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2d Loop the loop

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Hello, I'm trying to calculate a 2D loop the loop, but I don't know where to start(I thought it would be a variation of the sine wave, but I was wrong). Googling it proved unfruitful, (could online find programming loops and some brand of clothing :huh:).

So I'm wondering if anyone would be kind enough to point me in the right direction?

Thanks!

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rollercoaster loops are most commonly a [font=sans-serif][size=2][b]clothoid loop, [/b](nothing to do with clothing) unfortunately there is no analytical equation describing a clothoid; it involves fresnel integrals for a start! So you can only produce a numerical approximation to the shape of a rollercoaster loop :P[/size][/font]

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