Could you elaborate on how you came to that decision? I really want to understand how to think in graphics, and I feel like there aren't any good books that explain that.
Consider that a 2D bitmap is just a function p(x, y) = (r(x, y), g(x, y), b(x, y)), that assigns colors to (x, y) coordinates.
If you have a parametric curve c(t) = (x(t), y(t)), it’s easy to see that for each parameter value t, the tangent of the curve is going to point towards dc/dt = (dx/dt, dy/dt). You can take a perpendicular vector to this tangent by rotating it 90 degrees, and the two vectors will form a so-called tangent frame at t.
If you want to bend your bitmap around this curve, the key idea is to transform the domain of the bitmap. That is, instead of putting your bitmap pixel at (x, y), you would put it at something like c(x) + (dc/dt)(y) (some scaling factors omitted for brevity).
(In practice, you would want to invert this mapping, and map the pixels around the curve back to the domain of the bitmap, to avoid holes, but that’s an implementation detail. The key idea is thinking in terms of warping the bitmap’s domain.)
I don't agree that what you propose is less complicated. Deriving an UV mapping along the curve could be done, but for a cubic bezier spline is not exactly as trivial as you paint it. For an example implementation along a quadratic bezier spline, see https://www.shadertoy.com/view/NltBRB. A cubic bezier is more complex to map since you have to solve an equation of 5th degree. I also think that the author wants to keep everything in vector format to be able to draw the results with a plotter. You could displace the vertices of a straight vector model of the rope using the UVs, but I am not sure that it would be any simpler.
