3D Equation Curve to Create A Fibonacci Spiral

[Anonymous]

Hi,

Can anyone help me with the values to create the reverse of what I have achieved which in effect is a reversed Fibonacci Spiral.

My radii are reducing from the centre outwards where in fact they should be increasing in line with the Golden Ratio.

Many thanks.

cjj

[glenn-chun]

Hi cjj,

Let me show you how I would create a 2D golden spiral. Once you understand this in 2D, you should be able to figure out how to do this in 3D. All angles are in radians, not degrees, in this post.  I used the equations from following Wiki pages:

https://en.wikipedia.org/wiki/Golden_ratio
https://en.wikipedia.org/wiki/Golden_spiral
https://en.wikipedia.org/wiki/Logarithmic_spiral 

Add the following user parameters:

num_turns = 4
a = 1.0
Phi = ( 1 + sqrt(5) ) / 2
b = ln( Phi ) / ( PI/2 )

where Phi is the golden ratio and b is the growth factor.

The equation for the golen spiral, using the polar coordinate system, is the following:

r(t) = a * exp( b * t )

theta(t) = 1 rad * t

t min = 0
t max = num_turns * (2*PI)

You can change the spiral direction by adding a minus sign to r(t).

If you prefer the Cartesian coordinate system, use this equation:

x(t) = a * exp( b * t ) * cos( 1 rad * t )
y(t) = a * exp( b * t ) * sin( 1 rad * t )

Play with the growth factor by changing the user parameter b. For example, 1/4, 1/10, 1/20, etc.  The parameter a is just a scale.

Hope this helps,
Glenn

[Anonymous]

Dear Glenn,

Thank you so much. I would not have got to this point in a month of Sundays, so I cannot express adequately my gratitude other than to say your help will save countless thousands of cancer sufferers lives in due course.

Can you assist my mathematical naivety by helping me with two further issues please?

It is my understanding that each rotation of the spiral should be at the exact same angle to the centre. Yet as you can see from roughly generated sketch 1 below, the angle is rotating in the opposite direction to the rotation of the coil with every turn. The uneveness in the rotation I suspect is due to my hasty sketch!

And how can I control the smallest internal radii for as you can see it goes somewhat haywire in the centre, mainly I suspect because of the very small values. But also as I want to sweep a profile along the spiral path to generate a wire coil, there is a limit to the closeness of the spiral paths. I realise I could cut through an overlay of the spiral to cut the centre section out but I would prefer to control it properly in the first instance, if that is possible please?

The third sketch is of my parameters.

Once again, thank you so very much.

I have been struggling with this on and off for nearly two weeks! (night and day!)

I will simply 3D project this 2D sketch onto a a solid to create my 3D Spiral Coil.

cjj

[Anonymous]

that is a great solution! thank you very much!

[Anonymous]

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Hi there guys.

Just a quick question from here in NZ.

Would like to create a 3d model of the golden ratio spiral. As in link.

https://www.youtube.com/watch?v=qLU_Igs7hKs

Would program would I use? Inventor, AutoCAD, fusion, 3DS MAX or Maya?

The equations for 3d golden spiral modelling are as such, apparently:

Formula Fibonacci spiral
X(t)=sin(pi*t)*exp(t); Y(t)=cos(pi*t)* exp(t); Z(t)=0
If by the third, Z axis, instead of zero, set only exponential "exp(t)", the formula would be like this
X(t)=sin(t*pi)*exp(t); Y(t)=cos(t*pi)*exp(t); Z(t)=exp(t)
We get to 3D Fibonacci formula of spiral

Hope that's making sense guys.

Thanks, looking forward to any input.

Cheers B Lub.

[johnsonshiue]

Hi! This can be done in Equation Driven Curve in Inventor easily. Please take a look at post#2 in the thread and follow the instruction. Let me know if you have additional questions.

Many thanks!

[kelly.young]

Hello @Anonymous I see that you are visiting as a new member to the Inventor Forum.
Welcome to the Autodesk Community!

Do you have documentation you are trying to follow along or something you want to recreate?

If you can attach your attempt here for community experts to comment on further that would be helpful. 

Please select the Accept as Solution button if a post solves your issue or answers your question.

[kelly.young · Accepted solution]

@Anonymous what version of Inventor are you using?

Do you want it to be parametric so you can drive the distance or animate? If so you'd have to setup the Equation Driven Curve as stated prior. Here is a quick setup that might help made with 2019.

Please select the Accept as Solution button if a post solves your issue or answers your question.

[Anonymous]

Hey guys thanks for the prompt responses.

So I am using Inventor 2019. I have opened the Fibonacci spiral file attachment into Inventor.

That is basically the shape I am after. A 3d version of the spiral. So that is great.

https://autode.sk/2JgeZW4

The next step I am after would be to formulate it in a parametric equation so that it can be animated.

So my question is if someone could upload a workflow displaying the parametric equations for a 3d golden ratio spiral that can be used for animations?

I have tried to input the functions above from earlier posts but I have had no success in the 3d version of the parametric equation with Cartesian co-ordinate system.

Again many thanks for the help.

Regards Borei.

[S_May · Accepted solution]

it would work with excel

[Anonymous]

Hey guys. Thanks for the input.

By the way i have used the instructions from post #2.
The parameters and user inputs from post worked for a 2d equation curve

I would just need guidance for the 3d parametric curve if possible

[Cris-Ideas · Accepted solution]

Hi,

I have just used formulas from above post and got this.

Is that not what you need?

Cris

[Anonymous]

I don’t know if this will help you and although not as cool as all these 3D computer cad pieces of work... but I didn’t see this info so I thought I’d add it.  But one time I spent an hour or two plotting out all the math of a 3D fib spiral and what I came to was the 3D plotted points... as I got to the 3D spatial location after I used a good portion of my afternoon doing a bunch of calculus was that in 3D space ... was the 3rd dimension was actually the next set of the Sam fib numbers in 3D space... 

[Anonymous]

Thank you for this. I will check it out later but in the meantime, I am most grateful.

[Anonymous]

When you do let me know if that’s what you got as well