On Life, the Universe and Motorcars

For an effect for a client, I needed to make things whiz around in 3D space along smooth but unexpected paths. They would be travelling at all kinds of speeds from very slow to pretty rapid, so my curved paths had to be some kind of continuous function rather than a bunch of sampled points. So how do you define a curve? Well, it kinda starts over there, curves this way a bit, then that way, then up a bit and bends the other way.

That's a rubbish definition. We can do better. In fact, a clever chap named Paul de Casteljau already did by inventing what we know today as the Bezier curve. These are fairly remarkable things. You pick a bunch of points in space and the algorithm makes a smooth curve that starts at the first point and ends at the end point, snaking towards all the other points along the way. If you've used Photoshop or similar drawing packages, you've probably used a Bezier curve in its Cubic form (4 control points) before, in 2D.

What I needed was a 3D version, but using as many points as I cared to define. I came up with this simple editor:



In the editor above, you can use the controls shown bottom right to draw a 3D curve. They're more interesting when you change the depth a bit with A/Z, and you can see their 3D-ness when you move the camera around. You can use page-up and page-down to move in/out a bit, but since there's no screen culling you will see spazzy effects if you move in too far.

You can add as many points as you like, although it can get pretty slow. It isn't optimised at all really, since its just a utility for editing rather than a final piece. The rendering of the curve is ultra-simple too so if you add enough points, you'll just get a mess of straight line segments. The underlying curve is a genuine Nth order curve however, N being the number of points you've added.

So what can you do with these curves? Well, spangly 3D paths, like I said. Weren't you listening!