Spline Schmline, part 3

I’m a little surprised by the interest in splines. I can keep pumping it out. I need to get to the surfacing stuff eventually. I promised a few examples around that Model A. It turns out that splines and curvy surfaces use some of the same concepts. The main word I’d like to see in circulation is “interpolated”. To me, it’s just a word that demonstrates that splines and lofts are in some ways approximations.

Dimensioning Splines

Ok, I’ve held out long enough. There are ways to dimension splines, or drive splines from dimensioned sketch geometry. The obvious way to start is by just dimensioning the spline points.

I used the Fully Dimension Sketch function to apply dimensions and relations, but it didn’t add all the dims to fully define the sketch, but almost. I want to call your attention to 4 dimensions. Notice the two angle dimensions. These go between the spline handle and a construction line I added. Also notice the blue dimensions. These are created by clicking the spline handle with the dimension tool, and placing the dimension. The number is just the magnitude or stiffness of the handle. An important aspect of the dimensions for the handles is that you can use link values to drive them. The reason this is important is because symmetric sketch relations only work on these if you mirror an entire spline, you cannot make handles symmetrical within a single spline. Making a single spline symmetrical is difficult, and even moreso if you use handles.

Don’t get your hopes up for this kind of thing when it comes to drawings. If you put the image shown above on a manufacturing drawing, you’ll become unpopular with the shop. Nobody can really recreate anything from the dimensions on this view. It might be used to check stuff, but… I wouldn’t even go there. Use computer controlled manufacturing processes running directly from your 3D data to make parts with shapes like this. If you really need the shape, you need it enough to work with a different vendor who doesn’t have all manually programmed or operated machines. Really, come on, people, this is the 21st century.

Asymmetrical interior spline handles

One commenter asked what is the advantage of asymmetrical spline handles. The advantage is that sometimes you only want to affect the shape of a spline on one side of the handle, and not on the other.

The angle of the handle on one side of the spline point affects the angle on the other, but the magnitude can be different. Once you drag one side of the handle without the Alt key, you have broken the symmetry. If you do this, make sure you use the Maintain Internal Continuity option.

Controlling splines with lines and arcs

I’ve been holding out on you a little bit. There is actually a great way to control splines with lines and arcs which can be driven by dimensions.

In this sketch, the lines and arcs are used as construction geometry, and the splines are fit over the top, but make smooth transitions in the corners. Notice that you get the best of both worlds when you do things this way. You can fully dimension your sketch, plus, you get spline smoothing in the corners.

This is achieved with the Fit Spline tool, which you can find in Tools, Spline Tools.

Fit Spline requires that you input a tolerance value that represents how far the spline approximation is allowed to miss the selected elements by. The larger the tolerance, the less recognizable shape the spline will create. As you might expect, this function has all sorts of uses. Of course you have to be careful of any geometry created by software. Always check a spline of this sort with a curvature comb to make sure it does not have unacceptable undulations in the corners. This tool can be used on 2D and 3D sketches. We could have yet another long blog post talking about the possible applications and implications of this tool. It’s really cool, but it’s not a magic wand. You do have to be careful, because it can produce stuff you don’t want.

Using splines to approximate arcs

As I was preparing to write this piece on splines, I read in the SolidWorks forums that some fellow used a spline to approximate an arc because the arc had a radius too large to represent in SolidWorks. SolidWorks has a cubic envelope of 1000 meters per side. This arc was for a bridge. Honestly, a bridge shape should probably be a parabola anyway, and not an arc or a spline. See my post on Antoni Gaudi’s use of naturally occurring parabolas to design the support structure for arches and spires…