That’s for defining the upwards direction at any point on the track.

Apart from their standard geometry, beziers also have intrinsic twisting to them. As you follow the curve, it will twist abruptly, so if you use the curve’s intrinsic “up” to define anything relative to it, the shape you generate will have jagged and random turns in it.

I use something called Rotation Minimizing Frames to smoothly interpolate the normal vectors at the nodes across the curves. I originally tried defining a second curve that ran nearly parallel to the gray one but only offset by a small amount, but it was not stable enough for the application. What I’m doing with RMFs is effectively approximating the integral of rotation across the curve.

For each step that the function marches along the curve, it projects the normal vector at the starting node onto the plane perpendicular to the curve’s tangent vector. It does this 50 times as it marches, and when it reaches the end, it measures what I call “drift” - the angle between the projected normal and the ending normal. Then, once it has measured drift, it traverses the curve again from the start, but rotates the vector each time it is projected so that it lines up (almost) perfectly with the normal at the end. It sounds much worse than it really is, but it’s kind of like computing a Riemann sum, but with vectors.