Help modelling hyperbolic and catenoid type surfaces

Shpox

Hey guys, just after a bit of your assistance here. I'm trying to model a catenoid in the manner of loft. Ideally I'm trying to use two faces, for example two circles, one above another and then form this into a hyperbolic shape.

Here's a few example images:

I tried uses TIG's Edges By Rail but unfortunetly I'm only receiving one part of the arc/curve. I'd be able to achieve this with follow me convetionally, by unfortunetly, arc's don't have a face.

After acheving that, I'm attemtping to model these physically with craft mesh though I'd need the unfolded geometry first. Are there any specific unfold tools that would be useful? I have some sort of unfold plugin in SU that I'm yet to familiarize myself with. The other option is Pepakura.

Would really appreciate any assistance

TIG

EEbyRails sibling 'EEbyLathe' will take any selected 'curves' and extrude them around a circular path.
In this case place the curves the desired distance from ORIGIN the choose two point on a vertical axis on the Z/blue axis and enter say 18s to make 18 facets and 360 to close it into a 'cylindrical' form - for half a cylinder use 180 etc...

Another way is to draw a large circle for the path [centered at the ORIGIN] and a vertical rectangle [also located with a corner at the ORIGIN], onto the rectangle you place the curves, so as to make a face, as needed; erase unwanted parts. Then use the native FollowMe tool using the circle as path and the face as the profile. The extruded shape will form a cylindrical 3d mesh. Erase any unwanted top/bottom-faces and the circle-path.

pilou

Unfold by Jim Foltz

TIG

Flattery too http://forums.sketchucation.com/viewtopic.php?p=238568#p238568

Shpox

Thanks so much guys. TIG, I went with your second strategy as I'm still trying to familiarze myself with the Lathe tool. It worked out great . I essentially made a crescent shape from the rectange and made it revolve around the circular path.

Turns out I had flaterry already installed but trying to unfold the faces of a curved object proved really difficult. It ended up making some sort of alien creature as pictured below. Have included the .skp's incase you wanted a look Jim's unfold tool wasn't able to help too much either.

It's essentially the same concept of trying to unfold a sphere.

I also found curviloft here: http://forums.sketchucation.com/viewtopic.php?t=28586 which I think might help by defining the width of the catenoid (essentially by creating two catenoids).

Catenoid.zip

Shpox

Apologies for the double post but I also tried use the Lathe and I do believe I'm doing something wrong here.

Here's a double-screencap:

gilles

you set your axis at the wrong place, it should be place at the circle center.

mac1

Jim Foltz has published an eq_grapher and once you have the 2d cure then generation of the 3d by follwme or TIGs extrude tools should be possible. The reason I mention this I have no idea what so ever if some of the surfaces above get the cure you want. You can get some of the conic sections by the intersection of a plane and cone. Hyperbolic is one. Maybe you don't care??

pilou

But seems you will have a better and simple result (rectangular faces) with only the Follow me

pilou

With the Tig Lathe plugin
You don't need to draw a circle

Draw a vertical arc on the red axe
2 clicks on the origine axe
Move the mouse
Enter 360 or any angle you want

mac1

Conic sections .jpg
Here is what I think the curves need to be unless you don't really care about the conic section.

Shpox

@mac1 said:

Jim Foltz has published an eq_grapher and once you have the 2d cure then generation of the 3d by follwme or TIGs extrude tools should be possible. The reason I mention this I have no idea what so ever if some of the surfaces above get the cure you want. You can get some of the conic sections by the intersection of a plane and cone. Hyperbolic is one. Maybe you don't care??

Thankyou for this. Although the accuracy of the curve/crescent don't need to be any particular height/length, I won't quite be using equations yet. What you have posted though will be super handy in assimilating these Triply periodic bicontinuous cubic microdomain morphologies: archive.msri.org/about/sgp/jim/papers/morphbysymmetry/table/index.html

Beats have to use the ruby console. The big intention is so create architectural spaces through these minimal surfaces.

@unknownuser said:

But seems you will have a better and simple result (rectangular faces) with only the Follow me
[attachment=0:15env91x]late1.jpg[/attachment:15env91x]

Thanks for your diagrams. They were very helpful. Using the follow me definetly seems a bit easier. The only possible issue is creating the depth in the catenoid. I'd technically have to assume the same elevation 'crescent' to ensure each catenoid is uniform in width. This may present issues if I'm attempting to make a loft between two circles of unequal length, in which curviloft maybe be more suitable.

May I ask if you used any plugin to color all the facets of your catenoid? Or if it was done manually

I've also search the web to find ways to flatten curved surfaces. So far, no easy solution or luck

pilou

Some plugs can interest you
Quadralizer and [u]Quadfrom2tris by Tig

Multiples Offset by SDmitch

Contour lines by Didier Bur
or By Tig (works on Group & components)

pilou

Of course yes you have some plugins to color it
Some by Chris Fullmer
RandomPainter (used above and follow)
Color By Slope
Color by Z

mac1

@shpox said:

@mac1 said:

Jim Foltz has published an eq_grapher and once you have the 2d cure then generation of the 3d by follwme or TIGs extrude tools should be possible. The reason I mention this I have no idea what so ever if some of the surfaces above get the cure you want. You can get some of the conic sections by the intersection of a plane and cone. Hyperbolic is one. Maybe you don't care??

Thankyou for this. Although the accuracy of the curve/crescent don't need to be any particular height/length, I won't quite be using equations yet. What you have posted though will be super handy in assimilating these Triply periodic bicontinuous cubic microdomain morphologies: archive.msri.org/about/sgp/jim/papers/morphbysymmetry/table/index.html

Beats have to use the ruby console. The big intention is so create architectural spaces through these minimal surfaces.

@unknownuser said:

But seems you will have a better and simple result (rectangular faces) with only the Follow me
[attachment=1:2msqbybj]late1.jpg[/attachment:2msqbybj]

Thanks for your diagrams. They were very helpful. Using the follow me definetly seems a bit easier. The only possible issue is creating the depth in the catenoid. I'd technically have to assume the same elevation 'crescent' to ensure each catenoid is uniform in width. This may present issues if I'm attempting to make a loft between two circles of unequal length, in which curviloft maybe be more suitable.

May I ask if you used any plugin to color all the facets of your catenoid? Or if it was done manually

I've also search the web to find ways to flatten curved surfaces. So far, no easy solution or luck

You do not have to use equations for the hyperbola or the parabola and if fact for any of conic sections( circle, ellipse, parabola and the hyperbola ( single or double sheet). These come from the intersection of plane and cone and you can draw them using the native SU tools. For the catenary your are stuck. You either use several plugins, plot in excel and then import the x/y values to SU, or use soap skin bubble but I am not sure this will work. It is defined by the hyperbolic cosine function as y = cosh(x/a) or y = a/2( exp(x/a)+exp(-x/a)) where a is the ratio of the cable tension to unit length weight). A small value results in a "pointy" curve. As a designer you need to decide what you want and then go form there. I think it is close to a hyperbola so maybe use only that. Again that is choices you have to make as designer.
Some surfaces are not unfold-able but I have not none the research if any of these fit that category. That is your job as designer.

You are expanding considerably your original post with this last one. You have been given the info you need now have fun!
BTW: There even online calculators for the catenary or tables the power companies et. al. use also.
[attachment=0:2msqbybj]conic section_2.jpg[/attachment:2msqbybj]
This is my first shot at unfold. Try the same approach by vertical slices it nay be better.
**Update 4-15 1319 MST
Some search for self education found the following:

Warped and double curve surfaces are non- developable( spheres are double curved and hyperboloid and paraboloid double warped) meaning they cannot be created with the unfold tool like you are trying to accomplish. A sphere is double curved and we all know how baseballs are made=> with the odd shaped covers. Spheres are also developed by treating the "gores" like cylinders and laying them out that way. You can use the unfold tool to make one gore ( for the hyperboloid and paraboloid) and then you would have to bend and glue a number together with probably questionable results. A clay model should be easy( just like the follow me tool) to make, you could submit to 3 d printing($) , or ribs and then attachment of some type of flexible materail. Crazy thoughts. [ /b]

Hope someone with more knowledge base weights in on this??**

conic sctiont_2.jpg

pilou

http://sites.google.com/site/jimfoltz/sketchup/my-sketchup-plugins/eq-grapher

(file is linked page bottom site)

Shpox

Thanks for the all the responses. I'll shoot you guys a link of the work so far. I ended up creating a frame using two planes and used a flexibly fabric to get the shape as close as possible to a ruled surface. I guess the crux is that these shapes are invioble so the use of the hyperbolic parabaloid is closer to being suited.

Going back to sketchup, is there anyway to actually make this shape a solid or infill the faces from the inside? I'm currently using curviloft to create these surfaces, however when trying to traditionally subtract the shape from a solid in sketchup, I'm getting the 'this is not a solid etc...'.

pilou

@unknownuser said:

make this shape a solid

Maybe JointPuspull by Fredo6 for some of them

pilou

You can also use the Extrude Edges by Rails by Tig for 2 different circles of elipses or anything you want
Just trim the Rails and keep the curves between the second call of the plugin!
(For colors see previous page)

2 rails.jpg

Shpox

@unknownuser said:

@unknownuser said:

make this shape a solid

Maybe JointPuspull by Fredo6

Actually gave this a go. I'm extruding by 0.1 inwords or outwords, but no luck. I think the number of surfaces sketchup needs to make this geometry are a bit too much for multiple push pull.