4 ms·

Digital Geometry Processing with Discrete Exterior Calculus

64 points by santaclaus 12y ago

bjwbell 12y ago
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/paper.pdf http://www.cs.columbia.edu/~keenan/Projects/GeodesicsInHeat/...
jimhefferon 12y ago
Very nice. Anyone know how the graphics are drawn? I had a scan and didn't see it.
- maxerickson 12y ago
  It's mentioned in the faq: http://www.cs.columbia.edu/~keenan/faq.html http://www.cs.columbia.edu/~keenan/faq.html modo and tracing (perhaps by hand) https://www.thefoundry.co.uk/products/modo/ https://www.thefoundry.co.uk/products/modo/
  - jimhefferon 12y ago
    Thanks; I love the figures but for me that's too expensive (and requiring too much ability, I would guess). Back to Asymptote, I guess.
Ruud-v-A 12y ago
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.
- tel 12y ago
  There are other more rigorous versions of this material. Grady and Polimeni's "Discrete Calculus" is where I learned most of this.
mrcactu5 12y ago
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 http://s11.postimg.org/s8ph73t8z/birth_rate.png
- scienceisdead 12y ago
  Cool discrete 1-forms!
mathgenius 12y ago
Somewhat related: http://www.math.upenn.edu/~ghrist/notes.html http://www.math.upenn.edu/~ghrist/notes.html (and somewhat more high-brow, but still with a discrete flavour.)
zackmorris 12y ago
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.

64 points by santaclaus 12y ago

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/paper.pdf http://www.cs.columbia.edu/~keenan/Projects/GeodesicsInHeat/...

jimhefferon 12y ago

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

maxerickson 12y ago
It's mentioned in the faq: http://www.cs.columbia.edu/~keenan/faq.html http://www.cs.columbia.edu/~keenan/faq.html modo and tracing (perhaps by hand) https://www.thefoundry.co.uk/products/modo/ https://www.thefoundry.co.uk/products/modo/
- jimhefferon 12y ago
  Thanks; I love the figures but for me that's too expensive (and requiring too much ability, I would guess). Back to Asymptote, I guess.

Ruud-v-A 12y ago

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.

tel 12y ago
There are other more rigorous versions of this material. Grady and Polimeni's "Discrete Calculus" is where I learned most of this.

mrcactu5 12y ago

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

scienceisdead 12y ago
Cool discrete 1-forms!

mathgenius 12y ago

Somewhat related: http://www.math.upenn.edu/~ghrist/notes.html http://www.math.upenn.edu/~ghrist/notes.html (and somewhat more high-brow, but still with a discrete flavour.)

zackmorris 12y ago

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.