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Algebraic Geometry for Computer Graphics

courses.cs.washington.edu

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Re: Algebraic Geometry for Computer Graphics

#11

Post by mindcrime »

Algebraic Geometry as studied by Mathematicians often deals with very abstract and general issues that I admit that I don’t completely understand myself.

Nice to see this kind of honesty and/or modesty from an instructor!

Reminds me of the time I took Discrete Math at a local community college. We all showed up at the room for the scheduled first session, and found no instructor. We waited around about 20 minutes, and were about to leave, when a grey-bearded gentleman who looked to be of the instructorly persuasion rocked up and started unlocking the door. So we follow him in, and he gets in front of the class and says something approximately like:

"Hi, so-and-so, who was scheduled to teach this class, had to back out at the last minute and so the school called me. I'll be your instructor. I was a Physics major 60 years ago, and can do this math, but I've never taught this before and don't really remember anything about it. So we'll all be learning it together as we go."

It was an, ahem, interesting experience, to say the least. Luckily for me I'd had Discrete before and was only taking it due to a technicality that kept my previous credit from transferring.

Re: Algebraic Geometry for Computer Graphics

#12

Post by bmer »

godelski wrote: post #8

These are just slides btw and unfortunately probably not helpful without a lecture recording (which is not included). The slides really look great, but I wish there was commentary along with them. (they are not self contained)

Well, this is sadly the best we have in the field, where by "field" I mean: "accessible algebraic geometry for graphics".

Blinn provides some notes as to where his material comes from (see the page). He also mentions that some of this material was presented previously in some of his Jim Blinn's Corner articles. In particular:

* the "Lines in Space" series: https://ieeexplore.ieee.org/abstract/document/7047281

* the "How many different rational parametric cubic curves are there?" series: https://www.oreilly.com/library/view/jim-blinns-corner/97815...

Part of the reason why I posted this to HN is so that others can hopefully drop some more information on this "field".

See also the author's site: https://www.jimblinn.com/

Re: Algebraic Geometry for Computer Graphics

#14

Post by ncmncm »

I thought that algebraic geometry was really cool when I first encountered it. But people with a lot of experience insist that for computational processes it is slower than more familiar methods.

So it is convenient and intuitive for one-off transformations, but not preferred in computational kernels. I see room for both, and for quaternions, which I gather are also a bit slower.

Re: Algebraic Geometry for Computer Graphics

#15

Post by darzu »

tptacek wrote: post #6
darzu wrote: post #4

Earlier quoted context omitted.

Maybe it should be required that public or publicly funded universities have a set of relatively up-to-date lecture recordings for each course. Since covid, I know for a fact most UW CSE courses were/are being recorded and saved to Canvas CMS for students who miss lecture/have covid/worry about covid/etc. These should be made public! The hairiest issue here is when there's student participation. But you don't need ea…

The majority of the funding in several flagship state universities comes not from the state but from the operations of the university itself: tuition, fees, stores, programs. We the public literally did not pay for all these courses. And the rate on a presentation, speech, or training course, you'll find, is very different when it's delivered to a specific audience versus being put on the Internet for free.

UW receives 37% of its funding from the state, the rest comes from tuition[0]. In 2002, it was 70% from the state. And of tuition, at least ~25% of that comes from public sources (grants, subsides loans)[1].

And even if some public universities are self-sustaining now, that doesn't lessen the fact that public money was the major cause that started that flywheel.

And regardless of funding, UW, like all public universities, has an explicit directive to operate for the "benefit of present and future citizens of the State of Washington"[2][3].

As for course lecture quality, if it's worthwhile to the students, it can be worthwhile for the public.

[0] https://www.washington.edu/opb/uw-data/fast-facts/ [1] https://educationdata.org/how-do-people-pay-for-college [2] https://www.washington.edu/regents/ [3] https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130

Re: Algebraic Geometry for Computer Graphics

#16

Post by adfm »

earleybird wrote: post #9

Absent from his bio (and the wikipedia article) is his role in the construction of the Vegreville Pysanka(egg)[0] "Robert McDermott and Jim Blinn are jointly responsible for the precise mathematics and computer programming which implemented the geometric concept Accomplishment of the highly sophisticated and complex mathematics brought to a close the long-sought-after geometric definition of the faceted Egg." [1] Cam…

Don't forget Ron Resch[^1]. If you haven't seen his Paper and Stick film [^2], I highly recommend it. It's a fascinating look into the early beginnings of computer graphics filmed between 1960-1966.

[^1]: https://en.wikipedia.org/wiki/Ron_Resch

[^2]: https://www.youtube.com/watch?v=UXENKmAUL0E

Re: Algebraic Geometry for Computer Graphics

#17

Post by fanf2 »

bmer wrote: post #12
godelski wrote: post #8

These are just slides btw and unfortunately probably not helpful without a lecture recording (which is not included). The slides really look great, but I wish there was commentary along with them. (they are not self contained)

Well, this is sadly the best we have in the field, where by "field" I mean: "accessible algebraic geometry for graphics". Blinn provides some notes as to where his material comes from (see the page). He also mentions that some of this material was presented previously in some of his Jim Blinn's Corner articles. In particular: * the "Lines in Space" series: https://ieeexplore.ieee.org/abstract/document/7047281 * the "…

Amusingly, algebraic geometry is a very different beast than geometric algebra.

https://en.m.wikipedia.org/wiki/Geometric_algebra https://en.m.wikipedia.org/wiki/Algebraic_geometry

Re: Algebraic Geometry for Computer Graphics

#18

Post by scentoni »

ncmncm wrote: post #14

I thought that algebraic geometry was really cool when I first encountered it. But people with a lot of experience insist that for computational processes it is slower than more familiar methods. So it is convenient and intuitive for one-off transformations, but not preferred in computational kernels. I see room for both, and for quaternions, which I gather are also a bit slower.

I think you’re confusing https://en.wikipedia.org/wiki/Algebraic_geometry with https://en.wikipedia.org/wiki/Geometric_algebra which is a type of https://en.wikipedia.org/wiki/Clifford_algebra and a generalization of https://en.wikipedia.org/wiki/Quaternion

Re: Algebraic Geometry for Computer Graphics

#19

Post by dxbydt »

fanf2 wrote: post #17
bmer wrote: post #12

Earlier quoted context omitted.

Well, this is sadly the best we have in the field, where by "field" I mean: "accessible algebraic geometry for graphics". Blinn provides some notes as to where his material comes from (see the page). He also mentions that some of this material was presented previously in some of his Jim Blinn's Corner articles. In particular: * the "Lines in Space" series: https://ieeexplore.ieee.org/abstract/document/7047281 * the "…

Amusingly, algebraic geometry is a very different beast than geometric algebra. https://en.m.wikipedia.org/wiki/Geometric_algebra https://en.m.wikipedia.org/wiki/Algebraic_geometry

Just as computational statistics is a very different beast from statistical computation. Got an A in one and C in the other :(

Re: Algebraic Geometry for Computer Graphics

#20

Post by Sharlin »

mindcrime wrote: post #11

Algebraic Geometry as studied by Mathematicians often deals with very abstract and general issues that I admit that I don’t completely understand myself. Nice to see this kind of honesty and/or modesty from an instructor! Reminds me of the time I took Discrete Math at a local community college. We all showed up at the room for the scheduled first session, and found no instructor. We waited around about 20 minutes, an…

To be fair, it’s Jim Blinn, one of the pioneers of computer graphics, so his admission could be read as a polite way of saying that AG as studied by mathematicians is needlessly abstract and lacking any real-world applications :)
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