Authored by:
Kevin Atkins
Corporate Applications Engineer
Sensable
Wilmington, Mass.
Edited by Leslie Gordon
Resources:
3D-Coat
Delcam
Sensable
Other resources for basic CAD tutorials:
An Alternative to Nurbs
Computers for MCAD
The Changing Face of Model Annotation

Most engineers are familiar with geometric modelers with their solids and surfaces and Nurbs-based curves. Yet there are many cases where traditional geometric modelers are too slow or not a good fit for the design task at hand. Examples include modeling textures; shelling complex models; modifying and using scan data; designing complex organic shapes and artistic, aesthetic forms for manufacturing; adding highly sculptural detail to parametric CAD models; and combining hand-modeled and computer-generated forms.

Increasingly over time, the lines between different types of geometric modeling software have blurred, as each combines similar approaches and tools from the others. Newer, nontraditional approaches have accelerated this trend. For example, “hybrid” software from 3D-Coat combines what are called polygonal and voxel modeling. And PowerShape from Delcam, Salt Lake City, lets users model with solids, surfaces, and polygons. In addition, Freeform, 3D organic design software from Sensable, Wilmington, Mass., combines voxels, solids, surfaces, and polygons.

The combination of multiple geometry types in one package shortens design time and eliminates the need to learn multiple pieces of software with different user interfaces and ways of working. It also reduces the number of challenges inherent in getting separate pieces of software to efficiently talk to each other. These modelers complement traditional CAD packages.

As this blending of modeling approaches continues, engineers and designers need a working understanding of the advantages of each geometry format, when and how to combine them, and where to best apply them. Of course, the capability to model efficiently is crucial to streamlining the design and manufacturing of new products.

Different geometries solve different problems
Let’s take a look at four different geometry types, their pros and cons, the workflows they facilitate, and the types of products they suit.

Nurbs is short for “nonuniform rational B-splines,” with “B-splines” being the important bit. Years ago, manufacturing companies needed a way to mathematically capture the nonrectilinear shapes found in car exteriors, ships hulls, and airplanes in a way that was accurate and could be reliably repeated. It was easy to define straight lines and arcs, but a freely defined curve was another thing. In 1959, French engineer Pierre Bezier and French physicist and mathematician Paul de Casteljau, working independently, came up with a way of using control points to define and control a free curve.

Methods were also invented to control the curve with control points directly on the curve as opposed to on a control net. This made the definition and control of these curves more intuitive. The method works well to define straight lines, arcs, and circles as well as curvy shapes. Defining a 3D surface just extends this principle.

Extrapolating these simple examples into a fully finished design requires that the model follow the abstract rules inherent in Nurbs modeling. Mostly, the CAD software controls these rules, working behind the scene. The upside is that as long as the software follows the rules carefully, it can generate models that won’t fail. The downside: Sometimes the rules become so limiting or so time consuming to follow, the designer is forced to compromise his or her design, or give control to others later in the manufacturing workflow, for example, in applying textures.

When you need rectilinear, typical engineering models, Nurbs are great. Nurbs are best suited for products that have well-defined edges, are inherently smooth, rectilinear in nature, or can be parametrically defined. However, in situations where double compound curvature surfaces must join together such that the transition between them is aesthetically smooth, with the joint invisible, this can be a particularly tricky modeling task with Nurbs.

Polygons are another way to model a 3D object by creating 2D triangles and then connecting the triangles together. Increasing the number of polygons and reducing their size allows the accurate modeling of any shape below any reasonable manufacturing tolerance.

Polygons are also common in design and manufacturing work that relies on additive manufacturing (AM) for production. In AM workflows, polygons are used as the translation language that lets the CAD software “talk” to the AM machine.

Another common use of polygons is in scanning. Scanners export point-cloud data, but this is almost immediately translated into polygons for import into CAD software. Polygons generate a shape which will later be converted into a Nurbs model for further use in a traditional CAD system. However polygons have numerous downsides. They are less accurate and less precise than Nurbs, although boosting the resolution can partly resolve this. In addition, files can get so large that models become unusable. Polygons are not easily and randomly created on-the-fly, which limits applications such as scan cleanup. And polygon models are not necessarily manifold or watertight solid models. They can have overlapping open shells, which can cause problems in downstream processes such as additive manufacturing and must typically be fixed before the workflow can continue. Lastly, converting polygon models into Nurbs is often the only way to reuse these models later. The act of converting polygons to Nurbs is not trivial, giving rise to the need for specialty software, such as Geomagic Studio or Rapidform XOR.

Voxels — Just about everyone is familiar with how 2D pixels define a photograph. Voxels can be thought of as 3D, volumetric pixels. They are inherently three dimensional and can be arranged randomly in 3D space — like shifting grains of sand — to create different shapes. This inherent dimensionality means that designers modeling with voxels are not limited by the same rules that apply to Nurbs modeling, for instance, by the constraints of topology.

As with polygons, when voxels get smaller and smaller, the relative accuracy of a sphere represented by voxels will rise to the point that any deviation is smaller than the tolerances of the manufacturing technique being used to produce the product. Voxels let users perform a 3D version of the antialiasing commonly found with 2D pixel images such as adding triangles to the diagonals of a block model. The net result is that users can generate smoother models without taking the voxels down to micron sizes. An additional benefit of 3D antialiasing is that the software wraps the voxel model in polygons for import into additive manufacturing machines.

Voxel models are also inherently solid, manifold, and watertight. All the checking required when using polygon models — to ensure downstream manufacturing processes will not fail — is not required with voxel models. Also voxel models let users randomly add (or subtract) voxels on-the-fly, giving designers the creative freedom to simply push, pull, smooth, and carve models of “virtual clay.”

In addition, voxels work well for modeling textures. This is rarely done in traditional CAD software because the complexity of the Nurbs model would slow the software and make the model unusable. Because voxels are not bound by the same solid-modeling and surface limitations as Nurbs, creating textures is simple. And these textures are not just visual in nature, they are actually part of the model.

Voxels are well suited for modeling highly organic-shaped products and performing complex modeling operations such as shelling intricate shapes — operations which typically fail in Nurbs or polygons.=

Like any modeling approach, voxels also have downsides. For example, currently available voxel modelers do not support sharp edges well. And because accuracy and smoothness is driven by the size of the voxel, dimensionally precise and smooth models can get large in data size. In addition, voxel modelers are not history-based or parametrically driven, so some design changes can take longer than when done on a correctly defined Nurbs parametric model.

Subdivisional surfaces — The Catmull–Clark algorithm for subdividing surfaces (subD) was developed in 1978. It was primarily used for models in games, movies, and computer graphics. But recently, CAD modelers including Creo and Rhino have put subD techniques into their toolsets.

At the basic level, subD is a method for representing a smooth surface by continually refining a mesh.

By continually subdividing the control net, the software increasingly smooths the model. As the localized subdivision continues, it is possible to model details such as pockets. This lets subD modelers make smooth continuous models faster and more easily than traditional Nurbs-based CAD.

In addition, subD modeling lets users take the model back and forth through the various levels of subdivision without losing detail. Users can make gross changes to the overall shape at earlier stages of subdivision, while details added at later levels can be automatically regenerated. Another benefit, especially over Nurbs models, is that users can create complex models without trimming.

Subdivisional technology is best suited to smooth flowing shapes and concept creation. However, it, too, has its downsides. When designers want more rigid control over a portion of the model, it can be argued that Nurbs modeling is better. Also, subD forces users to undertake abstract thought processes to define and control the model, unlike polygons or voxels which are much more unordered in their definition.

Poly-Rep gets you there faster
No modeling technology is capable of addressing every modeling scenario for every workflow necessary to get a product to market. Fortunately CAD/CAM companies are adding more representations to their core functions to overcome the fundamental limitations of the different technologies.

For example, not long ago, most CAM software could only use Nurbs. Now, most programs can create toolpaths on top of polygons as well, effectively eliminating the need to convert a finished polygon model to a Nurbs model.

PowerShape software gives designers the capability of Nurbs to model, for example, a glass bottle, and then leverage the advantages of polygons to create a complex organic sculpt, such as a bunch of grapes with vines and leaves. It then wraps the sculpt around the Nurbs surface and passes the whole model downstream to machining.

In another example, Sensable’s Freeform is an organic voxel modeler which has evolved to provide poly-representational modeling. This lets designers move freely between surfaces, solids, polygons, and voxels. For example, a designer could scan a manually sculpted design that cannot be modeled in Nurbs, import the .STL file into Freeform for clean up, integrate CAD components and further modify the model as needed, and then either create mold inserts or export directly for manufacturing.

Poly-representational products help bridge the gap between the different types of 3D modeling tasks. This lets design teams choose the best format for each part of the design process, from concept modeling to detail engineering and on to manufacturing, minimizing the number of different programs used and streamlining design.

The result: better design
Interoperability between and within products is constantly improving, including their approaches to modeling. This is good news for everyone involved in product design. Poly-representational modeling software gives designers flexibility and creative freedom. In addition, newer, nonexpert CAD users can exploit inherent capabilities that only “super users”, or those competent in multiple design systems, were previously able to employ.

© 2011 Penton Media, Inc.