Can anyone help me convert these 2 similar equations into scripts I can use in MOI ?

(u+v)*cos(v), (u+v)*sin(v), v


(1+2)*cos(2), (1+2)*sin(v),2

They produce a spiral where there is a gradual increase in the distance between the developing spiral loosely as attached image - the equations allow you to alter the rate of increase between the developing spirals arms

They came from a friend of a friend who worked them out for me 20 years ago

Andy

This don't work with the Fx Graph 2D or FX Graph 3D by Max Smirnov ?
http://moi3d.com/forum/index.php?webtag=MOI&msg=6447.1

Hi Andy

Max Smirnov's script FxGraph3D was used, with X(u,v) = (u+v)*cos(v),
Y(u,v) = (u+v)*sin(v), and z(u,v) = v.
Also minU = 0, maxU = 3,
minV = 0, and maxV = 18.85, which is just over 3 * 2 * PI, to create just over 3 circular rotations.

3D spirals were produced, but they did not expand.

Switching modes did cause MoI to hang up, in one case...

I'm too busy to look further right now. Will try again later...

- Brian

There are scripts for several spirals on the forum.

Maybe Logarithmic spiral?

Hello Andy,

the result should be a surface - right?

Kind regards
Karsten

Andy,
I would suggest trying the LogSpiral script.
Set the exponent to something like .08, adjust to suit.
Set the number of Whorls to say 3.26.

Then place a vertical circle on the open end, say 2 units. Adjust radius to suit.
Sweep the circle along the spiral, using Pointed End checkbox.

Slice off the amount of 3D curvature desired.
Instead of a circle, a partial curve could be used instead...

Due to MoI's built in history, after the sweep, the radius of the circle can be changed, and the sweep also changes.

- B

// _IonicVolute script by Brian McMillin March 30, 2016
// This script is based upon the paper by Denise Andrey and Mirko Galli, specifically
// their equation derived from work by Dürer (1525), Giullaume Philandrier (1544).
// http://link.springer.com/article/10.1007%2Fs00004-004-0017-4#/page-1
// http://www.springerlink.com/content/r61qh2354m56qt31/fulltext.pdf
// http://www.emis.ams.org/journals/NNJ/AndGal.html
// http://www.c4dcafe.com/ipb/forums/topic/59105-ionic-volute/
// There are good pictures of the Ionic Volute's here:
// https://en.wikipedia.org/wiki/Ionic_order

// This is a 2D script, with z = 0.0.
// The "eye" circle has a diameter of one unit, and is placed at x,y coordinate (0,0).
// The "inner side" of the spiral begins at the top of the eye, at (0, 0.5). (The angle here is PI/2.)
// The spiral is made up of 3 whorls, and the "inner side" of the top of the spiral is at (0, 4.5).
// (note that b = 4.5 units is a fixed value in this script).
// The "inner side" of the bottom of the spiral is at (0, -3.5), but this will change
// if aValue is changed.(aValue = +3.5 units).
// (It is up to the user to model the "outer side" of the spiral, which may be done by
// doing a few sweeps, etc. The user can also scale the spiral with MoI.)
// Polar coordinates are used, which consist of an angle alpha, and a radius r.
// The equation is r = r(alpha) = 3.5 * tan(beta + ((alpha - PI/2)/(whorls*2*PI)) * (gamma - beta))
// The number of turns is whorls, which defaults to integer 3, as per sample Ionic Volutes.
// Angle alpha ranges from PI/2 to (whorls*2*PI + 1)/2, which is 13*PI/2 for 3 whorls.
//
// gamma = arctan(b/a) = arctan(4.5/3.5).
// beta = arctan(0.5/a) = arctan(0.5/3.5).

// Polar coordinates are converted to (x,y,z) using x = r*cos(alpha) and y = r*sin(alpha), with z = 0.

I'll modify the ArchimedeanSpirals script with the above formulas, to make the Volute script. But it is too late tonight to finish :-)

- Brian
So the volute appears to be Ionic, rather than Corinthian.

I see that there is also a Gibbs method.

Hi Brian

Thank you for your help with this

The Ionic / Corinthian element is not critical, I used the image as an example of the sort of spiral I am trying to achieve.

I am making a set of sculptural forms that I call 'pure forms', and these spiral forms are the key building start point, I am after spirals that increase at a constant % or increasing %

Attached some spirals I have built via Rhino by making say a honeycomb revolved shape and then using line on surface command that makes a line of best fit on the surface between a start and end point, its rough and ready but works after a fashion

Attachment comments-
T cog spiral - is fine and usable, made via Rhino
line for sweep - using log spiral script in MOI to generate the base form and rather than sweeping a circle I used a line, results shown here in purple - convert edge to a line quicker to do. Spirals formed are very similar to the original, I have tried rotating about 0,0. to compare but as the spiral does not go to the origin its does not revolve well
Aqua- A very open spiral form, but gives an idea of the range I am looking for the spirals, the central circular start was added on by me so is not clean / mathematically pure hence my trying to find a cleaner rote

I have hunted on the MOI forum for the IonicVolute script by Brian McMillin March 30, 2016 you mention but cannot find

Best wishes

Andy

Hi Brian

I have been searching the Forums a bit more and have come across the Vesicle script which is close to something I have had a problem with creating a clean S form - see attached image created in adobe illiustrator (and then imported into MOI later)

The red line is my best fit using as minimal a set of control points and anchor control arms so it makes a clean flowing double form. The dotted circular line shows my loose guide circles and centre's. Visually it has a slight flat zone between the 2 dotted circles at loosely the 60% high crossover section.
To refine this S shape further I had been wondering about using 2 opposing spiral forms and joining the ends together tangentially - will take a bit of juggling !

Any mathematically clean solutions that pop to mind ?

Best wishes

Andy

If you have some sufficient constructions points, seems a nurbs curve can pass by these ones! :)
Option By Point (not Control Points)

Sorry Andy, IonicVolute is not written yet. Those were the numbers and formulas needed.
It may take an hour or three to code, after work.

Have you tried a relaxed PolySkelion script?
There are also the Galaxy spiral script and the GalacticSkelion script, but they have limited range until they make a bunch of stray lines.

-B

Here is an alpha version for IonicVolute.
It works, but still needs some improvement or corrections.
I'm guessing atan may be a problem.
10 minutes to code, 10 minutes to debug, 30 minutes to fiddle.
- Brian

Edit: See post 7903.16 for updated, corrected IonicVoluteAlpha02.

Ok No problem Brian

Polyskelion looks good although the transition from one spiral to the next is not as smooth as I would want so may do manually for a clean S form, each of the individual spirals created are pretty good though

Your help with this is very much appreciated

Andy

Ok wow that was quick Brian

Can I make a donation for your time and effort ?

Possible improvements to the control the output

A) The spiral lines increase in distance apart smoothly, which is spot on :-) but can we control this increasing % in any uniform way ?

B) Also would it be possible to control the inner starting radius or diameter ?

The a & b values control in the script ? the size of spiral produced using the script seems to be about 25mm / 30mm - can this be increased if the maths allows or do I just need to scale up ?

atan - ? not sure what this refers to ?

This in effect will become the artist perfect set of french curves in MOI if you can devise a way to control A & B above

best wishes

Andy

Hi Andy,
No donations please, this is for hobby/ fun/ occasional utility ☺
The script can likely be improved. I do not feel that I have a good understanding of the math yet, including "a" radius, "b" radius, and eye radius.
-B

The IonicVoluteAlpha01 had a glaring error in the formula, bvalue instead of the correct beta.
The default parameters now re-create the volute with the "historic" proportions. The two end tangents are not horizontal.
Added a parameter for the eyeRadius, the inner end of the spiral. Renamed bvalue to bRadius.
In the event that the eyeRadius exceeds the bRadius, the bRadius is "inner" rather than "outer."
Negative values for Whorls or eyeRadius are strange. May add absolute value to them.

Next to do are sliders, counter clockwise, and start angle.

- B

Brian

Hey great, its working just fine thank you :-)

Look forward to the final version

Andy

Here is the "final" version of the IonicVolute script.

After creating one spiral, making a second spiral, with the only change being the "offset" parameter, leads to an interesting surface or extrusion, which can be filleted.

The notes were modified, and are in the .js file. The tangent equation was substituted into the logspiral4 script, with additional modifications.

- Brian

The "inside" of the spiral:

Great thank you Brian

The sliders are a big help to get things looking visually right for my projects

and your offset spirals look good, looking forward to playing with the script properly

I have updated my LogSpiral script to version 4

Again many thanks for all your work on this

Best wishes

Andy