Why NURBS are not the last secret

It has been suggested that my little excursion into new development techniques has left out the topic of NURBS. I am happy to comply. However, this is a bit of a difficult subject to get into. The very basic idea is this: Rather than using two-dimensional geometric units (like polygons), NURBS models are using curved lines as its basis. Unfortunately, no simple explanation I found was satisfactory to a lay audience (like myself). So let us start with a short step by step guide to NURBS modelling, courtesy of Brian J. Immel.

* Lets use the Birail 3+ tool to create our mountains. Create two curves in a semi circle shape. These will be our rail curves.

* Create a series of curves with varying heights to be the high and lows of the mountain.

* Hit the Birail 3+ tool and select all the riders in a clockwise motion, hit enter and select both the rails.

* Delete history on the NURBS surface.
* Create two more curves at the ends of the rail curves. These will be our mountain base curves.

* Select the curves that form the ends of the mountain and break them into two curves (Edit Curves > Detach Curve).

* Select the base curves and the two broken curves and hit Surface > Boundary. Repeat this step for the other end of the mountain.
* Create a layer and put the mountain in it. Name the layer Mountain and turn it to reference mode. Now our mountain is complete.

I am sure you understand how this differs significantly from polygon-based modelling. Joel has written a very basic description of what NURBS are and how they differ from polygons:

There are 3 types of geometry, Polygons, NURBS, and Subdivision Surfaces.

Polygons are 2D shapes. Mainly Polygons are color filled 3 or 4 sided, triangles or squares. Polygons are put together in different angles in XYZ to create 'meshes'. A mesh is just a group of joined polygons. (...)

NURBS (...) are curvy lines. It is like the Pen tool in Adobe Illustrator or Photoshop. These make nice smooth surfaces, not good for making hard corners like a box.

Subdivision Surfaces (...) are polygons with special areas that are super detailed and look like NURBS.

Though good to get us started, this was also a little brief. There is a more detailed comparison of those three techniques to be found at WebRef, but the server seems to be down, so I had to copy the article from the page´s Google cache.

The same head shown (left to right) in NURBS, subdivision (sub-D) surfaces, and polygons. Note that the NURBS model still needs a lot of rebuilding to get the mesh down to a manageable size; the sub-D surface is almost automatically clean and has dialable resolution; the polygon surface is lightweight but coarse.

Games use polygonal models exclusively. A polygon mesh, in its simplest form, is made of nothing but triangles. To add more resolution or detail to a model, you simply use smaller triangles. All 3D rendering hardware uses triangulated meshes as its ultimate data format, so this is the fastest and most efficient way to deliver geometry to a game. Although triangle meshes are very simple, working with them is not. For example, there’s nothing particularly intuitive about defining the shape of a human with a bunch of triangles. This is especially true when you have to carefully limit the total number of polygons in a mesh, as you do in a real-time 3D game. Probably the most essential skill to building 3D models in polygons is learning to make the most of the available polygon budget and to optimize the appearance of low-poly surfaces to make the most of what you’ve got.

For many years, NURBS (nonuniform rational b-splines) were considered the standard modeling format for film—and in many studios, they still are. NURBS excel in their capability to accurately define curves and surfaces containing complex compound curves. NURBS are also very intuitive for texture mapping. The down side to NURBS is that they’re a digital equivalent of rubber sheets. While you can stitch multiple sheets together to make surfaces that are too complicated to represent with a single sheet, it’s sometimes impossible to hide these stitched edges, particularly if the surface goes through dramatic deformations. Although to some extent NURBS are resolution independent—meaning you can view them from any distance and still see a smooth, unfaceted skin—in practice, NURBS surfaces are displayed using approximation, which can break down, showing holes or seams when you get too close.

Subdivision (sub-D) surfaces are the latest development in modeling methods used in games, television, and films. They work by fitting a smooth NURBS-like surface to a coarse polygonal cage. This lets you model with polygons to generate realistic, seamless surfaces that avoid many of the pitfalls of NURBS, while keeping the ability to create organic shapes typical of NURBS. Studios have been relying on sub-Ds for some time, but using them to model real-world objects is a relatively novel technique. Increasingly, modelers use sub-Ds to create characters and other models for real-time games because the sub-Ds let them produce high-res models for prerendered artwork and generating normal maps, as well as low-res polygonal models for in-engine rendering. These sub-D models can also be easily converted back to polygon models for high or low poly count use.

So NURBS have some pretty major disadvantages. There are clear advantages over the other two techniques, but they appear very specific. Apple´s Philip J. Schneider writes:

They can represent very complex shapes with remarkably little data. For instance, approximating a circle three feet across with a sequence of line segments would require tens of thousands of segments to make it look like a circle instead of a polygon. Defining the same circle with a NURB representation takes only seven control points!

These were some advantages and disadvantages. But how do developers weigh them up? Just how widespread is the use of NURBS today? The Wikipedia entry explains:

At first NURBS were only used in the proprietary CAD packages of car companies. Later they became part of standard computer graphics packages, including the OpenGL Graphics Library.

Real-time, interactive rendering of NURBS curves and surfaces were first made available on Silicon Graphics workstations in 1989. In 1993, the first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small startup company cooperating with the Technical University Berlin. Today most professional computer graphics applications available for desktop use offer NURBS technology, which is most often realized by integrating a NURBS engine from a specialized company.

So they are in widespread use, but not so for real-time graphics. Developers like Adger express the choice between polygons and NURBS like this:

According to most people, it's easier to model things like characters using polygon-related tools, as you don't have that pesky 'rectangluar topography' limitation that NURBS have. But later you get problems with texturing and animation.

NURBS are more suited to modeling real things, as you work with precise curves and lines instead of screwing around with polygons, and most products you see were designed using something that uses NURBS. NURBs parametric nature allows EXACT specification of curviture etc. Very handy for modeling exact things like boats, cars etc.

It should be clear from the above excerpts that NURBS are an interesting alternative to polygons in some fields, but will most likely not be used in any videogame console.

* NURBS are good for modelling curves but not so for corners and edges.
* Connecting planes using NURBS is difficult and leaves seams.
* Most developers work with polygons. Forcing them into NURBS-based modelling may not seem too attractive to developers and may not help third party support.

If anything, subdivision surfaces seem to be a promising technique that we may see more of in the future. But I am sure that the Nintendo Revolution will not force developers into non-polygon based modelling. For further reading that gets into the mathematical equations underlying NURBS modelling, I suggest this and this page.

Sources: Brian J. Immel, Joel, WebRef (Google cache), Philip J. Schneider, Wikipedia, Adger
Image sources: Brian J. Immel, WebRef (Google cache)