Spline Schmline, part 2

In the previous part, we talked about why we need to use splines. Now we will talk about how to use splines. Spline curvature combs enable you to evaluate the spline that you create, but what are the tools that enable you to control the curvature?

A seventh inning stretch, just a little early…

Well, I need to extend the analogy that I started with Jessica Rabbit. Jessica is more of a fox than a rabbit, and she got a bit of attention as a part of the post. Kim decided that I needed to give equal time to the other side of the aisle here, however you want to take that. Jessica Rabbit was actually Kim’s idea. It was such a good one, that I decided that I might go with her new idea for a follow on post, even though I’m not as enthusiastic about it.

This is a bit of a stretch and might require some explanation, so hold on here. You see, the word “spline” comes from the ancient ship building trade. But Kim thought that Gerard Butler from the movie 300 would be a good counterbalance to Jessica. Exactly how those ideas or the ones that follow are related, I can’t say. King Leonidas (Gerard Butler) never was on a ship, but there was some footage of ships tossing to and fro in the waves, as the Persians perished in the (water word that starts with P). I considered this as too flimsy a basis for such a serious blog as Matt Writes.

In a happy coincidence, Gerard Butler also played Beowulf in the 2005 movie Beowulf & Grendel. I don’t know anything about that movie, but I do know the 2007 movie Beowulf, which was all CG animation, and that one does have some footage of Beowulf actually on a ship, although Gerard Butler had nothing to do with it. Of course after all of this, I’m thinking that maybe we should have had Angelina Jolie as the terrifying Grendel’s mother instead of Jessica, but alas, that die has been cast, and we just move forward.

So, what we get here is a little beefcake for “the other side of the aisle”, along with a ship in a computer generated movie that allows me to continue the discussion about computer modeling, complex shapes, splines, sexy curvature, and relate it to real historical manufacturing processes through a study of etymology. Now if that isn’t dedication to researching the topic, I don’t know what is.

Spline Handles

The spline handles are the arrows you find at the ends and every internal spline point. Each handle enables you to control both direction and magnitude of the tangency at the point. The ball at the end of the handle enables you to drag both direction and magnitude simultaneously. The arrow head just controls magnitude, and the diamond shape just controls direction. All of these controls are also available through the PropertyManager.

As I’ve already established above, the word “spline” itself comes from the ship building trade. But it also has meaning in pencil drafting techniques. A spline is simply a flexible slat. In ship building the slats were wooden and were nailed to the spars of the ship to create the outer covering of the hull. You can see these slats in the second image above, with Beowulf’s ship. In drafting a spline is a flexible ruler that enables you to make natural looking curves. The curves look natural because they follow the math of bending an elastic material.

Think of spline handles as a way to clamp down the position while controlling the tangency direction at specific points on the spline, namely the end points or internal spline control points. The handle magnitude does not have an equivalent in real physical phenomena, but you can think of it as if you could change the material stiffness of a flexible metal wire by pulling an arrow.

The magnitude, or stiffness for internal spline points can be changed asymmetrically. This will sometimes affect the internal curvature continuity of the spline, meaning that at the spline control point, you may get a change in curvature from one side of the point to the other. You can avoid this by using the “Maintain Internal Continuity” option in the spline propertymanager or by dragging the magnitude arrow with the Alt key, which moves both sides of the arrow symmetrically.

When it comes right down to it, you can make an S shape with a spline with only the two endpoints, if you use the spline handles to control tangency direction.

The unlabeled arrow at the bottom of the image is pointing to a spline handle. This image labels many of the characters that come in to play in spline control and manipulation. This is not all of the items, however.

Control Polygon

Another way to control the overall shape of a spline is to use the control polygon. You can activate the control polygon for a spline from the RMB menu. To enable control polygons on splines by default, use the setting in Tools, Options, …

I have heard people say that they prefer to use the control polygon because they believe that they can get smoother curves with it than by using spline points. The control polygon does not directly touch the spline except at the end points. This makes it a little counterintuitive to use to adjust the spline shape, but it does work.

Curvature Control 

The Curvature Control enables you to assign radius to the spline at a specific point. This can make matching other curvature easier. Other evaluation tools include a Minimum Radius indicator, and an Inflection Point indicator. These don’t give you any control, but they do help you see what is going on.

I’ll have one more blog post in this spline series. That one will be more information about the original question about using dimensions to control splines. Regardless of what I say, there really are ways to do it.