An exercise: DRAWING A PARISIAN FENCE

TaffGoch

This attempt was a "proof of concept" model, to try out a technique I had in mind.

The same technique could be used to precisely match the frequency and repetition of the original posted images, with the right count of torus and circle segments. (I doubt I'll pursue that further, but thought others might be interested in the technique.)

Turn on viewing of "hidden geometry," to see how the follow-me path was drawn with the "Line" tool. (Model attached.)

-Taff

Torus_spiral.skp

Arc

Hi, guys, try the tours plugin (http://regularpolygon.blogspot.com/2010/07/plugin-torus-10.html)

pilou

@unknownuser said:

It seems to me that you may find an intermediate process to produce a really round shape, am I wrong?

I had not search to have a perfect round form
Maybe it's an hard way because you must play with the Helix parameters!
So maybe not the best trick for this problem
But as said previous you can deform it for approch the Sphere as your just previous post

pilou

@unknownuser said:

but this is the exercise!

Not for me! Form is secondary!
It was a trick for find the infinite closed path of the helix!

another trichky one : the Boy's surface By JPP

simon le bon

@Pilou

It seems to me that you may find an intermediate process to produce a really round shape, am I wrong?

@TaffGoch
It seems to me that we follow about the same method, and the sewing grows easily to a hard polycount

60x60=3600 ! I must be wrong somewhere

(picture coming from a study of TaffGoch model)

@Arc
Thank you to have discovered for us this Regular Polygon's plugin (Hello Regular ! )
The torus spiral can be easily rearranged with FredoScale

@Ely
Guy, You can't but come now to show us your way

*s

simon le bon

@Pilou

@unknownuser said:

I had not search to have a perfect round form
but this is the exercise!

@unknownuser said:

But as said previous you can deform it for approch the Sphere as your just previous post

@Myself

@unknownuser said:

60x60=3600 ! I must be wrong somewhere

(picture coming from a study of TaffGoch model)

I don't understand everything but i get an element of answer:

(picture coming from a study of TaffGoch model)

*s

simon le bon

Dear Pilou,
thanks for this Jean Pierre Petit's link.

(When I was young, I was a wild and rebel, and bad student. I don't know why I want to understand everything like I do by now)

First a trick concerning a problem I have met: When I wanted to reconstruct the complex set of spirals by copy/rotate the basic section, that produced here and there some micro-cuts in the continuity of the lines.
I have used StrayLines to locate and label them

Repair,

>I want to understand better how the spiral works:
1)taking back my model
24 sided circle; 32 segmented face shape; each segment is 24 subdivided.
Each 360° turn of the shape describes completely one of the 32 face's segments.
24 single edges are necessary to achieve this single revolution.

Consequently, the entire spiral is made by 32 turns and no edge is used two times.
and we find effectively 32X24=768 edges

1)taking back Taff's model

Each 360° turn of the shape uses 60 edges (because of the 60 sided based circle).

The entire spiral needs 3 complete turns of the shape to be totally described.

3X60= 180 edges of the spiral.

Each edge of the basic section (90 edges) is used two times.

2X90= 180 edges of the spiral.

As I can understand the law of this:

the shape must make a number of entire 360° turns
the complet set of edges(included into the basic section) must be used a complete number of times.
the number of edges used in the number of complete turns must meet the number of edges constituting the basic section used to produce the spiral.

here: 60X3=180=90x2

to be verified!

simon

pilou

I believe that is the same problem for what Tig had made his True Tangents plug
Circles or helix ar not real circle, just polysegments aproximation , so in the 3D space there are some losses of precision after some turns

I have remarked that with my previous try above, I had must corrected by hand the join continuity!

ely862me

Hmm so much theory ..what i did was simple,make a spring,make a copy of it,take a spring and adjust it with ffd(remember to let the top and bottom points untouched) in order to make from it the inside part of the spiral, after this take the other one and flip it along in order to continue(descend on the outside) the first one,then play with ffd on it in order to make the exterior part of the spiral(remember to let the top and the bottom points untouched).Then i used lines to tube plugin. And that s kind of it!
Ah..and before working them with ffd i flattened(with ffd) the top and bottom spires of the springs to make a smooth transition from a spire to another.

infinite spiral a.skp

TaffGoch

Colors help identify the six separate (yet identical) loop components:

-Taff

simon le bon

@Ely,

Hi Ely, I like your way: searching for simple and quick processes your solutions are refreshing
SketchyFFD (Free Form Deformation) is a good deal for sure
[Plugin] SketchyFFD (Updated Aug 22, 2009) by CPhillips
SketchyFFD (Updated 9 Feb 2010) revisited by gbabcock
Making springs:
How to make spiral 02 by SketchUp
SketchUp: KitoRaupp_Pottery
(May be you can do a little more effort to explain in few several steps in your Skp rather than just show the result )

@Taff

Hi Taff (I have noticed you are from the early morning, and I'm waiting my own awakening to read your posts ) Thank you for your colored exemples. I guess the same treatment as you've done with your Geodesic Weave Ball should be also very great

Additionally, I would invite people to visit carefully your warehouse collections they are mines

and don't forget the "Help Group Discussion"

simon
re: what a great thread!!

TaffGoch

More torus segments produce results that better approximate the original images.
(Well, duh!)

Model available at 3D Warehouse

-Taff

TaffGoch

Simon,

I tried the chipped-paint texture, but it was too "busy," and was a visual distraction.

A simple texture looks good though, when rendered:

-Taff

simon le bon

Dear Taff,

Simple is the best; it is a "réussite" . I see it in 2D, spirit relaxing.
(But is it so simple? I mean about the discrete raw of light)

'Cause you seem also from late in the night, I wish U a good one.

simon

simon le bon

@simon le bon said:

As I can understand the law of this:

the shape must make a number of entire 360° turns

the complet set of edges(included into the basic section) must be used a complete number of times.

the number of edges used in the number of complete turns must meet the number of edges constituting the basic section used to produce the spiral.

and
4)the number of entire 360° turns of the shape must be the minimum one (sorry for bad explanation. I think it is the meaning of :"Least common multiple" )
(It doesn't make sens for the basic shape to go around more than the necessary number!)

@unknownuser said:

to be verified!!!!

I take back Taff's model to make a try to validate my thoughts

Not bad what do you think! slb

TaffGoch

Simon,

I didn't pursue the precise defining of the calculations, but I sensed the general concept of the relationships.

When I started on my second model, I roughly estimated a "longitude-to-latitude" ratio that should (might) produce a more-complex, tighter spiral with less slope, and six loops.

As an intellectual pursuit, yours is a good mental exercise. (Perhaps, if it were mid-winter, and I was snowed-in, then I would have time to wrestle with a precise definition.)

-Taff