# How to measure the surface area of an arbitrary 3D object

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• bob012345
In summary, the conversation revolves around finding an easy way to get the surface area of an arbitrary shaped 3D object for the purpose of estimating surface area of 3D printed plastic parts which will undergo copper plating. Various suggestions were given, such as using computer algorithms or analog methods like using a thin, uniform layer or dipping the object in paint or oil. The importance of accuracy and the challenge of non-uniform coatings were also discussed. Finally, the methods of uploading images to the conversation were shared.

#### bob012345

Gold Member
I'm looking for an easy way to get the surface area of an arbitrary shaped 3D object. Getting the volume is easy by water displacement. What about area? Any neat tricks? We know different shapes can have the same volume and thus different surface areas so it's not a trivial problem. The purpose is for estimating surface area of 3D printed plastic parts which will undergo copper plating. Thanks!

Good question. Not so hard to do with lots of images and a clever computer algorithm, I guess. There are algorithms that will construct a surface Net of triangles from a digital 3D image - probably not a difficult bit of geometry.
I can't think of an old fashioned analogue method that would give an accurate answer. Perhaps if you could invent a way of laying down a thin , uniform layer that would fit over the object, then find out the volume of material used. A uniform layer could perhaps be obtained by using interferometry

bob012345
sophiecentaur said:
Good question. Not so hard to do with lots of images and a clever computer algorithm, I guess. There are algorithms that will construct a surface Net of triangles from a digital 3D image - probably not a difficult bit of geometry.
I can't think of an old fashioned analogue method that would give an accurate answer. Perhaps if you could invent a way of laying down a thin , uniform layer that would fit over the object, then find out the volume of material used. A uniform layer could perhaps be obtained by using interferometry
Thanks. I'm hoping to hear of or figure out a method without computers or sophisticated devices. Your uniform layer could be wax by dipping and then weight it. One difficulty is the inside would follow the hills and valleys but the outside might be smoother thus getting an approximation of the surface area. Of course, I can just estimate the area but that's not as much fun. What would Archimedes do?

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sophiecentaur said:
I can't think of an old fashioned analogue method that would give an accurate answer. Perhaps if you could invent a way of laying down a thin , uniform layer that would fit over the object, then find out the volume of material used. A uniform layer could perhaps be obtained by using interferometry

The OP didn't say how accurate he needs to be. Just dunk it in paint, measure the amount of paint used. Compare that with dunking an object of known surface area.

bob012345
anorlunda said:
The OP didn't say how accurate he needs to be. Just dunk it in paint, measure the amount of paint used. Compare that with dunking an object of known surface area.
Accuracy should be one percent or so. I think that's close enough. Your paint idea idea Anorlunda is brilliant but I would need to act fast and not allow it to dry first. Or maybe, that won't matter. Thanks!

You could also use oil instead of paint. The accuracy challenge comes if the coating is not uniform, say thicker at the bottom. That is why you want a viscous fluid with high surface tension.

bob012345
You could use strips of masking tape or food service film. Then, measure the tape or film. Alternatively, cut the tape or film into pieces of known area and fill in whatever gaps are left over and measure the oddball pieces. Just be careful to not stretch it.

bob012345
anorlunda said:
You could also use oil instead of paint. The accuracy challenge comes if the coating is not uniform, say thicker at the bottom. That is why you want a viscous fluid with high surface tension.
Dipping could result in non-uniform 'runs', which cause me to reject the idea initially. Perhaps dipping in a container full of small spheres (identical) could result in a uniform layer with only the edge effects at edges. Then it would just be 'quantisation error'.

bob012345
bobob said:
You could use strips of masking tape or food service film. Then, measure the tape or film. Alternatively, cut the tape or film into pieces of known area and fill in whatever gaps are left over and measure the oddball pieces. Just be careful to not stretch it.

You don't need to measure the tape. Just weigh the part on a sensitive balance before and after, then weigh a known size piece of the tape.

bob012345
jrmichler said:
You don't need to measure the tape. Just weigh the part on a sensitive balance before and after, then weigh a known size piece of the tape.
Yes, if one can tolerate lower resolution.

Use an analytical balance with 0.1 milligram resolution. You will have your 1% error tolerance if you use at least 10 milligrams of tape to cover the object.

How would you tape objects that look like these?

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Grinkle and sophiecentaur
anorlunda said:
How would you tape objects that look like these?

View attachment 228634
I wanted to reply with a picture of a 3D printed test device called a 'Benchy Boat' so you can all see the resolution and structure of a typical print we want to plate but I can't figure out how to add an image.

bob012345 said:
I can't figure out how to add an image.

There are two ways, (assuming you're using a web browser on a tablet or desktop, and not the PF mobile app.)
1. If the image is on your own computer, use the UPLOAD button next to POST REPLY and PREVIEW. After upload, then a new thing appears on the bottom saying THUMNAIL or FULL IMAGE. Click FULL IMAGE.
2. If you just have a URL for the image, click on the image icon (looks like a mountain range) on the editing toolbar. Then you can paste the URL.

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anorlunda said:
There are two ways, (assuming you're using a web browser on a tablet or desktop, and not the PF mobile app.)
1. If the image is on your own computer, use the UPLOAD button next to POST REPLY and PREVIEW. After upload, then a new thing appears on the bottom saying THUMNAIL or FULL IMAGE. Click FULL IMAGE.
2. If you just have a URL for the image, click on the image icon (looks like a mountain range) on the editing toolbar. Then you can paste the URL.
View attachment 228636
Thanks! As can be seen, the surface isn't only on the 'outside'.

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If the object was produced on a 3D printer then the original data is the best source of information about its surface area.
If you want to plate the object then I would imagine the plating thickness would vary quite a bit, according to the position of parts of the surface. Is it a conducting material or will you need to spray the model with a conductor first?

OmCheeto and bob012345
bob012345 said:
plastic parts which will undergo copper plating.

What is the process for plating the parts?

The suggestions seem to be along the lines of "plate the part with something easy to plate with" but if the practical application of this is to predict plating costs, maybe you just need to plate a part and see how much Cu it required. Looking at that boat, I imagine that viscous material won't easily wet the insides of the smaller geometries on the boat, and as already noted, non-viscous material won't be uniform in coverage.

This is a very engaging problem, by the way. I hope we come to a practical answer!

bob012345
sophiecentaur said:
If the object was produced on a 3D printer then the original data is the best source of information about its surface area.
If you want to plate the object then I would imagine the plating thickness would vary quite a bit, according to the position of parts of the surface. Is it a conducting material or will you need to spray the model with a conductor first?
It's ABS plastic. We will have to apply conductive paint first. The paint could be used to estimate the surface area too. It's also true if the original data the printer printed from is available, the surface area should be retrieved. I'm assuming I won't always have that data available.

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Grinkle said:
What is the process for plating the parts?

The suggestions seem to be along the lines of "plate the part with something easy to plate with" but if the practical application of this is to predict plating costs, maybe you just need to plate a part and see how much Cu it required. Looking at that boat, I imagine that viscous material won't easily wet the insides of the smaller geometries on the boat, and as already noted, non-viscous material won't be uniform in coverage.

This is a very engaging problem, by the way. I hope we come to a practical answer!
Thanks. I'm using Copper Sulfate solution. I'm coating the ABS plastic with a conductive paint. I tried a homemade graphite layer but have no success yet as the resistance seemed too high, in the 240,000 Ohm range.

Sam Phillips said:
you could use a 3D laser scanner to create a mesh of the object on a computer. From that you would easily get a surface area.
https://pages.shanti.virginia.edu/medianet/2012/09/28/scan-big-with-the-faro-focus-3d/

You might even be able to use photos to make a 3d model but the accuracy would suffer.
https://i.materialise.com/blog/en/how-to-make-a-3d-printed-object-from-a-photo-in-5-easy-steps/
That's possible. It's fun though to figure out how to do it low tech. I still like the paint idea. It only has to be calibrated with a known area and could be tested on a series of standard geometrical shapes.

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bob012345 said:
That's possible. It's fun though to figure out how to do it low tech.
But the model starts off as a high tech image with all the data. It would be standing up in a hammock to try to work out the surface area, ignoring all that data, surely.

sophiecentaur said:
But the model starts off as a high tech image with all the data. It would be standing up in a hammock to try to work out the surface area, ignoring all that data, surely.
True, and if the data is available at the time the print is plated, which could be years later, that's great but if it isn't, how do we estimate the area is the question. I also thought the problem is interesting in itself.

sophiecentaur
bob012345 said:
True, and if the data is available at the time the print is plated, which could be years later, that's great but if it isn't, how do we estimate the area is the question. I also thought the problem is interesting in itself.
I agree. However, the data could well last longer than the model and so it could all be done again. (But that assumes a good file backup regime. ) Also, in the future, 3D scanning would be available. This all depends on how accurate the estimate needs to be. I reckon the low accuracy of a low tech approach would actually be well within the predictability of the plating method. You would need to make a pretty complex electrode (some of it inside the cab) to get a good uniform plating. The Electric field inside a hollow region would need to be compensated for, I think.

bob012345
You can metal plate plastic. Search electroless plating plastic for some good information. Electroless nickel plating is known for even plating thickness, while electroplating makes a thicker coating on exposed areas.

bob012345
The "surface area" for a real object (versus ideal mathematical models) is not uniquely defined. It depends on how closely you look at the surface. For your very porous object, the surface area at nanometer scale will be much larger that at cm scale, for example. The surface area can be measured by gas absorption (see BET method) but even by this method the result will depend on the gas used. If you are talking about electroplating, the relevant surface may be the one related to the micro(nano)scale.
But my impression is that is some sort of overkill. A rough estimate should be enough. How will the knowledge about the value of the "surface area" influence your electroplating process?

bob012345
anorlunda said:
How would you tape objects that look like these?

Very tediously. It could be done, but I wouldn't. I would just take the surface area of the entire shape as a whole. If you don't think so, measure the area of one of the squares (or diamonds or whatever) of the egg, for example, and measure the area of the braid bounding it and see how much difference there is. All of the small ornamentation is not going to change the result much. You could even use whatever difference you measured to make an approximate correction to the area of the egg minus the braids. Part of figuring out how to do something is figuring out if what matters for what you want to accomplish.

nasu said:
The "surface area" for a real object (versus ideal mathematical models) is not uniquely defined. It depends on how closely you look at the surface. For your very porous object, the surface area at nanometer scale will be much larger that at cm scale, for example. The surface area can be measured by gas absorption (see BET method) but even by this method the result will depend on the gas used. If you are talking about electroplating, the relevant surface may be the one related to the micro(nano)scale.
But my impression is that is some sort of overkill. A rough estimate should be enough. How will the knowledge about the value of the "surface area" influence your electroplating process?
Well, a Sierpinski sponge has infinite surface area but I'm not going to worry about that! :) It just provides a better estimate for plating current needs to get the thickness on wants. But that can be figured by trial and error too.

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Perhaps a complex object could be held at a low temperature then micro fog droplets formed over the surface which would then be quickly weighed along with a known test surface.

Thanks all for the thoughts and discussion!

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