Unroll vs Squish which one is more accurate for this surface

[gurkan_bozkurt]

Hi everyone,

I’m working on a metal cladding roof model currently. Squish and unrollsrf commands gives me very different results in terms of boundary. What do you guys think? Which one should I trust?

Unroll vs Squish.3dm (14.2 MB)

[altamiro.aj]

I believe this post can answer your questions about it

Difference between unrollsrfuv and squish

A surface is developable, if it can be “unrolled” into a 2d shape without any compression or expansion. All developable surfaces are ruled surfaces and are only curved in one direction. _unrollSrf and _unrollSrfUV are the commands that should be used for those surfaces. _unrollSrfUV will keep the parametrisation to stay the same as in 3d. This useful for example if you want to _flowAlongSrf later - with the unrolled Surface as a base. _squish will expand or compress the surface to bring it …

[gurkan_bozkurt]

What I understood from that post is if unrollsrf gives you an output you should go with unrollsrf for better accuracy. Am I right?

[Tom_P]

I answered in the original post:

Difference between unrollsrfuv and squish

No ! Unrollsrf will not check if a surface is developable. below an example of a saddle-like-surface. it is not developable. _unrollSrf result in the middle _squish result at right. [image] because of the symmetry (mirrored / rotated) of the initial surface, you would expect the same symmetry in the result. - but unrollSrf does not deliver it squish does. A surface is developable if its gaussian curvature is 0 at all surface points, see above Wikipedia link. _curvatureAnalysis can so…

[gurkan_bozkurt]

Thanks a lot for your detailed answer Tom. I understand it much better now.

I was writing long reply about banana shape of the unrolled surface. While I was writing it, I realized edges of my surface are not the same length. Idk why I assumed they were equal. I guess I need to use unroll for this case and accept the banana shape.

[Jess]

Hi @gurkan_bozkurt

@gurkan_bozkurt

banana shape of the unrolled surface

If the stripes were conical then the unrolled srfs should be banana like.

However, the design intention looks like a revolved profile which is cut into concentrically pieces:

Then the unrolled srfs should be lens like ()

By identical rebuilding the edges with various lengths you’ve got lofts with a bit negative curvature, indicated by the blue color in the curvature analysis shown above. This may also cause the banana shape of the unrolled parts.

Anyways, the trimmed lower edges of the revolved profile are geometrically not precise, which may also lead to conical shapes. So hard to say if this will work without knowing the real conditions…

Jess

[gurkan_bozkurt]

Hi Jess,

I’m trying to keep the width of the surfaces as close to 500 as possible while solving that banana unroll problem.

Here’s how I’m currently getting these results:

I project a curve onto the surface, create some perpendicular frames, and then intersect them with the surface.

Then I loft the intersection results to get the surfaces. If you have any other suggestions, I’d love to hear them.

Grasshopper file:
BananaRolls.gh (260.3 KB)

Btw, how much Gaussian curvature is too much for UnrollSrf? :DD
I’m working in millimeters at the moment, and these numbers look pretty small to me.

[Jess]

@gurkan_bozkurt

I project a curve onto the surface

How did you create that surface?
I assume the original section profile is made from 3 lines with 2 arcs (fillets). These profiles have been trimmed and rebuild with identical control point count. Don’t do this if you want best results!

In your previous file the original surface was revolved (with concentric isocurves). Now these profile isocurves are parallel but the frames are still concentric.

Ideally you model the rationalized stripes from perfectly developable surfaces (cylindrical, conical, freeform curves extruded or lofted to a point and so on…)

@gurkan_bozkurt

Btw, how much Gaussian curvature is too much for UnrollSrf?

With negative curvature there is no limit. Rhino will unroll any surface if all isocurves from at least one of the uv-directions are all linear - I know, sometimes it sounds weird describing bugs

With positive curvature I assume they make the exact same test, but it is not possible to make a surface with positive gaussian curvature where at least one of the uv-directions are all linear (within file tolerances).

But the question is: How much compound curvature can be fabricated?
This depends on many factors:
What kind of material will be used?
How big is the compound area?
Is it in the center of the surface or along an edge or at the corner?
Metal is more flexible than rubber, but it needs a bit more energy to deform it.
In ship building almost anything is possible. In architecture a bit less, but still a lot.

But first let’s try to rationalize the shape perfectly…

Jess

[gurkan_bozkurt]

Thanks for your interest in the topic, Jess.

On the original surface, I drew some sections over the base model and just used some sweep commands.

Now I’m extracting edges from the underlying steel structure and rebuilding all of it with the same number of points (because if I don’t, the loft gives me a polysurface). Then I loft everything using the default settings.

I also tried using Revolve with the first and last curves as reference, but unfortunately it doesn’t give me the accuracy I need in the middle part.

@Jess

With negative curvature there is no limit. Rhino will unroll any surface if all isocurves from at least one of the uv-directions are all linear - I know, sometimes it sounds weird describing bugs

The surface is about 200 m long, and the Gaussian curvature analysis shows 0.00000000003 mm (if I understood it correctly). I feel like I can probably ignore that.

[Jess]

Hi Gurkan,

@gurkan_bozkurt

extracting edges from the underlying steel structure and rebuilding all of it with the same number of points (because if I don’t, the loft gives me a polysurface).

Polysrfs are no problem to unroll, especially when these are perfectly developable.(zero gaussian curvature).

@gurkan_bozkurt

The surface is about 200 m long, and the Gaussian curvature analysis shows 0.00000000003 mm

The length of the building doesn’t matter at all. It is the width - and from you initial model with the concentric stripes - I thought you want to fabricate from sheet metal coil 500mm, then banana unrolling should be avoided of course

Good luck, Jess

[davidcockey]

Excerpts on Gaussian curvature and developable surfaces from from previous threads:

@davidcockey

Guassian curvature is a very common metric suggested for assessing if a surface is developable, but it has a significant drawbacks for assessing if a surface is close enough to exactly developable.

An exactly developable surface has exactly zero Guassian curvature. But what is the surface is not “exactly developable” as sometimes happens in design.

How small is small enough for Guassian curvature? That is a non-trivial question, and one that I have rarely seen an answer to.

Is 0.1 small enough? How about 0.001 - that seems like a small number? Or should it be even smaller, perhaps 0.000001?

Gaussain curvature has units of 1/length^2. If millimeters are the length unit then Gaussian curvature has units of 1/mm^2. If meters are used then Gaussian curvature has units of 1/m^2. So the numeric value for the Gaussian curvature of a surface will be 1,000,000 larger if meters are used rather than millimeters. A Guassian curvature of 0.1 if meters are the length units use is the same as 0.009 if feet are used, the same as 0.00065 if inches are used, and the same as and 0.000001 if millimeters are used.

A second drawback to using Guassian curvature to assess if surface is close enough to exactly developable is it is difficult to relate Guassian curvature to other measures such as the amount of

@davidcockey

Neither of your surfaces is very close to being developable, even though the numerical value of the magnitude of the Gaussian curvature appears to be very small.

The Curvature command shows circles fitted to the principle curvatures at a point on a surface. A developable surface will have on of the principle curvatures equal to zero everywhere, and the corresponding curvature “circle” will have infinite radius, ie a straight line, everywhere. Neither curvature circle is close to a straight line over a large part of both of your surfaces. In other words they are not very close to being developable. But the magnitude of the Gaussian curvatures of your surfaces have very small numerical values. What’s going on?

The problem is the numerical value of magnitude of the Gaussian curvature by itself is not a good way to judge how close a surface is to developable. Gaussian curvature is a dimensional quantity with units equal to the inverse to the dimensional units of the surface squared. Your surface has dimensional units of mm so Gaussian curvature has units of 1/mm^2. Change the units to meters and rescale the model so that the physical size and shape stays the same. The numerical value of Gaussian curvature will increase by a factor of 10e6 or one million while the “physical surface” stays the same. The only change is in the units used to measure Gaussian curvature.

Check for developability using the Curvature command.

[gurkan_bozkurt]

Hi I have a new question :))

When I check it gaussian curve of this extrusion it says there is none but when I explode it to make a surface suddenly there is curvature. Is it normal?

Extrusion.3dm (19.8 KB)