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2D equation curve for a parabolic spiral

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Message 1 of 5
CJ.10E-10mm
1426 Views, 4 Replies

2D equation curve for a parabolic spiral

Can anyone please advise me what the 2D or 3D equation curve for a parabolic spiral, otherwise known as a Fermat's spiral would be?

 

I have found this info but do not know how to apply it:

 

 Fermat equation

 

X^n + Y^n = Z^n.\

Therefore in terms of the affine plane its equation is

 

x^n + y^n = 1.\

 

The Fermat curve is non-singular and has genus

 

 

I have also found this: $r^{2}=a^{2}\theta $

 

 

Please see image attached.

4 REPLIES 4
Message 2 of 5
JDMather
in reply to: CJ.10E-10mm

Are you familiar with using Equation Curves in general?

A while back I posted some examples that my students submitted. 

I think Autodesk employee has also posted some examples.

At one time there were several that were included in the Samples install, there should be a thread here with those attached.

Do a search and come back with more questions if you can't find the examples to help you work it out.


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Message 3 of 5
CJ.10E-10mm
in reply to: CJ.10E-10mm

Thank you, I will search later today.

 

Equation Curves do appear to a novice like some form of 'black art.' So I am wondering if there is a 'user friendly; App that allows one to configure the equation for any given shape in an Excel Spreadsheet?

 

Thank you once again.

Message 4 of 5
rdyson
in reply to: CJ.10E-10mm

If you can create x,y,z coordinates in a spreadsheet, IV will import them and draw a spline through them.


PDSU 2016
Message 5 of 5
CJ.10E-10mm
in reply to: rdyson

Thank you Rdyson.

 

Is there any chance you could assist me with my question on:Variable pitch helical coil with smooth blend please?

 

Thank you once again.

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