List of mathematical shapes and how to create them using Designscript

DesignScript
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@Marcel_Rijsmus hope it might be okay to ask about this on this thread, if not I will delete - I wanted to produce a Mobius Strip and have found some strange results; I’m wondering if someone more mathematically inclined than me might have an explanation?

image

A Möbius strip of half-width w with midcircle of radius R and at height z=0 can be represented parametrically by

x = [R+ s cos(1/2 t )] cos t
y = [R+ s cos(1/2 t)] sin t
z = s sin(1/2 t)

Image and formula from: Möbius Strip -- from Wolfram MathWorld

This is the result in Dynamo:

image
image687×846 30 KB

DesignScript (using number sliders for s and r):

s = -n..n..0.001;
t = 1..10000;
x = (r + (s * Math.Cos(t/2))) * Math.Cos(t);
y = (r + (s * Math.Cos(t/2))) * Math.Sin(t);
z = s * Math.Sin(t/2);
points = Autodesk.Point.ByCoordinates(x,y,z);
Mobius = Autodesk.PolyCurve.ByPoints(points);

Any ideas? I know that its meant to be a surface and I am generating points/polycurves so might be the explanation, but I suppose I wasn’t too sure how to generate it otherwise :blush:

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