Digital Geometry Processing with Discrete Exterior Calculus

This is very interesting, I did not know that the theory of differential geometry can be discretised so nicely. I admire how they build from nothing but elementary linear algebra and calculus, and end up at quite advanced topics like De Rham cohomology, of which I never imagined it had any application in computer science at all. That said, definitions are mathematically very informal, and it skips handwavily over topics like topology. But these details are arguably less important for doing computations.

My favorite curves, geodesics, aren't included in this revision of the notes (he says it'll be added to future revisions).

But you can download his paper on them at http://www.cs.columbia.edu/~keenan/Projects/GeodesicsInHeat/...

Somewhat related: http://www.math.upenn.edu/~ghrist/notes.html

(and somewhat more high-brow, but still with a discrete flavour.)

hackernews seems like the perfect place for this course. How many of us need GIS data? Or need to compute the rate of change...

Can't use the (x^n)' = n x^(n-1) on real data! I need to take a derivative of some GIS numbers have to compute a discrete gradient. In fact that's what I did to draw this figure of Puerto Rico

http://s11.postimg.org/s8ph73t8z/birth_rate.png

I wish I could find an open source 3D Delaunay triangulation library. Maybe some of this theory could be used to derive the code in a straightforward way.

Very nice. Anyone know how the graphics are drawn? I had a scan and didn't see it.