Spline Schmline, part 5: Kinks and Knots

Ok, you guys got me started on this. Now I can’t stop.

I’ve been reading a book about Rhino 4.0. After writing my own book, suddenly the flaws in other books just jump right out at me. It’s kind of painful reading, but there is some good content. In particular, this guy does seem to know something about splines, even if he doesn’t seem to know what to do with them.

Some terminology used in Rhino is not used by SolidWorks users, although it may be used by the people doing the SolidWorks spline programming. Words for this post are: kink, and knot.

Rhino uses the word kink to signify a sharp tangency discontinuity in a spline. In SolidWorks, you can get discontinuity within a spline, but the best way to get it is to simply create two splines that touch at the ends without any tangency constraint. Kinks in Rhino can be useful when you are trying to smooth a sharp edge into a continuous face. Again in SolidWorks, this is possible, but is usually achieved by using multiple features, which tends to break faces up. I believe this kind of thing can be done more smoothly in Rhino because Rhino allows internal kinks in the spline, where SolidWorks requires multiple splines.

To me, having used primarily SolidWorks for so long, splines are intuitively internally continuous, and its hard to think of any curve which is not continuous as a single spline. I’m not a big Rhino user, but this sort of thing seems to work out in Rhino.

The second word here is knot. What Rhino considers to be knots are what are called simply spline points in SolidWorks, the points along the spline used to create and manipulate the spline. As I understand it, SolidWorks splines are “piecewise continuous”, which means that a single equation is responsible for the curve between the spline points. So if a SW spline has two end points and an interior point, it would require two equations. In SW you can achieve a curvature discontinuity within a spline, but you cannot achieve a tangency discontinuity.This post doesn’t really add anything to the arsenal of what you are able to do in SolidWorks with splines, but it does make you aware that not all surface modelers out there have the same limitations that SolidWorks has with splines. It also gives us the knowledge that we could ask for something like a Rhino kink – a sharp tangency discontinuity It never hurts to ask. I would guess that SolidWorks has tried hard to maintain internal continuity, and may not have thought that internal breaks within a single spline would be something users deemed desireable. And maybe I’m the only one, but when you make a sharp edge that flows into a smooth surface, that sort of thing usually has to  be broken up into 3 separate surfaces (one on each side of the sharp edge, and then another on the other side of the end of the sharp).