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Hilariously fast volume computation with the divergence theorem (2018)

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Re: Hilariously fast volume computation with the divergence theorem (2018)

#32

Post by [deleted] »

diabllicseagull wrote: post #26
eterevsky wrote: post #4

Isn't the same as just taking every triangle from the mesh, calculating the volume of a prism-like polytope between it and its projection on one the planes, and then taking it with a + sign if its projection is oriented in one direction, and with a - sign if it's oriented in another? This kind of formula works based on the basic geometry.

reminds me of that 1994 paper that reinvented the trapezoidal rule

[deleted]

Re: Hilariously fast volume computation with the divergence theorem (2018)

#33

Post by srean »

aaa_aaa wrote: post #7
eterevsky wrote: post #4

Isn't the same as just taking every triangle from the mesh, calculating the volume of a prism-like polytope between it and its projection on one the planes, and then taking it with a + sign if its projection is oriented in one direction, and with a - sign if it's oriented in another? This kind of formula works based on the basic geometry.

Yes I remember doing something like that in 90s for a survey/map engineering cad application. After delaunay triangulation, calculating approximate voulume is easy. But this probably is a more general solution

Yes it goes by a couple of names. Surveyor's formula, shoelace formula.

The Surveyor’s Area Formula Bart Braden The College Mathematics Journal, September 1986, Volume 17, Number 4.

https://web.archive.org/web/20150406152731if_/http://www.maa...

Re: Hilariously fast volume computation with the divergence theorem (2018)

#35

Post by IAmBroom »

alex_suzuki wrote: post #22
arn3n wrote: post #2

I love these kinds of posts. Simple, fast, AI-free, and I learn something new.

(2018)

OMG, that absolute dummy didn't know something that a human did in 2018!

Are they not reading the entire internet every morning, when they wake up???

Re: Hilariously fast volume computation with the divergence theorem (2018)

#36

Post by alex_suzuki »

IAmBroom wrote: post #35
alex_suzuki wrote: post #22

Earlier quoted context omitted.

(2018)

OMG, that absolute dummy didn't know something that a human did in 2018! Are they not reading the entire internet every morning, when they wake up???

I was merely pointing out that the post was published in 2018 so AI-free is kind of implied.

Re: Hilariously fast volume computation with the divergence theorem (2018)

#39

Post by gloveone »

eterevsky wrote: post #4

Isn't the same as just taking every triangle from the mesh, calculating the volume of a prism-like polytope between it and its projection on one the planes, and then taking it with a + sign if its projection is oriented in one direction, and with a - sign if it's oriented in another? This kind of formula works based on the basic geometry.

Yes, the algorithm and its derivations are elementary and rather obvious for anyone decent at undergraduate level mathematics. But still, I am glad to see more people enjoying math!

Re: Hilariously fast volume computation with the divergence theorem (2018)

#40

Post by [deleted] »

elikoga wrote: post #5

My belly says the naive formula is summing the triangle pyramid volumes to the origin with sign in orientation. It looks like that's what they derived. Which is a generalization of 2d polygon area calculated by summing triangle areas for each edge, I was taught this in a math camp where we calculated map polygon areas on gis data. I remember math knowledge being hard to get pre AI era but I didn't remember it being t…

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