Geometry Processing with Intrinsic Triangulations (Day I)

Abstract: The intrinsic viewpoint was a hallmark of 19th century geometry, enabling one to reason about shapes without needing to consider an embedding in space---and leading to major developments in the 20th century such as Einstein's theory of general relativity. Yet 21st century digital geometry processing still largely adopts an extrinsic mindset, where the geometry of a polyhedral surface is expressed via vertex positions in n-dimensional space. This talk explores how the intrinsic view of polyhedral surfaces helps relax some standard assumptions in geometric computing, leading to algorithms that are more flexible and numerically more robust. In particular we will examine fundamental data structures for intrinsic triangulations, extensions of important triangulation algorithms to curved surfaces, as well as methods for finite element problems, finding geodesics, and computing discrete conformal maps.

[Kram]

You and your research team never fail to impress!

[mohamedmoussa]

The idea of using intrinsic meshes for finite element analysis is very interesting ...

[amiltonwong]

Prof. Keenan, thanks a lot for giving these impressive topics. BTW, would you also provide the slides downloadable? Thanks~

[pinklady]

Viewers, let the ads play out to their ends, so that this channel gets paid and makes more videos.

I love history of maths like you give dates to them. Thank you.

[hossamsaeed]

So fun to learn about!
@18:00 I think there is a typo in the length cross ratio here, it should be l_im instead of l_ij

[mehrdaddowlatabadi]

Nice presentations. what software you use for animations?

[gijsb]

I think there is a mistake in the definition of the cross ratio at 17:46. Shouldn't l_ij be l_im?

[AdamGenesisArt]

Dude, love your videos. I do art and watch in the [GxQ=Universe]

[columbusmyhw]

Is there a proof of the claim at 11:00, that that intrinsic triangulation can't be realized in R^3?

[kasali]

is this algorithm used in Unreal Engines visibility system, Nanite?

[nononono]

Most of this is going over my head, but could this be what Nanite is doing in UE5? The resulting triangulation looks so much like Nanite meshes.

[TacticalTruth]

"all soft of things that we know and love".
We must be from a different planet ☺️