Snail generation with logarithmic spiral and torus

Here is 2 ghx (one with GH 0.80066 and the other with GB 0.9.0005 ) for generation of snail with logarithmic spiral and torus.

Radius = exp (b*angle), in order to minimize problem I have done adimensional size. So the diameter is near 10 units.

In order to be fast I plug the circle instead of torus

First example

Attachments:

logarithmic_spiral_torus_v2_g0.9.ghx, 328 KB

Replies to This Discussion

Permalink Reply by CongChien on August 1, 2012 at 6:01pm

Nice job

Permalink Reply by spiral on August 1, 2012 at 10:45pm

Super, thanks to this excellent work

Permalink Reply by Duncan W on May 14, 2013 at 5:31am

This is pretty amazing.

I'm trying hard to create a loxodrome with Grasshopper but your definition escapes me as it uses mostly custom math rather than Grasshopper components.

How would you recommend going at a loxodrome using just Grasshopper components?

Permalink Reply by Laurent DELRIEU on May 16, 2013 at 2:10pm

I posted an example with equations, but it seems quite explicit. If you want a revolution different from a sphere, it is possible but a bit more difficult. See the link below http://www.grasshopper3d.com/forum/topics/loxodrome

Feel free to ask questions.

Permalink Reply by Fakinos Konstantinos on March 17, 2015 at 9:26am

very interesting work and thank you for the files! i would like to make a shell like the first image with your definition. I need to design again the part in second image to fit to next scaled part but also i need to find the math formula for each part to fit to the next. Also how can i avoid the first very small parts because are too small but use much RAM. pl any help? thanks!

Attachments:

Permalink Reply by Laurent DELRIEU on March 17, 2015 at 4:37pm

hello here is a fast modification, many thinks must be done in order to have a better interface. I propose to generate your shape with 2 sections. These sections are copied in order to have section 1, section 1, section2, section1 and section 1. So 5 section to determine the snail shape. But you can manage to have the number of shape you want.

Permalink Reply by Laurent DELRIEU on March 17, 2015 at 4:50pm

An example with straight section option on loft

Permalink Reply by Fakinos Konstantinos on March 18, 2015 at 5:14am

thank you for quick reply and for these interesting definitions! i will experiment with these. i forgot to say that i need to fit the sections also to the central axis, maybe for this i need the spiral curve and a center axis line and tangent points of sections to edges but i will see what i can do.

Permalink Reply by Laurent DELRIEU on March 18, 2015 at 2:51pm

Still a not clear script but on the axis. You need to move curves if you want to adapt the shape

Permalink Reply by Fakinos Konstantinos on March 18, 2015 at 4:33pm

wonderful! thank you for all that Laurent! i will study these definitions!

Permalink Reply by Laurent DELRIEU on March 21, 2015 at 2:20pm

Here is a new definition, more clean and more exact.

"Classicall" shell needs a ratio near 1.6. If you need to do to make a shell like a clam shell ratio must be very high 50 or more.

Sections curves could be closed, open, planar or non planar.

In the files there is the ghx, a 3dm with 4 shells and curves sections. A bitmap for texturing is also provided. Have fun.

Attachments:

20150320_Seashell_Log_Spiral_Uploaded.ghx, 364 KB
20150321_shells.3dm, 4.4 MB
texture _entiere.png, 321 KB

Permalink Reply by Fakinos Konstantinos on March 23, 2015 at 5:20am

I like the study of nature's geometric forms and analyzing of their symmetries, how math unfold from all these shapes, so this is amazing and great. Thank you very much Laurent! With algorithmic modeling one feels more closer with deeper understanding to nature's capacity of kneading forms through time. I would like to add here some researchers on this field, among others, like D' Arcy W. Thomson, Ian Stewart, Mario Livio who they have make studies on nature forms and geometries.