A Golden Ratio tool/macro?

Richard T. Balsley · February 2013

Okay, I was asked to come up with a building plan that uses a nautiloid shape. Has anyone attempted a building of this kind, and if so, did you use a macro or is there a tool in CC3 that allows you to quickly whip out a building like this? If not, what would be the best way to come up with something like this (and hopefully have the segmentations for rooms included to keep the proportions intact). I don't want to say too much about the concept as it's something being published, but suffice it to say the concept behind the building is that it's extruded.

Thanks in advance for any help.

Ralf · March 2013

Huh, not sure what shape you're looking for exactly. Do you have a example image, a rough sketch or anything?

Gathar · March 2013

Something like that, I guess ? http://www.visoflora.com/photos-nature/photo-grand-coquille-du-nautile.html

Richard T. Balsley · March 2013

Yes, very much like Gathar's link.

Richard T. Balsley · April 2013

Seems like it would also come in handy for an ancient Mesopotamian-sytle astronomer's tower with a spiral staircase that leads up to the top of the structure as such buildings had no interior.

JimP · April 2013

I would love a Golden Ratio building template for cities and buildings.

Richard T. Balsley · October 2013

I know this thread is a bit old, but I'm still in need of a tool of this sort. I was wondering how I could build my own macro to make Golden Ratio shapes in regards to the mathematics that I'd have to input that the program would recognize as the value I'm referring to. The reason I would like to have this tool is that it is not just for a commercial project, but also because it's found throughout nature: spiral arms of a galaxy, crest of waves, etc.

Monsen · October 2013

Could Joachim's spirals tutorial be of any help yo you here? He posted a tutorial in pdf form in his most recent post in the tread (as of this writing)

Joachim de Ravenbel · October 2013

Posted By: MonsenCould Joachim'sspirals tutorialbe of any help yo you here?

Thanks for the reference, Monsen, but in fact Golden Spirals are not built the same way.
It got me intrigued though, and a macro building a Golden Spiral was suprisingly quick to write once I realized that the Golden Ratio phi = 2cos(72°).

Joachim de Ravenbel · October 2013

Here it is:

MACRO GoldS
SELSAVE
SAVESETTINGS
GP Pctr 0,0
GP Pctr ^DOrigin point[0.00000,0.00000]:
GV R0 1
GV R0 ^DGreatest radius [1.00000]:
IFN R0 MacroDone
IFZ R0 MacroDone
GN aN 10
GN aN ^DIterations number [10]:
IFZ aN MacroDone
IFN aN MacroDone
GCOS phi 72°
GV phi phi*2
GV ang 0
:loop
GP P1 ref Pctr <ang,R0
ARCS Pctr P1 ang+90
GV ang ang+90
GP Pctr ref Pctr <ang,R0*(1-phi)
GV R0 R0*phi
GN aN aN-1
IFZ aN MacroDone
GO loop
:MacroDone
GETSETTINGS
SELREST
ENDM

The macro file is included in the zip file and should be placed in the CC3 root folder.
To use, load the GoldenSpiral.mac macro (using LOADMAC or Tools->Macros->Load Macros) and launch with the GOLDS keyboard command.

Example below with 20 iterations.

Joachim de Ravenbel · October 2013

This second version makes the Golden Ratio default but lets you choose another one if you so wish:

MACRO GoldS
SELSAVE
SAVESETTINGS
GP Pctr 0,0
GP Pctr ^DOrigin point[0.00000,0.00000]:
GV R0 1
GV R0 ^DGreatest radius [1.00000]:
IFN R0 MacroDone
IFZ R0 MacroDone
GN aN 10
GN aN ^DIterations number [10]:
IFZ aN MacroDone
IFN aN MacroDone
GCOS phi 72°
GV phi phi*2
GV phi ^DRatio [Golden Ratio]:
GV ang 0
:loop
GP P1 ref Pctr <ang,R0
ARCS Pctr P1 ang+90
GV ang ang+90
GP Pctr ref Pctr <ang,R0*(1-phi)
GV R0 R0*phi
GN aN aN-1
IFZ aN MacroDone
GO loop
:MacroDone
GETSETTINGS
SELREST
ENDM

Note: with a ratio of 1 you'll get a circle and above 1 the spiral starts from small to large. A ratio of 0 is not interesting but a negative ratio is quite funny...

Dogtag · October 2013

Beautiful!

JimP · October 2013

How do I use that to draw a building, town, castle, etc. ?

Richard T. Balsley · December 2013

Thank you! This is awesome and what I needed for a project.

Joachim de Ravenbel · December 2013

You're welcome.
I hope you'll be able to show us the result

Richard T. Balsley · April 2014

I'm working on the map, took me a while to get to it, but it's staring to come out. The problem I'm encountering is that when I use the macro, it causes CC3 to not recognize commands. Examples include zin2, zout2, and switching from one set of menu commands to another (e.g. CC3, SS3).

Joachim de Ravenbel · April 2014

Posted By: Richard T. BalsleyThe problem I'm encountering is that when I use the macro, it causes CC3 to not recognize commands.

Hi Richard.

When you load the macro file through the LOAD MACRO command, it also un-loads the standard FCW32.mac file containig all these commands you have lost.
This is standard behaviour.
I see two solutions
1. once you're done with the macro, use LOAD MACRO to load FCW32.mac again.
2. open both macro files (FCW32.mac and GoldenSpiral.mac) with a simple text editor like Wordpad, copy/paste the lines from GoldenSpiral.mac (or even from above) to the end of the FCW32.mac file, making sure there is a blank line between the last ENDM and the begining of the pasted text. Make also sure there is at least one blank line at the new end.

In this case, I'd go with 1. as you'll probably won't draw spirals every other minute...
Note that if you choose 2., you'll have to start again after an update as updates overwrite FCW32.mac with the new version.

Hope I'm clear.

Richard T. Balsley · April 2014

Yes, that helps. I thought it was a glitch in the system as I've never used macros up until this point.

One other strange thing that occurs is if I use any value ending in a 0 over 20. For some reason CC3 says it can't map it. I also don't know how you got your spirals to be as large as they are. When I draw mine, I have to scale them to fit the dimensions I need, and that's with increasing the size of the radius from 1 to 10.

Once I get the parameters of the map set up, I'll post some shots of my progress. Maybe I'll even do some for a fictional asylum based on the Kirkbride design.

Joachim de Ravenbel · April 2014

Posted By: Richard T. BalsleyOne other strange thing that occurs is if I use any value ending in a 0 over 20.

Sorry I don't understand that. Could you give a precise example with value and name of the parameter please?

Posted By: Richard T. BalsleyI also don't know how you got your spirals to be as large as they are

Change the greatest radius input (second).

Richard T. Balsley · April 2014

As to the first point, if I use a number like 50, it tells me that it can't process a value of 0.

As to the second, how large of a number are you using? I used 10 and it was still rather small and I was just curious as how to make them bigger without going through so much extra work.

Joachim de Ravenbel · April 2014

Which parameter are you using the 50 value with? If it's the ratio, it's logical CC3 finds it a bit hard because the last length is about 1e16 times the first one.

When the prompt asks for: Ratio [Golden Ratio]: just hit Enter to choose the default value instead of typing a value. You can do this with any CC3 command having default values in square brakets.

Also note that the Origin point is the center of the first arc. On the samples below, the double-arrow lines show the max radius between the first arc an its center point.

Richard T. Balsley · April 2014

Okay, so it's the iterations value that causes this error and it returns a value of the radius being equal to 0.0 although it starts at 1. I take it that the value of iterations can be no more than 20 or 35 (numbers that I've had work) times the max radius without the program generating the error.

Joachim de Ravenbel · April 2014

Posted By: Richard T. Balsleyit's the iterations value that causes this error and it returns a value of the radius being equal to 0.0 although it starts at 1

Yes that's it. A each new iteration the radius is multiplied by the ratio so with 50 iterations you have a radius of ratio^50: about 3e-11 reasonnably rounded to 0.

Funny thing, on my computer, when the radius gets to small it's rounded to 0.00001 so I don't get CC3 message you have and didn't notice anything wrong. Thanks for detecting this.

If you want a formula, the number of iterations should be under -5/log(ratio)/Radius input (under 24 for a Radius input of 1).

Or download the edited macro below that stops once the radius is under 0.00002.

Joachim de Ravenbel · April 2014

Edited macro text:

MACRO GoldS

SELSAVE

SAVESETTINGS

GP Pctr 0,0

GP Pctr ^DOrigin point[0.00000,0.00000]:

GV R0 1

GV R0 ^DGreatest radius [1.00000]:

IFN R0 MacroDone

IFZ R0 MacroDone

GN aN 10

GN aN ^DIterations number [10]:

IFZ aN MacroDone

IFN aN MacroDone

GCOS phi 72°

GV phi phi*2

GV phi ^DRatio [Golden Ratio]:

GV ang 0

:loop

GP P1 ref Pctr <ang,R0

ARCS Pctr P1 ang+90

GV ang ang+90

GP Pctr ref Pctr <ang,R0*(1-phi)

GV R0 R0*phi

IFN R0-0.00002 MacroDone <- add this line

GN aN aN-1

IFZ aN MacroDone

GO loop

:MacroDone

GETSETTINGS

SELREST

ENDM

Richard T. Balsley · April 2014

Here's a sample of the work in progress.

Richard T. Balsley · May 2014

Near completion!

Dogtag · May 2014

Looks AMAZING! Can't wait to see the finished map.

I hope no one would need to vacate the structure in a hurry from one of those inner rooms, though! Yikes.

~Dogtag

Richard T. Balsley · May 2014

Well, it's a living building for Mutant Future.

Dogtag · May 2014

Ewww!

And, cool.

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A Golden Ratio tool/macro?

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