How to find the volume of irregular object?

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How to find the volume of irregular object?

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Hello.

What have you tried so far?

Is this math or physics or other? Are you supposed to do a calculation or suggest an experiment? Can you show the homework task?

Edited by Ghideon
Cleared up and added stuff. Initially posted in a hurry on phone.
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By computer algorithm? Start from calculating bounding box of mesh. Then "split" volume to boxes with known size x, size y, size z. If box fits all inside initial mesh, you count it all in. If it's all outside, you don't count it (e.g. concave object). If it's partially in and partially outside, you have to repeat evaluation but with smaller boxes just that box region (e.g. divide size of box by 2). Repeat subdivision, until it's above some threshold tolerance. That's brute-force algorithm of volume calculation in 3D space by computer algorithm..

ps. Instead of boxes you can try spheres instead. The smaller sphere, the slower algorithm, but the larger precision. One could put smaller and smaller spheres inside of closed mesh till some threshold if they all fit inside of mesh. So you need routine which checks if "mesh is inside of mesh entirely, partially or not at all". Which is pretty basic for primitives like box or sphere.

Edited by Sensei
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If it’s a physical object, you can measure how much liquid it displaces when submerged

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Volume can be calculated by displacement of water, 1mL of displaced water is equivalent to 1cm^3 of volume of the object

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7 hours ago, swansont said:

If it’s a physical object, you can measure how much liquid it displaces when submerged

At the first sigh it appears to be ultimate answer. But rethink it a bit. If your object is concave this solution can make regions where still gathered air. Also if object is somewhere empty it will give incorrect results.

If object is not convex and solid this solution might give wrong answers.

""How to find the volume of irregular object?"

Irregular object can mean concave object..

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If the water idea were not possible for some reason then how about slicing the sharp points off and cutting it into a central cuboid and several pyramid or dome shapes. These individual shapes might be easier to measure and have their volumes calculated from their dimensions - then add them.  I guess it depends on just how irregular the shape is and whether it can be cut up into regular shapes and their dimensions measured or not.

PS - I don't necessarily mean to physically cut the object. Just measure its dimensions and cut it up mathematically into more manageable shapes (if possible - depends on how irregular it is).  That or an estimation averaging the irregularities to regular shapes and adding their volumes.

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6 hours ago, Sensei said:

At the first sigh it appears to be ultimate answer. But rethink it a bit. If your object is concave this solution can make regions where still gathered air. Also if object is somewhere empty it will give incorrect results.

If object is not convex and solid this solution might give wrong answers.

""How to find the volume of irregular object?"

Irregular object can mean concave object..

Those are details of proper lab technique (ensure no air bubbles), rather than being a critique of the concept. Any method will have potential errors introduced if poorly executed.

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I guess it is a historical question. Look at Archimedes, it was the problem the King of Syracuses asked him to resolve. see https://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html

IOW If you know the material of the object & its density, simply weight it.

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• 2 weeks later...
On 5/29/2019 at 8:55 AM, CryptoKelli said:

Volume can be calculated by displacement of water, 1mL of displaced water is equivalent to 1cm^3 of volume of the object

You should try what she said. I think it will be easier.

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