So now that you know what continuity is, you’ll want to know how to analyze the continuity of your curves and surfaces in your CAD system. Each system has its own specialized tools, but there are a few common ones that are available in basically every CAD package: porcupine (aka “Curvature Combs”), Zebra, and color gradation. In this brief video, we’ll take a look at these three analysis types, and explain what they mean and how to read them.
In our last tutorial, I talked about different types of continuity, but I didn’t get into ways of knowing whether your geometry is continuous or not. All Class-A surfacing tools provide at minimum a few basic tools for analyzing curvature.
A “Porcupine Analysis” is the most common method for analyzing the smoothness of a curve, and to analyze continuity discrepancies between curves or surfaces. Though the porcupine analysis purely used for curva-linear elements in space, it can be used to evaluate surfaces by using an intersection plane.
Each “comb” in a curvature analysis graph represents an inverse magnification of the radius at that point: the longer the comb, the smaller the radius (or the greater the curvature).
As you can see in curve A, a line shows no curvature comb, because it has no radius (or, more correctly, it has an infinitely large radius). Curve B has a constant radius, and therefor the combs are all of equal length. Curve C has a varying radius that inverts mid-way in what is known as an “ogee,” an “inflection,” or a curvature-inversion. Notice that the combs always exist on the outside of the curve, opposite the radius.
If two curves are not tangent to one another, their curvature combs will appear “broken”, and will not touch one another at their extremities. This can be difficult to visually discern in some cases, so the curvature graph may need to be amplified.
Here we can see the curve A is tangent to curve M, and that the radius of curve M is constant across its length. These curves have a G1 relationship, because even though their direction is the same at the contact point, the radius is clearly not.
In this case, however, we can see that the radius is the same at the contact point, making these two curves curvature-continuous, or “G2” continuous. The longer combs on the M curve here show that the radius is tighter here than in the previous example, and that it varies over the length of the curve.
Here we have a fully G3 continuous curve, as evidenced by the smooth curvature combs. The graph is showing us that not only are the curves tangent, but their radii are equal at the contact point, and that radius is increasing at the same rate.
When I drew this curve, it looked perfectly smooth on-screen. But the curvature analysis shows me that the curve is actually far from smooth: there are lots of dips and lumps on it that may be visible in my final model.
When I drew this curve, it looked perfectly smooth on-screen. But the curvature analysis shows me that the curve is actually far from smooth: there are lots of dips and lumps on it that may be visible in my final model.
Curvature combs are used primarily for curva-linear elements, but what about surfaces? One common technique for rapidly evaluating the curvature continuity of a surface is known as “zebra stripes”. G1-continuous surfaces will make themselves very obvious when zebra-stripes are applied, because the stripes will “break” at the seems between surfaces.
G2 curvature continuous surfaces will yield much smoother zebra stripes. Though this technique is very convenient for quick surface checks, I still prefer to use an intersect-line and a curvature comb for a deeper analysis, since the result is of much higher fidelity, and is generally more reliable.
Another means of analyzing curvature across a surface is to map colors across it according to different levels of positive and negative curvature. In this example, tight curvature (small radius) is called out with a blue color, and any surfaces that have zero curvature or less (inverted curvature) appear in red.
The tools discussed here are widely available in CAD packages. Knowing how to use them will make your surfaces much more reliable.
Have fun surfacing!
