Hilariously fast volume computation with the divergence theorem (2018)
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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)
#2I love these kinds of posts. Simple, fast, AI-free, and I learn something new.
Re: Hilariously fast volume computation with the divergence theorem (2018)
#3I'll accept any kind of jocularity in the current climate!
Re: Hilariously fast volume computation with the divergence theorem (2018)
#4Isn'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.
Re: Hilariously fast volume computation with the divergence theorem (2018)
#5My 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 this hard.
No idea what the author means by "which are equivalent to rendering the mesh and then sampling the render".
Re: Hilariously fast volume computation with the divergence theorem (2018)
#6Did they also work on the graphics stack for the Asahi project?
Re: Hilariously fast volume computation with the divergence theorem (2018)
#7Isn'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
Re: Hilariously fast volume computation with the divergence theorem (2018)
#8Did they also work on the graphics stack for the Asahi project?
Sadly, there is no way to find out, f.ex. by a quick Google search.
Re: Hilariously fast volume computation with the divergence theorem (2018)
#9Isn'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.
I wonder if this could be reversed to give an intuitive “proof” of the divergence theorem.
Re: Hilariously fast volume computation with the divergence theorem (2018)
#10Did they also work on the graphics stack for the Asahi project?
Yup!