You can simplify the math a little.

Letting d be the desired diameter, m be the slope of the stripes, and I introduce k for the modulus subexpression:

r = d / 2

k = (V + m * U) % d

s = k - r

You use Sqrt(r * r - s * s)

but:

r * r - s * s

is

r * r - (k - r) * (k - r)

which is

r * r - (k * k - 2 * r * k + r * r)

which is

r * r - r * r + 2 * r * k - k * k

which is

k * (2 * r - k)

which is

k * (d - k)

So we don't ever need r and the solution is:

k = (V + m * U) % d

Sqrt(k * (d - k))

I made a function out of that - it's going into matmatic extras!

Been playing with the functions - renders real fast on a square. But on the cylinder it sucks.

I think its because the geometry of the sides of the cylinder - long thin rectangles must cause some issue.

I don't have time to try it now, but you might want to make a cylinder in some other tool that has no end caps and uses a lot of small polygons. Maybe triangles would be better than quads, too.

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