Help with 'unfurling' a curved surface?

Hi all

Just wondering if anyone can help?

I’m trying to help my brother out with a bit of a headscratcher.

He’s a stained glass window craftsman and wants to check his maths regarding the size to cut a sheet of glass so that it can be drawn flat, glazed flat and heated/bent into shape afterwards.

We’ve got the dims of the glazed dome, and he wants to check the size of the yellow panel if it was ‘unfurled’ and flat.

Is there any plug in or fancy way of doign this at all? It’s not something I’ve come across before?

Thanks and best wishes


First thing I would try is Unwrap and Flatten from the Extension Warehouse although I don’t think that will really work in the desired way since it doesn’t stretch or deform the faces that the surface is made from. TBH I’m not sure there is an extension that will do what you want. It seems to me that an isosceles triangle with sides of the same length as your partial dome would be the right shape to start from.

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Ah thanks Dave, will try the plug in.

I guess what I have in my head is when you see an image of the earth unfurled from it’s mercator projection and made flat and all the countries look weird.

Was hoping there’d be some sort of extension but no worries, and thanks for the reply.

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Unfortunately, the topology of a sphere is different from that of a plane. There is no way to map a sphere or part of a sphere to a plane (or vice versa) without distorting it in one way or another. All mapping projections are tradeoffs on what distortions are acceptable. For example, Mercator keeps lines of latitude and longitude straight on the map plane, but we all know that the distance between longitude lines decreases from the equator to the poles, so the east-west direction must be stretched on the map.

I think your brother will have to plan on doing the bend first and trimming to required size afterward, as the edges will also be stretched while bending. I would guess that some industries that regularly bend materials to complex shapes, such as auto body panels, may have software that handles the problem, but I know nothing about it.

The extension @DaveR mentioned works because SketchUp actually represents a curved surface as a collection of flat polygons. You could get an approximation that way, but be ready for errors! It is very likely that the unfolding would yield numerous tears in the flattened result.

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Thanks so much for the thorough reply - I really appreciate it.

Best wishes.

That’s what I was trying to imply.

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When you use my extension, make sure you unwrap this in parts, i.e. do the colored surface first and then the other side (instead of everything at once).

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A lot depends on your bending method but generally you would create a ‘former’ to bend over or into.
If you bend into it is usually best to have a piece of glass larger than needed so that it ‘grips’ the former and doesn’t just end up as a molten mess in the bottom of the dip. You then trim to size after.
If bending over you can cut to size but you’ll tend to get texturing on the glass in the center where it has to be touching the former the whole time, and getting the pivot point correct is quite tricky.
Unfolding won’t really work, you need to work with the dimensions, including the radii and the chords.
If it is for a specific job I would suggest your bother get in touch with a competent glass bending firm.
If it is something he wants to learn and do himself then it requires a bit of trial and error to get the bend right.
Also, type and thickness of glass comes into play in not a small way.


Thanks for the message, box, appreciate it.

They’re all pretty experienced and have trialled it out of wood - I think they were just seeing if I could help/remove some of the guesswork trial & error.

Doesn’t help that I don’t know what I’m talking about! :rofl:

I have significant experience with this and can speak at length about it.

But as someone with 45ish years of working with the many facets of glass I can sometimes add a hint or two.

Would love to see the conflagration this would involve.

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Here are some photos he has sent. The tape is to cover up the trial and error!

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I had to do something related in timber once for a large curved roof on a circular building. I have also used the second half of this technique for laying out eyebrow dormer timbers.

I assume this is a portion of a circle, but if not this should still work. This method is tedious, but will get you close enough to be able to sand / file / fair out by hand.

I drew a circle with 120 segments (3º per segment, if we divide by 360).
Cut this into a quarter circle, exploded curve of the line.

Push pull and this will show the lines from the end point of each segment.
I made this a group.

Then I made a large rectangle and rotated it 45º in plan view and used the solid tools to cut away a miter.

I then deleted the edges to I am only left with the curved ‘glass’.

Going to the straight side of my shape I rotate copy the group to lay on the ground plane. Then you go to each segment and rotate 3º so it keeps getting ‘unrolled’ onto the ground plane. You need to deselect the plane that is lying flat and move to the next one.

The more segments the arc has the more tedious this becomes. We could double the number of circle segments and rotate 1.5º but this likely would be open to more errors.

I then copied the flat group and trimmed off the ‘extra’ bit

You could print this full size on several sheets if you had access to a plotter and then transfer to a thin bendable plywood or cardboard to test.

You can also draft this direct on a material if you plot it out - I used to do this with complex curves for timbers in eyebrow dormers, but full scale template is faster.

This isn’t 100% accurate as the straight edges on the mitered side would be a changing curve, but this would get you close enough to template and fair out by hand. I would assume this is the ‘bottom’ of the glass because we haven’t accounted for thickness.


Wow, @bmike thanks for the response! Thats great! Will give it a go. Thanks again.

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Thanks. Sometimes I geek out over this type of thing.

I don’t have any of the unwrap plugins but once you isolate the surface like I did maybe they will automate this.

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Absolutely bmike!
Now that you’ve isolated such a nice curvy face Alex’s
“unwrap and flatten” will shine. It should do that tedious unfolding part for you in the blink of an eye.

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Looking back, I assumed the surface curved in all directions, but the results being shown now are for a bend in just one direction, which means it is conformal and should flatten nicely. Too much time working with compound curved boat hulls, I guess…

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Like @slbaumgartner I thought it was a complex curve you wanted. If just two curved faces and a mitre you can do that with Flattery, which gives you and svg output as well so can be sent straight to a plotter at the right size. Unfold is more automatic but can be problematic. Flattery is pretty basic.
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Thanks so much for all the input guys, it’s been really interesting and think we got there! Thanks again. :slight_smile:

just tried this plugin, it does the job well too…