineering, and NURBS modeling for architecture.