In CAD/CAM, the future is NURBS

Modern Machine Shop, June, 1992 by Keith Briere

What is a NURB? No, it's not a small, furry animal. It's a powerful and versatile new surface modeling technique in CAM.And it's here to stay.

If you're an NC programmer, process engineer, or tooling engineer, the real test of any new advancement in computer-aided design/computeraided manufacturing (CAD/CAM) is this: Can the design be cut?

In other words. can the CAD model be. machined efficiently and with optimum quality? Or will you have to spend time modifying the design to make it manufacturable?

For designers, the evolution of CAD/ CAM over the past 20 years has been a boon. Indeed, most of the advancements in CAD/CAM in the last 20 years have been driven by the needs of the design community. But for manufacturing engineers, it's often been a different story. As CAD designs have increased in geometrical complexity, so have the manufacturing challenges they pose-challenges not just in machining, but often in the mere ability to share information.

It's not surprising, then, if some manufacturing veterans are looking with "guarded" optimism at the next step in CAD/CAM-- the emerging Non-Uniform Rational B-Splines (NURBS) surface modeling technology.

NURBS technology offers a unique method of defining 2D and 3D geometry types--including points, straight lines, arcs, conics, Bezier, and conventional B-spline geometry. With NURBS, you can build molds, tools and dies for today's most complex designs with unsurpassed precision, speed and quality. This versatile and powerful tool helps speed time-to-market, produce higher-quality parts, and ensure that the answer to the most important question of all--can it be cut?--is a resounding "yes."

A Brief History Of Surfaces

One of the advantages of CAD/CAM is that using its high-level functionality doesn't require in-depth understanding of the base mathematics. Although it's true that the higher your level of understanding the more you can get out of the system, even non-mathematicians can fare quite well. To that end, let's start with a simple review of the technologies that have led us to the edge of the NURBS revolution.

One of the earliest surfacing technologies was the Coons Patch, a foursided, curved surface component. Developed in the United States in the early 60s, it was first used to design ship hulls--large, relatively simple curved surfaces with few radical changes in directions. The needs of the automotive industry were different, however. Automotive surfaces are smaller, directions change faster, and revisions in aesthetics and style are much more frequent. The primary limitation of Coons Patch technology is that it doesn't lend itself to modification of the interior of the patch. Only the boundaries, or splines, can be revised to change the curvature of the surface.

Bezier mathematics--named for Pierre Bezier, a French automotive engineer--is the foundation of many French CAD/CAM systems and has attained wide acceptance in many U.S.based systems as well. Developed in the 60s, Bezier curves, or cpoles, differ from splines in that instead of controlling curvature by passing a curve through a series of points, the endpoints are fixed and curvature is influenced by control points not on the curve itself. These control points are connected by a control polygon that creates a type of framework for the curve. The curvature can be varied by manipulating, or "pulling," these control points. Bezier curves have the advantage of easily representing and manipulating aesthetic automobile body designs.

The Basis-spline, or B-spline, was developed in the early 70s, and while it's similar to Bezier curves in its use of a control polygon, there are some significant differences. B-splines use a succession of polynomial segments to represent a curve as opposed to Bezier's single segment. As a result, more complex curves can be represented by a single, continuous entity. Knots are points on the curve that correspond to the ends of each segment. A knot has a parameter associated with it which defines the degree of flexibility, allowing the knot to be used as a "hinge." This property allows non-tangent entities to be represented by a single curve. In lay person's terms, a B-spline can have sharp corners (Figure 1).

In the late 70s, rational equations were added to the B -spline. In a rational B-spline, the control points can be weighted by a fourth, or homogeneous, component. Unlike a non-rational Bspline, a rational B-spline can represent a segment of an arc or conic without approximation.

And then in the 80s came NURBS, or Non-Uniform Rational B-Splines. The non-uniform property of NURBS refers to the manner in which the curve progresses between the knots, or segment ends (Figure 2). The major advantage here is that ripples or loops that occur between unequally- spaced points are eliminated.

Now that we have discussed the what, here's the why. Of the many advantages the development of NURBS offers over other surfacing methods, there are three areas that most directly affect the manufacturing community: fewer surfaces, easier editing and accurate data transfer.