"Dave Matthews" <dav### [at] mnwestedu> wrote:
> That was my next concern, also.  The "bunching" would be especially
> noticeable for relatively "thick" knots, like your image.  I suppose for
> the spiral stairway, one solution is to measure the actual length of the
> spiral spline, rather than the center one (?)
But my spiral spline (which I use for the handrails) is already bunched,
because I calculate it using a translate-rotate transform combined with the
central path. In any case, I think the stairs are fine as they are. As long
as they don't turn into a continuous ramp, I quite like the idea of varying
steepness! This is one reason why I've made them simple planks without
risers in the version above. I think it looks quite medieval... :)

I've had a quick look at KnotPlot, but I think it'll be a bit of a haul
learning to use it and then extracting splines. On the other hand, I've
managed to find some examples of more complex knots expressed as parametric
equations - these would be ideal, because I can easily substitute them for
the trefoil in my SDL. All I have to do is increase the step count. This
would be better from an artistic point of view, too - I'd quite like to
have a viewpoint on or close to the stairs, and still have plenty of knot
in view. This would be perfect!

>  I'd really like to see what you could do with other knots
> (maybe whack 'em with a few cannon balls!)
I haven't tried that yet - but I will this week. I shall post anything that
looks good, never fear!

Bill

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