Spline Schmline, part 1

Splines make some people squeamishly uncomfortable. You can’t put dimensions on them, so how do you manufacture it? How do you make parts fit together if you use splines? How do you run QC to check your parts?

There are a lot of misconceptions about splines. The first is that you can’t put dimensions on them. And the second is that if you put dimensions on them that they become fully defined. The Third turns out to be that if you fully define all the points on a spline, that you can’t drag the points around anymore. Each busted misconception in its own time…

I have good answers for each of these misgivings and misconceptions, but I’ll get to those later. I want to start by addressing why splines are so important, infact indispensible.

Great curvature, baby!

Ok, this is going to sound sexist. That’s because it is. So sue me. If you’re male, there is no way to pretend you don’t notice this kind of stuff. Some types of curvature just draw your eye. That’s all there is to it. Just to keep it kind of cartoony and not too explicit, let’s use Jessica Rabbit from the movie Who Framed Roger Rabbit as an example, because she’s a great example.

Splines are sexy. Jessica just wouldn’t be the same if she were just straight and round, drawn with lines and arcs. Jessica, and just about everything else that we think of as “products”, needs curvature, and in particular, changes in curvature.

The reason why splines are so necessary is that they are the one way we have to make shapes that look organic. Organic shapes are never perfectly straight or perfectly round, they are constantly changing curvature. We as humans are programmed to react to organic shape. Jessica Rabbit’s organic shape provokes a reaction, and product design tries to evoke the same kind of reaction. It’s not a coincidence that they both cry out “empty your wallet”, and we dutifully obey.

If Jessica has an equivalent in the automobile world, it is probably something like a 1960 Corvette. Yow. They both look great in red. Nice headlights! Love those rear fenders. How does it look with the top down? It’s no coincidence that product design is so sexual. It’s no coincidence either that they are both beautifully curvaceous.

Splines or lines and arcs?

Cool shapes in product design is all about curvature that changes smoothly from one radius to another rather than simply a series of tangent arcs that change from one discreet radius immediately to another 

discreet radius. Look at these two surfaces below. Which one looks better to you? The one on the right is less lumpy. I think most people would say the one on the right looks better. Of course the one on the right is made with splines. You can almost see the lines and arcs in the one on the left.

Of course it is possible to make splines look very bad if you are trying to do that or are very inexperienced. I think a lot of people make the mistake of thinking that a spline with more spline points is more controllable, and thus a better spline. The truth is that you DON’T want to try to force a spline. The thing about organic curvature that makes it so appealing is that it looks natural. The natural materials are bending or being formed in a natural way. Splines have a very natural way of bending. I’ve been told that the math governing how splines interpolate shapes between points is very much like the natural bending equations for elastic materials.

Interpolated shapes

I classifify shapes into two camps: analytical and interpolated. Analytical shapes have a specific equation that can be written, for example a line or circle each has a familiar equation that you may have learned in high school geometry. A spline I believe is a series of 2nd or 3rd order polynomials. With an analytical shape, you know exactly where every point along that shape is going to be even before you draw the line or the arc. With a spline, you just put down the control points, and SolidWorks interpolates the curve between the points. This concept follows through to features such as the boundary, loft, fill and sweep. You put down the profile curves, and SolidWorks uses the Boundary feature to interpolate the surface between the curves. The difference between analytical and interpolated curves and surfaces is very important. They are not interchangeable.

Arguments against splines

People who don’t trust splines typically talk about dimensions or repeatability. When I create splines in SolidWorks, I never fully dimension them. Its useless to dimension splines. Different CAD packages evaluate splines differently, even if the spline points are all in the same place. Even SolidWorks between releases evaluates splines differently. Even if you were to use a spline on a drawing and fully dimension all of the spline points, the spline could never be exactly recreated based on those dimensions.

The only way to transfer spline based manufacturing data is to send a completed 3D model, and for the manufacturer to use a computer controlled method. Paper drawings may be useful for notes, and reference dimensions but typically not as a way to specify a complex surface or curve. This is most of my business. I don’t remember the last real drawing I gave to a molder, I just hand off 3D data.

Practice with splines

See the spline here with a lot of points looks lumpy. When I first started working with splines, I thought this was the best way to get great control on a shape, but it turns out that the more you try to control the shape, the lumpier it gets. Notice that the second spline is much smoother. This is because you just let the spline math do the work for you. My general rule of thumb is that you add a spline point for every change in convexity (convex up changes to convex down). So you have the two endpoints, which would make a straight spline, a middle spline point, which would make a convex or concave spline, and then a third point which gives the undulating S shape.

In the second set of images, I have applied a curvature comb to the splines. This is a way to visually evaluate the spline. The curvature comb represents the instantaneous curvature at that point along the spline. If the curvature comb changes sides of the spline, that means the spline has changed convexity. Notice that the comb on the top spline confirms that it is lumpy and the changes in curvature are too abrupt. The changes in curvature in the lower spline are much more gradual. Changes in curvature are represented by the change in the height of the comb.

Just for reference, curvature is the inverse of radius, or c=1/r. If you have a large radius, it means small curvature. Small radius (tight corner) has large curvature. Notice that the curvature comb is taller in kinks of the top spline. Notice that in flat areas of the spline (almost linear) the curvature comb is almost zero height.

More to come…

We’ll talk more about this topic later. There is a lot to know about splines.