smooth 3-D curves –
I'm working on modelling mathematical knots. Some are expressible in closed form (like the trefoil ) but generally the path or paths are given as...

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The simplest method would of course be to evaluate the curve functions with a denser set of parameters. Otherwise, to approximate the intermediate...

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Here is a simple subdivision using the classic 4-point scheme:
weight = [-1, 9, 9, -1] / 16;
function interpolate(nodes) =
nodes[0] * wei...

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I have written several programs to do this, at varying levels of ambition, since the mid 1980's. All have
been in either C or Java, not OpenSCAD...

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In my post I did just that. But instead of getting analytical tangents, the tangents where approximated using a central difference (s[1]-s[-1]...

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Thanks so much, thats just the ticket. I rearranged to eliminate the let and added a function to recursively apply the subdivision.
weight...

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Just a note to emphasise the power of the current OpenSCAD. I used the approach to creating closed tubes developed by NopHead to create knots fro...

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