

Digital Geometry Processing with Discrete Exterior Calculus - santaclaus
http://www.cs.columbia.edu/~keenan/Projects/DGPDEC/

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Ruud-v-A
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.

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

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bjwbell
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/...](http://www.cs.columbia.edu/~keenan/Projects/GeodesicsInHeat/paper.pdf)

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mathgenius
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.)

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mrcactu5
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
Cool discrete 1-forms!

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zackmorris
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.

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

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maxerickson
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
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.

