Calculate the Volume of an Object

[davew_nz]

Dennis, Thanks for the plug in, very quick work. I have just run a few tests on some core shapes and answers are below. all based on 1x1x1 sized objects. I found that the default 12 pointed circle in AC3D when you create a round object caused a discrepancy in the result but as I subdivided the object the result moved closer and closer to the expected value (as you would expect but interesting to see)

__________Math_______Plug-in (default Circle)__Plug-in (after subdivide x3)
Cube______1.0________1.0
Pyramid____0.3333_____0.3333
Cylinder____0.7857_____0.75
Cone______0.2619_____0.25
Sphere_____0.5236_____0.48447_____________0.52137

Once again thanks for the plug-in excellent work.

Regards

Dave

[Dennis]

Originally Posted by davew_nz

I have just run a few tests on some core shapes and answers are below.

I initially thought the discrepancies here are largely due to the lack of smoothness of polygonal objects versus "real world" smooth objects.

But I did a couple of tests, and I find that the number changes depending on where in 3D space the object is placed.

I'll take another look at this and get back with my findings.

Thanks,
Dennis

[Dennis]

I performed a couple of fixes to correct a couple of calculations, but have overall bad news on the volume calculator.

I did some research and found a couple more articles that use the divergence theorem to calculate 3D volumes. I created an implementation that takes a different approach (using the same theorem) from the one I use, and it consistently comes up with the same result as my existing algorithm, inaccuracies and all.

Both implementations also have the unfortunate effect of changing the results with a simple Divide on the object, which, one would think, should have no impact on the volume.

Further investigation yielded that this is a known issue with many volume calculation implementations based on this theorem. There are supposedly solutions that address this, but it's not something I would have the time to research/implement.

Meanwhile, I've left the page up with the volume calculator, and have added a disclaimer at the top:

"The resulting calculated volume using this algorithm known to be inaccurate, and any results from this plugin should be taken as an estimated volume at best. For some geometry, testing has shown a +/-25% discrepancy in calculated volumes from actual volumes."

I'll leave it out there for now, but this is still, unfortunately, not a working solution...

[davew_nz]

Dennis, Thanks for all of your work on this.

Dave